RESEARCH AND DEVELOPMENT OF NEW DESIGN METHOD FOR POWER TRANSFORMERS. FINAL REPT., MAY 53-AUG 55. (CONTRACT DA 36-039-SC-52656).

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP81-01043R002500190001-9
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 318
• Document Creation Date: December 23, 2016
• Document Release Date: September 6, 2013
• Sequence Number: 1
• Publication Date: October 17, 1957
• Content Type: REPORT

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STAT
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STAT
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RESEARCH AVD DEVELOPMENT
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FINAL REPOAT
Period covered: May 1, 1;,53 to Ang.30,
:for
Electronic Parts ale.MAterials Branch
Signal Corps Engineering Laboratories
Feet Monmivith; Paw Jersey
and
Electronic Components Laboratory
Wri A-.1
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STAT
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ARMOUR RESEARCH FOUNDATION
of
Illinois Institute of Technology
Technology Center
Chicago 16, Illinois
RESEARCH AND raVitiarOMEM
--stirilwrvaltarammeamixivemimo
LT =a =UM =anvil
AIMS Minns=
Final Report
Period Covered: May 1; 1953, to lur, 30; 195
Oblects To conduct research 4nd development leading to a
Ammt4evii sathAA feepo iftela4m4 reszol Or OmialmairrOr rArIgn
wows Abler rvwww. vsmaawairamightup 0AUU 1,A0 .1.014644-401JUVW MUU01U
for component tecting in accordance with Squier Signal
Laboratory Technioal
of October 6, 19S2.
Copy No. .4t5
March; 1956
in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
STAT
Inamatill111
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ARMOUR RESEARCH FOUNDATION
of
Illinois Institute of Technology
Technology Center
Chicago 16, Illinois
RWEARCH AND DEVELORM
OF at
Fallsi5Mts
ftal Report
Period Covered: May 1, 1953 to Aug. 30, 1555
rot: To conduct research 4nd development leading to a
sign method for power transformers, and to fabricate models
Piu component testing"Aa accordance with Scalier Signal
IJMUVrImwms,
of October 6, 1952.
STAT
STAT
Copy No. Mar h, 1956
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,??????? ?
TABLE OF COFRES
TABLE OF OONSTERT
LISTOF TABLES . ? . ....? OOOOO ? ? ? ? ? ?
LIST OF mustramon . 3 OOOOO ? ? ?
FUMEOOOOOOOOOOOOO ?..???????
ABSTRACT ????? OOOOO
ACKNOWLEDGMENTS
I. INTRODUCTION .? OOOOOO ??
OOOOOOOO .
II.atSWIALS OF DEMON PROCIDME RIVISIONS ? . . . 3
Basis of Design Procedure OOOOOOOOO . . . . . . 3
Design Procedure . . OOOO . OOOOOOOOOO 6
Design of High Voltage Transformers . . ? . . . . 12
III. WINDING CURREN? IENSITIEVOSSES AND HEATINO . . . . .
15
IV. OPIUM CORE STACK RATIOS 17
V. TRANSFORMERS WITH tINBALANM MAGNETIZATION .28
References 29
%floral Properties of PagmAtic Circuits With Unbalance 31
Effect of a Non-Magnetic Gap OO . OO 33
Net cihme.,4+.? for efbta4l.4-261 " lag"veriarental Data . . . 35
Tait Rartl+All semi %aeon Cirraves lA
dpv
39
140
141
ii
0111
1
Comparisons of Data
.... . OOOOO ? Oa OOOOO
Properties of a Core Joint a -
Half-Wave Rectifier Supply Transformer .
? 0
? ? ? ? ?
Transformer Circuit Frequency Components
Primary Current OOOOO ?? ? ? ? ? 0 ? ? ? 0 ? ? ?
load Tests ? ? ? . ? ? ? ? ? ? . *******
Optimum licitation and Flux Density
Regulation and Turns Ratio . *
Design Procedure for a Transformer with
Unbalanced Magnetisation ?. ??. ? . ? . ? ? ? ? . ?
VI. CORRIF.V-IDMINO TRANSFORMERS
Requirements and Construction
Leakage Reactance and No-Load yoltago .
Nnn?Mksonaiwit4w
Was TiVer C
?
53
56
59
59
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?????-?????'', .1?4111 MT.". ?
???? _..__t_-_,
Design Procedure ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
VII.anwormnarnm 121A1SVORISR8 WITH
=UMW frauTiffix?ATTON ? ? ? . ? . ? ? ? ? ?
Design Procedure ? ? ? ?******* ? ? ? ? ? ?
'ma
VIERAIUt-SUPPLY TRANSFORM. . ? ? ? ? ? ? ? ? ? ? ?
&squaw ?
Flux Density . ? ?
Vibrator Voltage Relationahip
0 ? ? ? ? ? ? 0 ? ? 5 ? S ? ? ? 0 ? 0 ?
0 ? ? ? ? ? ? ? OOOOO ?
? 0 ? ? ? ? ? ? 5 0
Loss andVAhM arms V oltipis
?Aida' Capacitance
0 ? ? ? ? ? ?
? ? ? ? 4 ? 5e ? ? ? ? 5 ? ?
Vibrator Transformer Operation With
%balanced Negnetisation ? ? ? ? ? ? ? ? ? ?
Leakage Reactance and landing Layout ? 4 ? ? ? ?
Narign becedure . ? ? ? ? ? ? ? ? . ? ? ?
Low.cApiniTturit FILAMENT TRANSFORMER
? ? ? ? ? 111 ?
Construction . OOOOOO ? ? OOO O ? ? ? a ?
Calculation of Capacitance ? . ? I S 0 ? ? a.. a a
Leakage Reactance
Capacitance and Leakage Reactance Checks ? ?
Regulation and Sin .?????????? ? ? ? ?
Wodification.of Basic Design Procedure
Wailing Space near
Transformer Layout
Design Checks
? ? 0 5 OOOOOO 0 ? ? 0 a.0
X. INSIIMMENT TRANSFORMERS
Tram+Vimmairms
Current Transformers
XI, MaNWANY at 121310N PROMNE AND
TreftwatA' TOTS Fur.= CALCIUM% .
Step-bry-Step Design Procedure OOOOO ?????
Calculation of Temperature Rise
XII. reSION PROCEDURES PREVIOUSLY PRESENTED
Filament Transformers
musulAramoxurmoura . ? a a a ? ? a ? 0 ? 0 a a ? ? ?
70
74
74
76
82
82
84
87
87
87
93
95
97
100
101
103
104-
107
109
109
129
1112
142
6
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????
11^
iI
1
Rectifier-6*NT Trans:mere ? ? ? . ? ? ? ? ? ? 113
nn. mincei PROCIDURNI TRAISPIONIt WITH UNBALANCED
MONSTIZATION...... . . . . . ? ? ? ? 1117
nv. DAIIas TRANOURNIR WITH nagera
MAONSITIATION ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? . ? 161
Iv. maw MOCIDURN: CURRENT-LIMITINO TRANSIATONCRS . 170
XII. Tier MDT!: TRAWKOIRIMS, ?w 176
XVII. DEMON FROMM: c?ufatsimninun TRANSFORMER
MTN UNMAN= MAONMEATION ? . . ..... . 187
IVIIL INEANPLE: CURRENT-LINCTINI IMANSFIMM WITH
UNBLIANCED MAONETIZATION ? . . . . ..... . 193
XII. MIMI PROCIMM: V'IBRAIOR-SUPPLY TRANSFORVERS . 203
XX. EXAMPLE: VIBRAIOR-SUPPLT TRANSPCSNER 209
M. ISSIGN PROC!ME: WW-CAPACITAN2 TRANSFOIMIRS 218
MI. EXAMS: DaroN OF LOW-CAPACITANCE TRANSMINER 229
xrai, coNclOSMIS 238
XXIV. REUMMENDiraiS 241
XIV. LOGBOOKS ? ...... ... . ? ? ? ? ? ? 41; 2b2
a I r STAFF 03NTRIBITIORS 212
aranswar 243
fimertArlerw A ? ilitITTYPRT AM LITUTIIMIIN Onnal T
AK comma* 411 town mr,a. xiaor nue r vim iriwas %it aw
IMIDING LOSSES ? ?. 246
AP'PENDIX B: OPT11011 again DENSIT1 DISTRIBUTION
DJA PLANE . . . . . ? ? ? 11) 0 ? ? ? ??.? ? 248
251
APPENDIX c NscupLssLA1ImoN . . ? ? ? ?
AMU./ D: Mr& TRA13YOR SMITICATIONS
AND TEST Rifanuivi ,
? ? ? ? ? ? ? ? ? ?
255
A1PPB011 Bs TEST DATA JC H TRANSFORPERS WITH
lanDAT nem punstrffuTioN ? . . .. .. ? ? ? ? 279
AHEM F: COBREANON OF NATION, TABLE,
AND Plan AMBERS 291
APISNDU 0: LIST OF PRICIPAL SDIBOLS 293
wan
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L/ST OF TABLES
Table N!
4.1 Values for Minima C + I 27
ir 4.2 Comparison of Optimum Transformers of Various Types 27
IL Si Effective Saps The to Joints 30
9-1 Data for Loir-Capacitance Models 91
Ir9-2 Dielectric Constants 92
11.1 Values of K for Approximate Temperature-Rise Equation 117
f11-1A Values of (ATA) far Standard Conditions Eh
11.2 Suggested Flux Densities for Silicon Steele at
Various Frequencies 119
11.3 Typical Core lass and Imitation of ?resew= Coves as
Percent of Epstein Values for Silicon Steel 119
114 Typical Vanes for Core Loss, Excitation, and Regulation 119
13.4 copper vie Data 120
? fr? 11.6 layer Inaniatim and Margins for Mechanical Strength 121.
Irri 114 Enissivity of Surfaces 134
11.7 Tube Thiekness for Mechanical Strength
121
EMI 1" ft e..ee..?....., 114...m In.-?"1"--As
.1..a. 1.71114411.11". a' %As ail gaVir4.1.... 134
El *
114.0 Thermal Conductivity of Potting Compown-dm 135
II f limn coil oridient Parameters 136
" 1..) A
asTansci Minding nee Paeweter 137
I 11-13 Design Equations
11-14 Temperature Calculations
A.Alm'AX
339
1111
I12-1 Constants for Rectifier Transformers and Circuits 1145
12-2 Ratio of MS Secondary Current to Average Load Current
II for Fun-Wave Rectifier 146
II f 12-3 Ratio of Peak Secondary eurrent to Average Load Current
for FUI1-Wave Rectifier 11A,
..,
1 I
i 12-4 Ratio of RMS Secondary Voltage of Belt the Winding to
Average Load Voltage for Full-Wave Rectifier
13-1 Ratio of RIS Secondary Current to Average Current
for Half-Wave Rectifier
,
152
146
[
for Half-Wave Rectifier 152
13-3 Ratio of DNS Secondary Voltage to Average Load Voltage
13-2 Ratio of Peak Secondary Current to Average Current
I1 ror Tifilf=WAve Rectifier 159
I 1
1 I
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=ma
? ?-????? ? ?W.111 7E?????? ? ???`" ???????-??? ?^??????0
Tabla
19-1 Suggested Flux Densities for Silicon-Steel Cores
triLwskr-Supplty Tr0118f011110r0
10.9 %nil owl illpratitin VolUmode, ft:4w *yr
Voltage Systems
21-1 Tewerature-aise Itireseter of Iter-Capaeltanee
transform
?
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? 'Ir.?. a
LIST OF ILLUSTRATIONS
4-1 Scrapless Ludnaticas
it.2 Stack Ratios For Shell type With ME Laminations 21
Ii-) Stack Ratios For Simple Type With DI Laminations 22
Stack Ratios FCC Core Type With VI Laminations 23
4-5 Stack Ratios For shell Type With am in Laminations 213
54 Relations Between Induction And Field Strength 30
5.2 Circuit For Magnetic Tests, Requiring A
La* raiddatancre 37
5.3 Circuit For Magnetic Tests, Using An
Auxilialy Trans:maw 37
5.4 BIWA Ralf4eve Rectifier Circuits 43
Wave Shapes In Nalf4ave Rectifier Supply Transformer 44
5-6 Equivalent Circuits Of Component Voltages
VI" Mvadmacca 47
5.7 Equivalent Circuits Of Component Voltages With
Non-Linear Magnetising inductance he
6.1 kamples Of Nigh-Leakage Reantance Transformers 60
6-2 iquivalent Circuit of A Transformer With Quantities
Referred To The Secondary 8P1 63
8-1 Vibrator, UAW Capacitor, and Transformer 75
8.2 Wave Shape Of Transformer Input Voltage And Fluic
Showing Effect Of Timing Capacitance 75
9.1 Core And Windings Of Low4apacitance Traneformer 88
11.1 Temperature Rise And Winding Dissipation 122
11.2 Term F If Winding Space Factor (Revised) 123
11-3 Coasts...us For Design Equations 124
11,13 a----"ic Cow:tants Sorapiess kv-I Shell type 125
n..5 Constants For Cores With Scrapless VI Laminations 126
3.1-6 ResisUvities Of Copper And iatedm= 127
3.1.7 Power Transformer Nomograph
114 Heat Floe Analogue Of A Transformer
11-9 Neat Transfer Coefficient Of Radiation
11-10 amide To Suv...face Timr-&-atur-e nag
',ti anaonAndGFor Wuund Gore -
Dasip Curves (60 CPS) 153
-tft
128
vii
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'
Ise
13-2 Core Loss Of Wound Core - Daldgn Curves (60 CPS) 1511
13-3 Recitation And Gap For Stacked Cor i-Design
Curves (60 CPS)*00, 0,0
13-h Core Loss Of Stacked Core-Dasdin Curvet (60 CPS) 156
13-5 bnitatipon And Gap For Wound Core-Design Curves WO cra)
13.6 Core Ion Of *and Cano.Desien Damask (1400 CPS) 158
13-7 Excitation And Gap For Stacked Core-Design
Curves WO CPS) 159
134 Core Loss Of Stacked Cor Design Cum*Crin) 160
214 Capacitance, Rating, And Space Factor Function 226
C-1 Conventional Soraplese EX Ionainations As Cut From
Meet Magnetic Steel (Two Sets) 253
C-2 Useably Of Conventional Strapless Laminations
(One Layer) 253
C-3 New Strapless El Laminations As Cut From Sheet
Magnetic Steel (Two Sets) 254
C.14 Assembly Of New Serapless Lamdnations (One Layer) 254
D-1 Photograph Of Current-LiW.ting Transfom-rt Atat
Transformers With Unbalanced Magnetisation 256
D-2 m-c.1
Photograph Of Vibrator-Supp], And
Low Capacitance Transformers 257
Excitation Of Wound Core 80 Kilolines Per Sq. In.
(60 cPs) 281
8-2 Excitation Of Wound Core At 100 Maims Per Sq. In.
(60 cps) 282
I-, Core Lass Of Wound Core At 80 Kilolines Per Sq. In.
(60 cps) 283
SA C44 We TARR Of Sinniro &ties. vx; Eikairiea
(60 CPS)
Er..5 Excitation Of Stacked Core (53 CPS)
E-6 Core Loss Of Stacked Care (53 CPS)
E0-7
Excitation Of Wound Core (400 CPS)
E-6 enra Loo 1W Wpwrinrati 11sie)
Excitation Of Stacked Core (400 CPS)
E-10 Core Loss Of Stacked Core (4400 CPS)
Sq.rr
In
281i
285
286
287
opp
cu.
289
290
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MIAMI AND DIMINNINTCI
NW resterirMrligiammais
REPO=
The purpose of this investigation is the development of a nee
*1_14 improved method for the design of certain types of electronic power
transformers. The method should yield an optima design without the need
for repetitive trial procedures, and should be readily understandable to
an engineer not normalky associated with the transformer industry.
ABSTRACT
The emp design method for electric power transformers vhildh ves
developed under Contract No. Di-36.039 SC-5519 has been extended and modified
to make it suitable for the more special trpes of power transformers. It
has been intended that the design methods for these transformers mould be
used by electrical engineers who are not normally associated with the trans-
former industry. Satisfactory designs can be obtained with little or no
repetitive trial procedures. The following types of transformers have been
investigated during the current contracts
1. Transformers with unbalanced magnetisation.
2. Current-limiting or high-reactance transformers.
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_I 40.I *4 MAP iiaariamieasamalreav ohs
Ihinat a WWI 11,00?11116 IIIIMIAMPAI.11/4111 1011414 IMO
Imam" arguiasel
smairnatiotatinin_
4. Vibrator-supply transformers.
5. Low-capacitance transformers.
6. Instrument transformers.
It is assumed that the transformer desigmr is ffivan infill"m"nn
on power rating, voltages, currents frequencies, ambient temperature,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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STAT
INPNOM
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maximum temperature rise, and other requirements and limiting factors per
to the circuit in which the transformer must operate. The design
procedures account for operating temperatures to 200=0, ambient temperatures
to 200%, absolute pressures between 30 and 1.32 inches of mereamy, power
rating's to 5 kilovolt amperes, HMS voltages up to 50 kilovolts, and frequencies
from 25 to 2500 cycles per second.
Design methods have been developed for each of the above types by
study of the theoretical principles of operation and by compilation of emr
pirical data from developmental models. This approach has yielded empirical
parameters 'which have been incorporated into design equations. Elimination
of trial procedures has required that ultimate limitations of a given design
be used in the initial design equations. The most universal dealp limitation
is the operating temperature. Therefore parameters which are functions of
losses and sise are particularly important.
In order to provide supplements to well-known transformer theory
and data, a Ant' has been made to determine the approximate distribution of
current densities which minimise losses and teenerature rise. Another study
has yielded optimum stacking ratios for given types of laminations. It was
found necessary to obtain and compile new data on eagnetic materials as a
basis for the design of transformers with unbalanced magnitisAtimm. opt.
development of design methods for current-limiting and law-capacitance
transformers has required an investigation of transformer leakage firm and
leakage reactance in order to determine haw these quantities could be
accounted for in the design. In addition to the development of theoretical
relationships, there are presented detailed design procedures and examples'.
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ACKNOWLENIMENTS
During the investigation valuable suggestions and guidance have
been received from M.. Irving Bemis, project engineer for the Electronic
Parts and Materials Branch, Signal Corps Engineering laboratories, and from
Mr. Gene Tarrants and Lt. Carl K. Greene, project engineers for the
Electronic Components Laboratory, Wright Air Development Center. In addition,
acknowledgment is due to the government representatives and industrial con-
sultants of the Interservice Program and Guidance Group on Audio, Power, and
Pulse Transformers who have offered many helpful suggestions.
The participation of the Gramer-Halldorson Transformer Corporation,
Chicago, Illinois, as subcontractor has been very valuable, especially in
the constructing and testing of experimental transformer models and in aid
with transformer design problems. Contributions by Mr. Forrest E. Zimmerman,
Design Engineer, and Mr. Fred R. Cooper, Vice President for Enrineering.
are gratefully acknowIddged.
xi
.00
TEN
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RISEARCH AND DEVILOPNINT OF
tleaniMir Mromicas
I. INTRODUCTION
This is the final iMpUrlie OIL 1VilrearCh PrWella CUI".72ilieribrid Jairig
the period Nillw lp 1953 to August 31, 1955. This study has been a contin-
uation of the investigation carried out under Contract No. Di-36-039 SC-5519.
The major objective of the sta4y has been to develop &slot procedures for
certain typos of transformers Ai& have special requirements. In addition
to being characterised by special requirements, these special transformer
types are used in relatively small quantities and comprise a amall percentage
of the total electronic power transformer production. Limited utilisation
and special design probl= have resulted in the widespread use of repetitive
trill design, model construction, and model test procedures for obtairieg
satisfactory designs. To eliminate or reduce repetition of design calcula-
tions, arid to place the design problems on a more orderly basis, efforts have
been directed toward the compilation of theoretical and experimental data,
and application of the principles of the design method developed under
Contract No. DA-36-039 $C-5519 to these transformer types. The special types
of transformers studied may be grouped according to the design problems
involved as follows:
(1) Transformers with unbalanced magnetisation for
use with rectifier supplies or coehlimad rectifier
and filament supplies,
(2) Current-limiting transformers for either rectifier
illa....usaairrt valmappliee
(3) Current-limiting transformers with unbalanced
magnetisation for rectifier supplies,
(h) Vibrator-supply transformers,
(5) Low-capacitance filament transformers,
(6) Instrument transformers.
The ranges of electrical characteristics and operating conditions
which have been given major consideration are:
1) Pbwer output up to 5 kilovolt-amperes,
2) Operating voltages to 50 kilovolts,
3) Prequencies from 25 to 200 cycles per second,
4) Pressures as low as 1.32 inches of mercury, corresponding
to an altitude of about 70,000 feet,
5) Operating temperatures to 200 degrees CI and ambient
temperatuTes from-55 to 200 degrees C.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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????
However, the design methods presented here may be found to be
applicable outside of these ranges, such as for tomperatures above 200?C.
For related information dealing with the materials for and construction of
miniaturized pow transformers and inductors capable of satisfactory oper-
ation at ambient temperatures of 200?C and operating tepperatures in the
order of 325 to 350?C, attention is directed to the reports from Contract
No. AF-33(600)-21i120, nfiniature Power Transformers Having i Vide Temperature
Range", Bell Telephone Laboratories.
This report has been divided into two parts. The material in the
first part, which comprises the rirst ten chapters?gives the essentials of
the basic design procedure as developed on Contract No. DA-36-039 SC-5519,
and presents the theoretical considerations, experimental work, and deri-
vation of the design procedure for each of the special transformer types
which have been studied during this contract. Also included in this first
part is a continuation of the study of optimum transformer proportions as
they are affected by changes in the stack ratio of cores assembled from
scrapleas laminations. In addition, one chapter has been devoted to a
consideration of winding current densities and how they influence transformer
losses and heating.
In the second part are a step-by-step design procedure and an
example design for each of the special transformer types considered. A
summary of the basic design procedure and method for calculating temperature
rise is also presented, together with the design procedures which were
derived during the previous contract for ordinary filament transformers,
autotransformers, and rectifier-supply transformers. The derivations of the
design procedures and additional information about the last three transformers
is contained in the final report of the nrevirom nnacv.act. However, the
design procedures for them have been repeated in this report in order to
make it as comprehensive as possible. To provide correlation between the
two final reports, the corresnonding equation and figure numbers used in
the final report of the previous contract and in this report are given in
Appendix F.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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IF
I ..
11 v .
I1 .
1I ' where B 41 1=44AIMIPIllim.mm fari density in kilo:Lines per square inch,
is
Vo (int?iBAlizle5 volts, (2-1)
III1
1
I
i
N = turns comprising winding.
core space factor, the fraction of core cross
L. gross moss-sectional area in square inches,
If * frequency in cycles per second,
section occupied kr magnetic material,
IJ
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+or
II. MSSENTIALS MISSION PBOCEDNUtialEr REVISIONS
The design procedure developed under Contract No. DL-,6O39 SC-5519
is briefly discussed in this chapter. This material is also given )s10 so
that subsequent changes Which have been mode be introduced. A step-by-
step smmairy of the design method, as applied to filament transformers, is
given in Chapter U.
Basis ofidsiga Procedure
Ptir a sinusoidal variation in flux, the ES voltage of arty winding
I 1
1.1
t A = current density in the conductors in 1d1oamperes
1. Immo square in
AC = area of the core window in square inches.
fth;
II! I Multiplying (2-1) and (2-3) ii790 an expression for rating
The HMS current is
ta
? T asperse, (2-2)
and assuming that the wirding being considered occunies half nf the avail-
els window area and that current density is uniform in all windings, a
substitution May be made for RMS ampere turns, NI, to give
41
---C nrC" amperes,
whereIc ? winding space factor, the fraction of total core
111MOW area occupied by conductor cross section
2-3)
W = VI = 72417-f Fi B A Ac Ai volt amperes. (2-4)
Cambinatiraa of
?r
AAL.- ----A.--A.- -A
titnie LiaLLLelg.
w 1
f Fc Fi
A
D
" ? A Ai volt-amwes,
t
(2-5)
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,
wtdch is the general transformer equation. It may be of some aid in recog-
nising ayibols used if it is noted that quantities with the subscript "i*
refer to the iron core and those with subscript *c* refer to the winding,
which is usually made of copper conductor.
Nquatiam (2-5) may be transformed into another, lob/gib relates
rat.ing to temmature rise.. This neannee of iltamnereture rise is taken as
winding power dissipation per unit area of exposed winding surface, in watts
per square inch. This quantity has been Chosen because the transformer
winding is the part moot vulnerable to excessive temperature. The procedure
requires the prediction of transformer temperature when a design is being
begun, and the use of a simple, reasonable relation between temperature, ?
transformer geometry and losses is the key to reduction of cut and. try
procedures in design. A study of the design algebra has shown that an
error in the Choice of allowable watts per square inch has a reduced effect
on errors in core and vire sizes, a result supporting the validity of this
approach.
In the design equations, transformer proportions are represented
by dimensionless constants which are independent of size. Important dimen-
sions, lengths, areas, and volumes are found by multiplying these dimension-
less constants, or ratios, by a function of the characteristic linear
dimension, which is a measure of size.
Characteristic linear dimension:
4
fa klA A
v c
Mean length of magnetic circuit:
es ft 1 44ftrawmkger
m Alitummoo
Mean length of turn of the winding:
m -b4 inches
Gross cross-sectional area of core:
Ai *c 4` square inches.
Area of window:
Ac = d 42 square inches.
Exposed surface area of the winding (sum of all winding surfaces
except those in contact with the core):
Sc = e ?2 square inches.
( 2- 6 )
fn "11
14
.4T
(2-11)
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Exposed core surface area:
8 = g 42 square indbes.
(2-12)
A gewral design equation is then developed as follows:
Winding losses, assuming that current density is about the same in all
windings (the validity of this assumption is discussed in Chapter III):
Wc ? A2 p times (animator volume) watts, (2-13)
where A = current density in kiloamperes per square inch,
1 p ? material resistivity in microhm-inches.
Conductor volume imereA F cUbic inches,
c c c
where Fc is winding space factor.
Winding losses then become:
Wcis62pmcATcwatts,
c
The dissipation per unit exposed winding surface is
We A2nnAF
rwa"
trcialilmirMOIMEMMOI.
Solving for current density:
Il S
watts per square inch.
iciloamperes per square inch. (2-16)
Substituting for A from (2-16) in equation (2-5) yields
a I q
C
al 137' f VC B At Ai V A-717-17; 6e;
Finall;y, substituting for Ar. A4 from (2-6), nt from (2-8), A from (2-10),
and for Sc in the numerator Trost (2-11),
volt-amperes (2-17)
IIMEINSSISOINEWISIBleb
le 7
= ,r.fFjBtI' c
Ypbide 0
11111=1111011111111111111110111111111111?111.1111.1111111mm
1 II p V
Wr f B 17/2 V C C
Ea- ? =T. volt-amperes,
c
(2-18)
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1
t 11
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4`
.11 ?
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which is the design equation sought. The term i?isa combination of
dimensionless ratios, and is designed K. Equation (2-18) is the basis for a
design nomograph to be used for any typic of core and proportions. This nomo-
graph is given in Fig. 11-7. Its function is to aid in solving for the charac-
teristic linear dimension, 4, which is a measure of physical size required.
The de-4aable pr-portion; and type of core can be ron-"- esttmeted
near the start of the design. Values of KA and other geometric parameters to
be used lave been tabulated for several types of cores in Figs. 11-3, 11-1,
and 11-5. The constants a, bs co dj e and g are calculated from proportions,
while the constants III through X4 are functions of a, bp c, d, e and go comp.
blued for ease in caMlatine deign values. The proportions of the core
illustrated are only a few of the maw that can be used. For other proportions
than those given by the figures, the designer can use constants for the core
type most eisalar? or estimate the opwwkw,its by interpolation.
For proportions which are greatly different from those given, a
new set may be calculated. To do this'll core of the desired proporioneo,
but of an.y size may be taken. First the product of windov area and gross core
cross section AC Ai is calculated. Then the characteristic linear dimensioni
Ai WU (24) p
?is
w 11-717C
is found. Since the areas of the window and core cross section have been used,
the parameters c and d can be found immediately from (2-9), Ai is c 44, and
(2-10), Ac? d 42, respectively.
Mean length of magnetic circuit, m4? is simply the average length
core flux path. For this study the 18ngth is calculated asousing that
the flux makes a right angle turn ilhe corners of stacked cores having
square corners, and that the flux follows a circular path at the corners of
wound-type cores. Then the parameter, a, is found from (2-7), mi w a S.
Mean length of turn is used to find the parameter; b. Since coil
are always rounded, the mean turn for the simple or shell types of
the perimeter around the core leg plus pi times the window width; and
core type, an turn is the perimeter plus pi tiges half of the window
Then b is found from (2-8), mc b S.
EXpesed surface area of the wtrding is the sum of all outside sur-
face areas except those facing core surfaces, assuming that the ends are
smooth and that the coil exactly fills the window. Side and gild areas are
included. Then the constant e is found from (2-11), S e 4'. Exposed sur-
face area of the core is found in a Xanngm similar to that for the winding,
awl the constant, g, is calculated from (2-12), S g 42.
nf tha
corners
core is
fbr the
width.
Design Procedure
The first steps in the design procedure are the study of the speci-
fications and ti-m selection of a core type, core material, grade and thickness
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-.WNW
? .40.
of lamination, and type of enclosure. A stack height to lamination width
ratio, so of 1.5 is recommended, since this value gives a core of reasonable
proportions for most designs. A discussion of the influence of stack ratio is
presented in Chanter IV.
The allowable winding dissipation We which must be determined
at the start of the design in order to apply ecnomograph, is calculated
from
AT 1.25
14 41) watts per square inch,
where AT = winding temperature rise, ?C,
X = parameter from Table 114.
2-19)
The parameter X, is used to relate the factors which have the most important
effects on temperature rise. The values of K given in Table 114 and equation
(249) were arrived at after evaluating considerable test data, various de-
signs, and theories of heat transfer. The variables considered are: trans-
former type, that is, open, compound-filledo and oil-filled; 47116 of core,
simple, shell, or core; frequency; and ambient temperature.
Another impartant quantity which must be estimated at the start of a
design is the winding space factor F ? The factors which have the principal
influence on space factor are: physical size of the transformers numberof
windings, and operating voltage. These are related by the expression
= .08 login WI.' F (2-20)
where W.' = equivalent rating based on 60 cycles and
L 1106C rise,
F a factor from Fig. 11-2.
Figure 11-20hich is a revision of Fig. iO3 of Contract DA-16039 sc-5519,
along with a discussion of high voltage designs, is given at the end of the
chapter. Since the physical size of a transformer is affected by both fre-
quency and temnerature rise, the expression used to relate the equivalent
rating W:ri, to the actual rating W 0 is
Wr
.74 3
(k) (g)
volt-amperes
(2-21)
When estimates for the allowable winding ril=Q4n-t4e*iftana winding
space factor have been made, nomograph scale values to be calculated are
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t?
KW
e
Or F
ana p s
r
? ???
.1
where Kio is found from Figs, 11-3, 114, or 11-5 for the appro-
priate core and stacking ratio,
W is output volt-amperes,
F is core space factor, which is generally specified
F1 by the manufacturer,
f is frequency, or if frequency is variable, the low
end of the range,
p is winding resistivity, usually copper, the value of
Fig. 11-6 increased by two per cent or more.
To find the characteristic dimension it from the nomograph, the
proper values are calculated for Scales A and F. The line between these
points determines a point on Scale C. Next a flux density in kilolines per
square inch is chosen using Table 11-2, to determine a point on Scale B.
The line between the points on Scales C and B locates a point on Scale El,
which determines it in inches.
The next step is finding the core might, and from this the core
losses and excitation. Unless limited otherwise by specifications, it will
usually be desirable to keep core losses below 20 per cent of output volt-
amperes, and to keep excitation below 80 per cent of output volt-amperes.
Core loss, excitation and regulation ranges of typical transformers which
have been manufactured might serve as an additional guide in setting limits.
These ranges are given in Table 11-h, for two frequencies. Core weight may
either be calculated using the material density, or may be given by a lamina-
tion or core catalogue.
Core weight equals core volume times material density.
N1- mi Ai Fi Si pounds,
Mi m ^~.0 weight in pounds,
(2-22)
mi = mean length of magnetic circuit in inches,
A. = cross sectional area of the core in square inches,
F. = core space factor,
61. = density of core material in pounds per cubic inch.
Then for m. and Ai may be substituted the quantities of (2*7) and (2-9)
that core teight becomes
SO
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11
I
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m = a c Fi 81 43 = 1: F b 43 pounde.
(2-23)
i
1- Since Ca c) depends only on care proportions, this product is tabulated as
Ki in Figs. 11-3 or 11-5.
Nov that the weight is known, total core loss, W1, in watts, and
excitation.; W ; in volt-amperes can be calculated using &yes giving the
characterisitei of the magnetic material corrected by the appropriate factors
from Table 11-3. The curves give core loss and excitation in watts and volt-
amperes per pound respectively for ideal conditions of utilisation, and the
correction factors account for additional loss and excitation due to joint
effects, corners, stresses and other factors. Data for a frequency other than
the desired value may be Wiwi to estimate the core performance, because core
loss varies roughly as f1?4--
, and excitation in volt-amperes varies as f, at a
fixed density B. Gore loss and excitation may be checked to find if one or
both exceeds the specified values. If one value is excessive it will be
necessary to choose a new flux density, find a new 4 from the nomograph, and
calculate a new core weight from (2-23). If both values are considerably
below those specified it is desirable to raise flux density in order to reduce
core size. When a value of 4 appears to be satisfactory, all core dimensions
may be found.
Figures 11-3 and 11-5 give the ratio of the width L to linear
1:
dimension. Then,
L a (74 4 inches.
(2-24)
A lamination size is chosen, such that equation (2-6), AA4 = 44 is satis-
fied. For stacked cores the stack height is calculated lin8h that this is so.
For choosing from completed cores, such as a -mound type, a core should be
selected strol tb=t "Ain prrtAil^t 4s opprov4m=tely *^"n1 4.^ *he fo"""
power of the characteristic dimension. It may also be desirable to round off
dimensions, and if 4 is changed somewhat because of this, the new value is to
be used in subsequent calculations.
A design value of use in checking core dissipation is the care sur-
face area. In terms of 4 this is
"Ile
.2
r arimgm.
/ iew"
t4-0)
where Si is exposed core surface in square inches.
Core dissipation, in loss per unit exposed surface area, can be found as
MO' in watts per square inch. TO avoid excessive core tenneratures which
nay be damaging, it seems advisable to keep this value from exceeding the
dissipation per unit area of the minding, W,./Sc.
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,???? T TTA. VVV? VV..... ? T. ? V
Coil exposed surface area is
S ? e 42 16 K3 42.
Copper loss can now be estimated from
Wc
If in air s watts.
C pc c
Per cent winding lose is then approximately
(2-26)
v= 100 per cent. (2-28)
"r
Tt . weight of conductor required for the design is volume of conductor times
density.
)1 on A F 5 pounds (2-29)
0000
where m6 is mean length of turn in inches,
is density of conductor material in pounds per
cubic inch, for copper equal .321.
umbstitutionsammadeformeand Ac from (2-8) and (2-10),
M sbdFC b = K4 FC bc 43 pounds. (2-30)
C
The privinnt (b A) has been "b"*"t"ao r1isco V V41'2=o 41 ni'1) and 11-5.
The next design calculation's are the wire sizes. An equation for
circular mils per ampere is used. From (2-16) the reciprocal of current
density in square inches per kiloampere is
b d
? F
e c
Then circular mils Der. ampere =
b d
011/ Tc7c. 7.
V Tr;
4000
7r A
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11
145005111M10.1114".""""mo.?????????----
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CX
K F )
-pfe We 5 0 P
where x5 ? V.
(2-31)
? 41.0.
The circular mils required for each winding is the result from
(2-31) times rated current for the winding. While secondary current is speci-
1144 primary current is calculated from
(2-32)
Wire sizes are to be chosen from Table 11-5, using the closest values avail-
able.
From equation (24), the turns per volt of a winding is
105 105
Ve
Prf Fi B Ai 1l.144717111j
Substituting for A4 from (2-9)9
?
(2-33)
K6
? turns per volt, (2-3h)
fF
where K
6
105 .
fir c
Equation (2-33) is preferable, but equation (2-34) is useful for estimating
turns early in the design procedure. The turns far any winding may be found
by mmatiplying (2-33) by the rated voltage of the winding. A correction
should be made for regulation so that rated voltage is obtained from the trans-
former at full load. This could be done by decreasing primary turns, or in-
t""=-411.'e aPOOndary turns, or both. The amount of the total change in per emit
should be appammdmately equal to the per cent winding loss as determined
earlier.
There have been applications of transformers in which part of a
secondary winding supplies a separate load. In such cases, IF should be
calculated from the total load in the usual way. Then vire sizes for each
part of each winding should be selected according to the ENS current in that
part or winding.
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? ???? ??? ?11.1111 VW."'" a
?
The nest step is the layout of the coil. Mast commonly a layer
-
insulated mdading will be used. Timm wire with one coat of enamel or other
film insulation will be used for slims smaller than AND No. lh, and either
one or two coats of insulation above that else, depending on care taken in
construction. Tables 1106 and 11-7 are included to help in laying out the
winding. The important check to be mode an the coil layout is that the coil
adequately fills the window space but is not too tight. Typical per cent
build measured as a proportion of the window width is blo to 90 per cant.
Men a design is completed to this point, other checks awyr be made,
particularly on those quantities close to their limiting values, such as
losses and regulation. In particular, a check of the voltage ratio should be
made. First, winding resistances are calculated by multiplying the resistance
per unit length (corrected to operating tesperatwe from Fig. 11-6) by the
number of turns, and than by the mean length of turn. The mean length of
turn equals the length of the imide tom plus pi times the build-up of the
winding. The primary voltage is than calculated from
V a n [711 + Is (Rs + ao/n21 volts, (2-35)
where R:el and E0 are the secondary and primary resistances
respectively,
n is the ratio of primary to secondary turns.
The turns ratio should be adjusted it the calculated primary voltage differs
appreciably from the specified voltage. Another calculation to be made is
temperature rise. A method, which was developed on Contract No. DA-36-039
SC-500, is summarised in Chapter II.
p.e.sl.f&ransformers
The formula for calculation of winding space factors, as derived in
the final report for Contract No. DA-36-039 SC-5519, is
F m .08 log-- lr
--iu r
(2-20)
1
m equivalent rating based on he
r rise and 60 cycles,
F is a term to account for number of windings
and working voltage.
Shortly after that report was issued, it was found that the re-
sultant space factors were too high for the higher-voltage designs, in that
there was inadequate WiThlOW space. The reason for the difficult has been
discovered and a revision o( Figure 110 of the previous report h4 been made
to obtain better values for the tare "Ff. The revised values are given in
Figure 11-2 of this report.
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? ???
The difficulty results from the design practices used for the units
upon 'which the original figure was based. Mese units had at least one high-
voltage winding designed for a very low current density. &all wire sixes
are no difficult to handle that it is common to select some minima size,
such as No. 110 AND, for windings Aire heating:would ordinarily permit a
smaller cross section. For application of the design method in such cases,
the remedy is to use a space factor, for purposes of calculation, which is
smaller than the value obtained in the completed design. This is accompliahed
Wyse of the revised figure. lien though a wire size might be chosen which
is much larger than wad be required an the basis of heating/ liAdtatiann
alone, there will usually be little effect on overall transformer size. This
results from the fact that space occupied by a high voltage winding nay be
small compared to surrounding insulation, no that a change in wire size has
little effect on insulation clearances.
The allowable winding dissipation WAA0, for use in the nomogrgpb,
should be calculated in the usual wq, but falai values will often be less.
It is not practical to attempt to design all high voltage units to operate
near next= permissible temperature rise, and even if this were done by
using extremely small wire sizes, there would be little saving in space and
weight.
However, the revised figure for mr, does not solve the problem in
designs for which the calculated space factor lc is negative, or for which
the two right-side terns have opposite signs an about the same magnitude.
This situation is likely to occur with high-voltage units of emall equivalent
ratings. When this is the case, it is recommended that the space tutor re,
and the characteristic linear dimension 4 be calculated by assuming that tSe
working voltage is 5000. Then the calculated 1 is increased by 0.3 inch for
each additional 5000 working volts of the required design.
In either of two cases: (1) when a wire sum larger than the cal-
culated value is selected, or (2) when 4 is increased by 0.3 inch per 5000
volts, modifications are necessary in the Aftffiffn pricAmwpA. In -"e (l) it
may not be known that a wire silts snot be enlarged until it is selected, in
which case the normal method for calculating:Wilding losses, per cent regula-
tion and conductor weight (which would have been calculated in previous-steps)
are invalid. In, case (2), calculation of these quantities should be deferred.
Circular mdls per ampere is calculated from the standard equation. (For case
(2), use the value for 4 corresponding to 5000 working volts). Wire sizes
are next computed and increased to the minimum practical size where necessary,
in either case.
Tarns per volt should be calculated, and preliminary turns for each
winding can then be determined. Next, resistances of each winding should be
calculated. An Ammoirente correction for the regulation for each !Finding
can be made using the product of rated current times calculatAd resistance.
wfri 44i4112 iftemamal immell+rstrip. ^4" .fteam& .A.AA-- A? AA__ Ak?,...a_t__
&imp ame.w.ww vow. waisawro vmsal.ww ww 'maw mwmwrammum. vvalowsw wAs. !maw& wamwavis aa Limuuwu
by 'tic* secondary preliminary turns must be increased and primary turns
decreased, respectively.
For use in tamxTimaart-rise calculations, total losses may be
found as the BUM of current squared tines resistance for all windings.
Minding exposed surface area. is
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??%.?? 111?111 411??? I ?? ? ??? ? ?? ?????
(2-26)
where X is a geometric parameter given by Fig. 11-3, 11414
S is characteristic linear dimension, inches.
(for ease (2), use the final Talus after
increasing S by 0.3 Ladd per 5000 working
volts.)
Finally, the weight of conductor for each winding is length times pounds
per unit length.
? ????
or 11-5,
I
Il
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? 4
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In. WINDING CURRENT DISITIESI LOSSES AND RATING
In the calculation attire sizes for the different windings of a
transformer, the design procedure developed under Contract No. DA-36-039
SC-5519 yields equal current densities in all windings, at least to the
extant that equal values can be achieved with a finite number of available
wire sizes. The possibility that advantages might be derived by unequal
current densities has been studied with respect to:
1) Conditions for minim total winding losses,
2) Conditions for minimum hottest spot temperature rise,
3) Insulation selection - possible use of different
materials for different parts of the transformer.
A straightforward solution may be obtained for UN -:first problem,
and it is shown in Appendix A that minimum total losses are obtained when
the available window apace is so apportioned that current densities are
inversely proportional to square root of the product, mean length of turn
times apace factor of the windings. This holds for any number of windings,
and for the different layers of any one winding.
A solution to the second problem is much too difficult to obtain
except for simple geometric configurations. However, simple configurations
are available as a qualitative guide to transformer characteristics. For
such purposes, the transformer as a heat source may be likened to a sphere
or to a section of a cylinder. Another possibility is that a side of the
winding might be likened to part of a plane.
Several observations regarding temperature rise are applicable to
a heat source in the form of a sphere, cylinder or plane. Hottest-spot
taw:Arab/re rise is the sun of the rise from the surface of a body to the
ambient plus the rise from the hottest spot to the surface. In the steady-
state, the surface rise of a simple body depends only upon total losses and
not upon loss distribution, so long as the distribution is gymmetrical.
Therefore a transformer can be expected to hava approximately minimum surface
rise for a given rating when current densities satisfy the condition of
Apppneie A. For a simple body and a fixed amount of generated heat, the
entire body would have the same temperature if the heat sources were
distributed uniformly on the surface. In this case, hottest-spot temperature
Is the same as surface temperature. Although this condition is not desirable
for application to transformer design because of the high resulting losses,
it does indicate that there may be some advantage in generating more beat
per unit voleme near the surface than far ,..f,ram the surface. Similarly
=vim= coil rise is obtained if the same heat sources were placed at the
point (sphere.) 'or points (cylinder or plane) farthest away from the surface.
Therefore it is seen that the practice of choosing the same current
density for all windings is a compromise which gives higher total losses and
surface rise than the possible minimums, but which give a lower hottest
snot-to-surface rise. It is difficult to say what distribution of current
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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density is best, but factors of importance are the coil thickness, coil thermal
conductivity, surface heat-transfer coefficient and the difference between in-
side and outside turns. in attempt has been made to analyse a cylindrical
heat source, but the algebra is very involved. However, a heat source con-
sisting of an infinite plane of thickness 2x0 has been studied. Conditions for
minimum total rise of thia soave are given in Appendix 110 with the restriction,
for simplicity, that current density be linearly distributed from the center
to the surfece of the pilimme. For the plane source, it is found that if the
coil thermal conductivity is very high the current distribution should be
about conetant across the plane; and that if the surface rise is very smell,
the current density should be low at the center and high at the surface. These
characteristics of the plane, modified by the condition for minimum total looses,
justify the use of a uniform current density in transformers until more precise
information is available,
The study or conditions for minimum loss and minima transformer
temperature rise indicate that it Is not feasible to attempt to operate the
transformer winding at an almost uniform temperature throughout. In units
designed for a high temperature rise, the differences of temperature within
the coil may be so high that different materials can be used for different
portions. Thus it may be possible to use materials less resistant to highest
temperatures for the coolest parts of the winding, thereby reducing expense.
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IV. OPIUM OORB STACK RATIOS
The purpose of the study of optimum core stack ratios has been to
carry further the investigation of optimum transformer proportions which was
reported under Contract No. DA-36-039 3C-5519. This previous work considered
general transformer proportions where all geometric ratios are assumed to be
variable. However, certain widely-used NI and UI laminations have fixed pro-
portims, so that the proportions of a core can only be varied kr, chia,..***, the
stacking ratio. This is defined as the ratio of core stack height to lamina-
tion leg width (center leg of a shell-type core). Naturally it cannot goner-
ally, be expected theta quantity to be minimised can be made as small by using
laminations of fixed proportions as it would be for laminations having all
proportions flexible.
Since the previous analysis was made, computing equipment has be-
ams available which has greatly shoplifted the work of calculation. Your
types of transfoTmere using garagese laminations have been analysed. Three
of these use oommom laminations* The fourth Is a transformer using the new
El lamination conceived during the previous contract* For a discussion of this
lamination, see Appendix C. This is included for comparisons and as a guide
in case this lamination is manufactured at some future time. The four trans-
formers considered are:
1. moll type using the scrapless SI lamination of Figure 44a.
2. Simple type using the scrapless UI lamination of Figure 4-lb.
(The winding ncircles one long leg.)
3. Core type using the UI lamination of Figure h-lb.
winding consists of two coils, one on each long leg.)
40 Shell type using the new SI seraplesa lamination of Figure 4-1c.
The general equations for analyzing a transformer fello tiv"1 weight,
volume, losses or cost are applicable to any of the types.
Con m A mn V
c c c
I ? ni mi Ai * ni V.1.
where C or total weight, volume, losses or cost of the winding,
'" 4014,1001.1. WW4W140, VILULLIMPO, J.volow, or VUOU CAL Witif uvru
n = weight, volume, irmirimm or cost per unit volume of
the winding,
n weight, volume, losses or cost per unit volume of
the core,
mc mean length of winding turns,
m - mean length of core magnetic circuit,
An = area of core window,
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waymormastoramoTimpoisiniailimm,
(a) LI LAMINATIONS
"sr.-. m ???? --? ?,? ??????????
(b) UI LAMINATIONS
3L
2
(c) NEW Er LAMINATIONS
FIG. 4-1 ? SCRAPLESS LAMINATIONS
II
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A arse of ears cross section,
VO * total volume of the winding,
T. total volume of the core.
Another necessary quantity is a weighting factor for winding and
core. This
?
(44)
1) For the shell-t transformer using the common 11 laminations
of Figur* 4-1a, equations with substituted values for mailiiid
ammo become
C nc (3 2) (2+2e+)L
I is ni (02) (6L),
where s is the core stacking ratio
kWh*, dividing by ni, and replacing the ratio nini by X, gives
C * Ie (j)II, 3 (4 4, 11
28) f 601 1,3
(4-3)
The r4-ht aide of (4-4) in A fonetinn of the throe veriables L, a and K. It
?/
is desirable to minimize this quantity, keeping the product of window and
core cross sectional areas A A. constant. This product is
3
A0 A ? k4 ? (z L2) (eL2 )41
Aire k is used in this chapter in place of At for the character-
istic linear dimension so as to avoid a script symbol.
Solving for L give:
L (4-6)
(1--)
SUbstituting for L in (4-4) gives a function of stacking factor a and
weighting factor K.
La 4 A
6n,k3
r 1 _ 01/
f..4%/414 T 11.
LE:
t4 .75
...) ?
(4-7)
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This function is plotted in Figure 4-2 with s as abscissa and X as parameter.
Another function which has been calculated is the ratio of total winding
weight, volume, losses or cost to total core weight, volume, losses or cost.
1 +
co.r. ai
a
(11-8)
2) Similar equations can be derived for the s le- trans-
former using the UI laminations of Figure 4-lb. With va ues su ituted
in (44) for meanWareass
C n (31,2)(2 4. 2s 4. OL
I ? n4 (se)(12L)
Also, C 4. I
--ni w [1( (3)(v+ 2 + 2s) + 12s3 7,3.
Since AO Ai mg k4 Is
Then I, ? k
5575
Equation (4-10) becomes
c.+_ Eir el 2+ 2 4,
6n kJ
Similar to (14-8) is
C K
2s
Equation (4-13) is plotted in Figure (14-3).
+ a)
A)
-I -
2e'l
(3).75
(4-9)
(4-1o)
(4-12)
(4-14)
3) The equations for the core-type transformer using the HT ltistrina.
tions of Figure /4-31 are
9
C 211n (317)(2 + 211
I n (51,2)(121)
I.
37)
(4-15)
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? "nor virr-4. a -? ?-??-?
LAMINATIONS
FIG. 411-? 2 STACK
:NOILIONIA
I 4.*
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.11."
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111,11 v.' ?
0
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41111111//1111
:NOLL3W14
1 + 3
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0
1
CI LAMINATIONS
I
I
.
1 i!I
1
11,1
I / /
.0
II I
L 1
10
SNIP
'it
ink
160
.m4
X
0211 : NO113PRIA
1 + 3
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4???? ?
?mrio mr?-??? ?
LAMINATIONS
OUP
11111111.
0
?
0
rft
31 I" :N011314114
+ 3
WIMP
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? Virma a -
? I.
?
FOR CORE
a
vi
L.
Akt NNW
Imo 'NW
NM,
IMO
Ll
awl
Jr
On- /91141,
'NW
0022
s tiouptin4
+3
NOD alft
w-cr IDN1
1
I ed
elk ?
lb/
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ii
MI I
?1222.
I 4 3 010U.3tiftj
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? w. now 'WIMP 411,?.
?
I
dl
1
C + I [1( (3)(11-1Uir ? 2e) ? 12s3 L3
z
Ao Ai s k4 go (311) (InF)
L
C.'
61-70'
1K (1g fi e) 2eJ.NJuyon).
A 4. ? .
C.Fr;
T
iguation (449) is plotted in /Iwo 444.
(4-18)
(1140)
4) The eque.ions for the shell-t transformer using the now
la*ln$tiCfl of Figure 4- o are
C ? no (3L2)(2..-2w4w)L
2%
I? n . )(10L)
[Illr (3)(2 + w + 2a) 4. 10e:1 L3
4
A 2 2
A al k ? (318 HAM )
i
C
?????-
7?
on ir1. L.
4, 1.
K 2 +
58
T.
Figure 4-5 gives the results at aviation (4-25).
(4-21)
(h-22)
(4-23)
(445)
(4-26)
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1
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The stack ratio used in Figures (4-2) to (4-5) effectively estab-
lishes the ratio of winding sise to core Bias. Mier ratios could also be
used: the ratio of window area to core cross-sectional area Ae/41, the ratio
OA, or the ratio of winding volume to core volume Vo/Vi. Table 44 gives the
optimum values af these quantities for several values of the weighting factor
K. One interesting result is the fact that C/1 has a very large range for
weighting factors from .2 to 5. The range is much larger l'cab *crania's lamina-
tions than for generally,* variable acre proportions. It is concluded from this
result that the practise of making the total value C associated with the winding
equal to the total value I associated with the core, is not a very good ap-
proximate rule for strapless laminations.
It is of interest to compare the different types of scrapless lamina-
tions with each other, and with the general types studied previously. This is
readily done by calculating the function II/ni for the optimum *Wilting
ratio in each case. The previous value for area rrodust Ac Al is 6.25 has been
used, and thus the quantity k is determined. The results are given in Table 4-2.
The results for transformers No. 5 to 8, ehich have generally variable pro-
portions, are taken from the previous work. Although Nos. 5, 7, and 8 were
calculated with rounded core corners, a comparison of Nos. 6 and 7 gives a
rough gauge of the difference between rounded and square corners.
Several other comparisons can be made from Table 4-2. One notice-
able feature is that Nos. 5, 7, and 8 are each more economical than Nos. 2
(simple), 1 or 4 (shell), and 3 (core) respectively. The given differences
indicate the loss incurred by using scrapless laminations. Comparing the com-
mon scrapless SI lamination No. 1, with the new scraplees RI lamination No. 4,
shows that No. 1 is more economical for large K (typified by total losses),
whereas No. 4 is more economical for small K (typified by total weight).
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11 i4
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.P10
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Ob
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0. ? IP ? '00 ?
V. TRANDPORNIRSWITH 013ALANCED MONETIZATION
A transformer with unbalanced magnetisation presents a complex
problem in finding relations among the electrical quantities. Difficulties
arise as a result at the nonlinear relationship between the core induction
or flux density and magnetic field strength. This factor is of less importance
when either the unbalanced magnetisatiom or the superimposed alternating in-
duction Is all, because existing design methods for such oases are reliable
and widely used. In a transformer, however, alternating induction is always
much larger, and the nonlinear characteristics of the material make it im-
practical to apply algebraic analysis for Obtaining relations among the mag-
netic quantities. The principal variables are the instantaneous values of in-
duction or flex density and the magnetising force. Other variables are the
configuration of the magnetic circuit, the type of joint used and the grade
and thickness of the material.
The superposition at D.-C and alternating components of magnetising
force on magnetic materials gives characteristics which are qualitatively
similar in some respects to the case of an alternating magnetisation alone.
In both instances the magnetic quantities may be related by. a hysteresis curve,
which is usually given adth induction or B as ordinate and magnetising force
or H as abscissa. With an unbalanced magnetisation, the curve is dissymmetrical
and has time-average values of Band H which are unequal soros In addition,
the average values of B and g are not simply related to each other by the D-C
magnetisation Characteristic of the material. In power apparatus, the hysteresis
loop is narrow, with or without an unbalanced magnetisation, so that the rela-
tion between B and H is practically single-valued. Therefore the maxima and
minimum values of induction and magnetizing form respectively are directly
related brytte DC magnetisation characteristic.
In general the parameters which must be determined in the design
of magnetic circuits are: a suitable material, a satisfactory value of flux
density, proper preportions for the magnetic circuit, and the non-magnetic
gap in the core. It is desirable that the resulting device be as small as
possible for the required power rating. This means that operating densities*
flux density In the core and current densities in the windings should be
made as high as design limitations 11111 permit. Such limitations may be core
or winding losses, voltage regulation, efficiency of the unit or permissible
beating. The most universal limitation in power and commnicatian equipment
is plralssible temperature rime. RANOratlen of othere.vrtant.
to be met, excessive temperative must be avoided. characteristic of almost
all power equipment is that tammeretere rise increases as size decreases, for
a given oatput. To obtain maiiiam rating with least material, the designer
should approach the permissible operating temperatures of both core and winding.
The quantities which determine whether the magmatic circuit has been properly
designed are the core loss and the magnetising reactive power required by the
core. Rither of these quantities may limit flux density in the core. in
physicaliremall apparatus, the contribution of the magnetising power to the
heating of the windings is usually the important design limitation, while in
large equipment, core loss usually fixes the limiting flux density.
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8
References
Published works which have been found to be of the greatest value
will be briefly reviewed. Two excellent and extensive bibliographies have
been published by Mal and by Klee, which include almost all of published
raferennes ATIA natowitim which beve been found an the subject of unbaanced mag-
netisation. These lists were primarily intended to present a background on
magnetic amplifiers.
, Same of the earliest important contributions were made by lima and
others3A who found that for acertain DC magnetisation, the superposition
of an alternating field may either raise or lower the average value at in-
duction. Another study of the effects of A superposed alternating field on
permeability and losses is that of Spooner'. Recent tests have been made by
Battelle Memorial Institute? under contract No. II 36.039 8C-38255D but the
results given apply only to relatively low values of D-C magnetisation.
While some of the references give techniques and circuits for the
measurement of magnetic properties with D-C magnetisation, others emphasise
and compare different circuits for obtaining losses and effective inductance.
These circuits are in two general classes: null-balance or A-C bridge types,
and direct measurement types. In the bridge circuits, a coil on the magnetic
sample constitutes one arm of the bridge. The DI-C magnetising force can be
supplitd through the same winding or by a second winding on the sample.
Harris' deals with different types of bridge circuits. Charlton and Jackson8
have presented a circuit for direct measurements, using two similar cores with
two windings on each. Windings of each coil are connected in series to the
A-0 supply and to the D-C supply: an arrangement which yields non-sinusoidal
flux wave shapes in the cores, and which gives results difficult to interpret.
Many references deal with the characteristics and the design of
transformers where one winding carries direct current. In 1927, Hanna9
published a classic article on design of reactances and transformers, which
relates inductance, direct current, magnetic field, core geometry and air gap
In the core. Curves presented by Hanna make it possible to select an optimum
air gap. However one sheet of design curves is valid for only one A-C flux
density. Most of the data and design methods published subsequently are ap-
plicable only to much smaller A-V densities than would be used in transformers,
and it is usually assumed that the incremental permeability of the magnetic
material is independent of A-C densitzt Following Hanna, data and analyses have
been given by many others such as Lee". The book of the HIT Staff-1 gives
typical data and points out that a core air gap may be usedjo obtain more
nearly constant inductance over a cycle of operation. Lege has extended
the method of Hanna by an orderly design method for transformers
and reactors carrying unbalanced direct current. Further analysis of this
problem is given by Carter and Richards13, who also show that average induc-
tion and average magnetic field strength are not simply related unless I-C
induction of density is small.
An important factor in the design of transformers supplying a
half-wave rectifier is the type of output filter circuit. Schade has
given widely used curves which relate transformer secondary and load quantities
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???? ????????????,
4
? ,??? ?????, g ??? ????? .? ? ????
4.
TIME
?
Ii
FIG. 5-1 --RELATIONS BETWEEN INDUCTION
AND FIELD STRENGTH.
_
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according to freemen load resistance, filter capacitance and circuit
resistance. Seely' has also studied the interesting half-wave rectifier
output circuit consisting of an inductance and resistance in series.
General PrIperties of Magnetic Circuits with Unbalance
The non-linear characteristics of ferromagnetic materiels cause
considerable complication in an analysis of magnetic circuits with unbalanced
magnetisation. The problem consists essentially of relating indnotion or flux
density B and magnetic field strength H. A typical D-C magnetisation curve is
given in Pig. 54. When the material is subjected to alternating values of
B and M: about some average values, the /LC curve describes the approximate
performance. Qualitatively, there are two rather different conditions:
comparatively small variations and comparatively large variations, As noted
earlier, the references which give extensive algebraic relations among the
circuit quantities cover the case for small variations in B and H. To solve
circuit problems, it is desirable to use additional data in the form of in-
armmental permeability, or the ratio of change in B to the change in H. When
small B and H variations are occurring in the steep region of the magnetisation
curve, the value of incremental permeability is much less than the slope of
the DC magnetisation curve. Also, the incremental permeability is not
greatly affected by the magnitude of the B variation.
In the second case, where the variation in induction B is large, the
D6C curve describes fairly well the relation between B and HI a fact which is
used for the following qualitative analysis. During operation under unbalanced
conditions, the exact function consists of a displaced (non-symmetrical)
hysteresis loop, enclosing an area proportional to losses per cycle, as for
magnetic materials operated without an unbalance. With a large variation in
Bp the quantity corresponding to incremental permeability is some average
slope of the D-C characteristic, and this magnitude is greatly affected by the
magnitude of the variation in density B. This added dependence pakan thia
second case more complicated than the first; inasmuch as incremental mime-
ability is no longer approximately constant as it is for by values of alter-
nating density. Therefore the term incremental permeability has little sig-
nificance for the second case. It is found that the most useful means for
understanding the problem are: a graphical analysis of the magnetic quantities
and a study of frequency components of the electrical quantities.
The 41seerfeet variables el-4dt determine the charecteristiee of a
magnetic circuit are the average and variable components of induction B and
magnetic field strength BC, the geometry and material of the magnetic circuit
"A 4.-kAl fr"IndnIqr of variation. Average flux density is defined as Bo, and
the average field strength is defined as A sinusoidal component of flux
density is assumed, which is defined as B. This is one half of the maximum
variation about the average Bo. Important geometric parameters of the sag-
nettle circuit are the dimonnions and the type of joint used. It is assumed
that the flux density is uniform in the core at every instant of time. In
general, the presence of a joint in the magnetic circuit makes the field
strength non-uniform around the magnetic circuit. Therefore the given average
field Err is an average around the core circuit as well as being an average in
time. This quantity can be related directly to the direct currents in the
windings surrounding the core. If there is a direct current Ipc in one winding
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of II turns then the average field strength may be defined as
Rix is w NC
m oersteds, (5-1)
Idlers a. is the an Laneth of saeratic circuit in centimeters.
Average flux density is not simply related to the average field
strength Iwo The relation between these quantities is demonstrated by
Ms. 54. If an average value of flux density Bo is assumed, with a super-
imposed variation B, then the resulting function of field strength H is
uniquely determined by the D-C magnetisation curve, insofar as the hysteresis
effect can be neglected. The average of the H function must be B. This
establishes a relation between Be, and H. It can be seen that average flux
density cannot be readily determined from the magnetic characteristic by
graphical means, since repeated trials would be required, assuming each time
a certain value of average density. In a closed magnetic circuit it Is also
difficult to determine average density by experimental methods. The only
possible way is to trace the magnetic history of an initially demagnetised
specimen.
From the foregoing discussion it is found that the magnetic varia-
bles of a given magnetic circuit are uniquely determined by the average and
varying outpatients of flux density. Mince both of these together determine
the unbalanced magnetisation Itc, it can be reasoned that the performance
could also be described by the 'nines of B and Hpc? which are readily deter-
mined. Unbalanced magnetisation is defined by equation (54). If a sinusoidal
voltage or component of voltage is applied to a winding of the core, the
voltages are
whore i is the current function of time,
R is the resistance of the winding,
0 is the flux in the magnetic circuit,
I is number of turns;
t is time.
( 5-2 )
If it is assumed that the iR voltage term is negligible in compari-
son with the induced voltage term, and if the applied voltage is sinusoidal;
v cosatt, (5-3)
then equation (5-2) can be solved for flax to obtain
V V
.2! /Costa tdt Bin t ?if a 00 +
? N MLO '0 .111
where 00 is the average component of flux,
011 is the peak of the alternating component.
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J
This developnent shown that the existence of an average component of flux is
ccepatible with the fundamental relations between applied potential and flux.
Therefore the operation of a magnetic circuit can be described entirely in
terms of fl (which is 01 divided by net cross-eectional area of the core) and
BBC?
Effect of a Non-ffegnetic Gap
In addition to the other physical properties of. closed magus tic
circuit, core poetry and notarial, an iiportant variable is the non-magnetic
gap which may be introduced in same cases to Obtain improved characteristics.
The presence of a core Joint of any type has an effect on pert rmance which is
similar to that of the non-nagnetic gap. In most applications of magnetic
cores to power apparatus it is desired that the self inductance at a given
winding on the core have the highest value possible. When there is no un-
balanced sagnetisaticn present, the highest self inductanos is obtained when
a core Joint of minimum reluctance is used. If the DC magnetisation curve
of Fig. 54 is considered to be a plot of flux density or induction B against
average magnetic field strength If around the entire magnetic path, then the
Introduction of a non "eagnetic gap increases the value of If for each value of
H, or bends the curve to the right. This effect is undesirable when there is
no unbalance and maximum inductance is required.
EL gap may yield an increase in self inductance when a core has an
unbalanced magnetizing current in one winding, which can be demonstrated
qualitatively. The change in the magnetization characteristic of the core
than tends to reduce the average flux density' Bo of the core. The quantities
B and Hoc are considered constant and independent. Therefore the maximum
flux density (H + 80) is decreased and so is the maxima field strength cor-
responding to (B 4 Bo). The cost of obtaining this advantage is a decrease
of slope of the B-H curve in the regicms of low HO In another sense, in-
0402.4.11Famommit mamkoh4141j.. famoemn111. 0Anmw4neo m ~alo% is 41iaimasomoi mae ..am
high values of H and decreased at low values of H. Since. it is apparent that
a sufficiently, large gap would decrease self inductance in any case, there
smurbe some optima value of non-magnetic gaps whiCh depends on 8, abc, core
material and geometry. In a transformer with unbalanced magnetization, the
requirement of maximum self inductance is equivalent to a requirement for
obis= magnetizing current in the winding which provides A-C excitation to
the core.
The quantities B and Bbc am a used to predict w.g.rvtle characteris-
tics of various cores of various shapes and sizes. Similarly, it 12 desirable
to express nen-magnetic gap in a manner such that the results for one size
and shape can be used fcr others. It can be shown that per cent non-magnetic
gap should be used, or the ratio of air gap length to magnetic circuit length.
Consider a magnetic circuit having a uniform cross section and air gap carrying
a flux which does not vary with time. The magnitude of flux is
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SW
A tamotive force
"'DC m re (stance
.1s N
W eimmarosavenionmarerroreme maxwells
Ali IN
176r.*
r-i -g
(5-5)
where N ? number of winding turns,
= winding current, amperes,
m ? length of magnetic iron circuit, centimeters,
1'4 ? relative permeability of the magnetic material,
Ai 01 net croes-eeotional of the magneticnn 111
Mrwww.mw.rip
m = effective length of the non-magnetic gap, cm,
A 66 effective cross-sectional area of the non-magnetic
gap, sq. cm.
The two terms in the denominator of (5-5) are the reluctances of iron and
gap respectively. Then since pm = Br C Alp (5-5) gives for flux density
.14 N IN
BDC A lines per sq. cm. (5-6)
m, (14; +
m g
Ry has been defined in (5-1) as the average magnetomotive force in oersteds
around the magnetic circuit, neglecting the length of the gap in comparison
with the length of the iron, so that (5-6) becomes
BDC
BDC 1.--Plines per sq. cm.
(!...I.!)
PA *j Ag
Equations (5-6) and (5-7) shay that only the ratio of lengths Tem
and not each independently, affects the relation between Bric and Nix.
ratio At/Ag is a correction factor for flux fringing at the gap, and has a
value sligntlyless than one for relatively short gap lengths. Equations
(54) and (5-7) do not hold in general when there is superimposed alternating
flux in the magnetic circuit. They are given hero only to show that the ratio
of lengths is important.
Although it is evident that the ratio of gap length to magnetic
circuit length is most important, another consideration is the minimum ef-
fective gap length obtainable in particular cores. This effective gap length
is present because at the necessity for joints, and depends very little on
the size of the cur0. Thus, the minimum effective gap ratio of a small core
(5-7)
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111111.0.?
????
I
is higher than that of a large core, when both are constructed with the best
possible joint. Table 5-1 gives suggested effective gap lengths for different
cases.
Tible.5-1
EFFECTITZ GAPS DUE TO JOINTS
Core
Stacked laminations,
interleaved lx1 or 2x2
Stacked laminations,
butt joint
Wend core, two
good-quality butt joints
Gap-Inches
.001
.005
.001
The values of Table 5-1 can be considered as a part of the term
mg. Actual total spacing to be placed in the core joints is then
m (A) m inches,
(5-8)
where the ratio me/mi is to be given from magnetic Material curves, and mi
in found during tHe design. If the calculated mg is equal to, or less than
the value of Table 5-1, no additional spacing in the joint is necessary. If
calculated mg for a wound core were, for example, 10 mils, then 9 mils (total)
of spacers sHaild be placed in the joints.
Test Circuits for ObtainintAmental Data
AS discussed earlier, two major methods have been used to obtain
data on magnetic materials subjected to superimposed AC and D-C magnetization:
bridle or null-balance circuits, and direct measurement. A basic objection to
bridge circuits is that a non-linear impednace is being tested, which makes it
impossible to obtain a true balance. For determining incremental perweebilities
and core losses at small A-C flux densities, the American Society for Testing
Materials (ASTMi A34-48) specifies an Owen bridge and a magnetic sample with
two windings, one to serve as an are of the bridge, and the other to carry
direct current. In addition to a distinction according to the varicus types
of bridge circuits, the magnetic sample may have one or two windings for ex-
citation. When only one winding is used, a combined A-C and D-C excitation
source is used as the bridge input. This leads to some difficulty in control
of the source. On the other hand, when two windings are used, precautions
must be taken to prevent transfer of pacer from the A-G circuit to the D-C
circuit. This is accomplished by using a large inductance in the D-C circuit.
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?
Because of the difficulties associated with bridge circuits, a
method of direct measurement Is preferred. Direct methods, in general, do
not usually yield the accuracy obtainable from a lull-balance circuit. A
suitable degree of accuracy in measurements on magnetic materials is achieved
when the measurement error is a small fraction of the variability of the
material among identical samples. From this standpoint a direct method should
give reasonable absolute and relative accuracies for typical data. As for the
bridge circuits, a direct measurement can be made on a sample which has either
one or two windings. When one winding is used, A-C and D-C excitation sources
are interconnected. Adjustment of the input and maintenance of sinusoidal A-C
wave shape can be obtained only with testing apparatus of unusual versatility.
Therefore a sample with two windings should be considered. The simplest ex-
ample of a circuit with two windings is shcwn in Fig. 5-2. Wally, the in-
ductance in the D-C circuit should be infinite, such that no A-C current flows
in the DC winding. When this situation is obtained, the total core excitation
at any tine is the sum of the instantaneous primary current and the D-C secondary
current. The parer measured by the wattmeter is composed of the primary winding
losses and the core losses, while the battery in the secondary circuit supplies
the resistive losses of the secondary winding, the choke, and the control re-
sistance. Practically, it is desirable to use sufficient impedance such that
power transferred from the A-C winding is negligible. This could be accom-
plished with a choke many times the size of the sample under test, and suitable
for carrying the direct current. An alternative is to measure the real and
reactive power components in the D-C circuit.
A solution to the porblems presented by the circuit of Fig. 5-2 is
provided by the circuit shown by Fig. 5-3. An A-C voltage can be introduced
in the D-C circuit in such A manner as to oppose the voltage induced in the
DC winding around the test sample. This is accomplished with an auxiliary
transformer which need have only the sane turns ratio as that of the sample,
and be capable of carrying the direct current. With this circuit there will
still be a relatively small net AC voltage in the D-C circuit which is due to
distortion of the induced voltages from a sinusoidal wave shape. This in tarn
is caused by resistances in the primary circuits of both test sample and aux-
iliary transformer. The net induced voltage will be of harmonic frequencies.
However, since the net voltage is of relatively low magnitude and of higher
frequencies, a very small inductance in the D-C circuit is adequate. The
presence of an AC current can be detected with an oscilloscope or with the
RMS-reading ammeter as shown. If the reading of the meter is the same with
and without the primary or A-C winding being energised, then the A-C com-
ponent is negligible.
The circuit of Fig. 5-3 has apparently not been used to obtain data
an magnetic materials. The circuit is essentially the same as that of a simple,
walla-connected magnetic amplifier in which load reeistame is very small
and control-circuit (comparable to the D-C cirmit of F4a. 5-3) impedance is
high. The major difference between the magnetic amplifier and the test cir-
cuit is that the flux density variation in the magnetic amplifier is not sinu-
soidal, and the maximum value of B is limited to the saturation value. Also,
the maximum current corresponding to maximum H in the magnetic amplifier is
determined apprarimately by instantaneous applied voltage and load resistance,
rather than by maximum Bi? as in the test circuit of Fig. 5-3. Because of these
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where I ei RHS load component of primary current,
pl?
Is e RHS secondary current,
Irc e average secondary current.
Aus the case of an unfiltered output resistance (the first load circuit of
Fig. 54, the secondary HMS current is li.57 Ine, and the primary component
of load currant, from 5-10, is 1.21 I. Thenfore primary current may be
less than secondary current, but the &Maim of excitation in practical
designs will make it greater.
Total primary input can be calculated by summing in-phase and
quadrature volt-ampere components. The Ilya component of output volt-..
amperes is secondary voltage times the load component of primary current.
WipL a Vs IpL al Vs
(5-31)
Other real power components are the winding losses 1% and core losses W.
The magnetising component of excitation power is
22
- ) Awe W is the excitation volt-am)eres given by
ex i ex
the curves. Leakage reactance is neglected, so that the difference between
primary and secondary terminal voltages (with unity turns ratio) is due to
resistance drops in the windings. Approximate primary current is approximate
input volt amperes divided by primary voltage Vi,.
Ip wvi2 si tr. V OW,A + + Wi)2 + W:x
P P
where W = approximate total primary volt amperes,
rp
V = primary voltage.
(5-12)
A more refined method than equation (5-12) is not lustifiable in
view of the variable amturs of excitation among similar cores. However,
the results obtained with the equation tend to be a fee per cent low. A
reason for this is that both W and V. have melte*. harmonic components of
the same frequency which are errecaria added in quadrature regardless of
serteml ilhaes. An inspection of Fig. 5-5c shows that the wand harmonies of
the two components are actually in phase (of the phase +12 cos 203t), so that
the approximate calculation might be expected to give a low result.
Load Tests
During the magnetic tests which have been described, only direct
current flowed in the secondary winding of the test transformers. In order
to check these results, several tests were made on Models No. 1 and 3
loaded with a half-wave rectifier. The optimum values for the non-magnetic
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gap were found to check; that is, the same gap gives minimum primary current
during load tests and minimum excitation during the no-load or core tests for
corresponding A-C flux density and unbalanced magnetisation.
B-H curves for the load tests were found to be similar to those
for the core tests. The density 11 was applied to the vertical plates of an
oscilloscope using induced voltage from a core winding fed through an
integrating circuit. The magnetizing force H is proportional to the
difference of primary and secondary currents. One primary and one secondary
transformer lead were connected together and to one end of a small resistance
The primary and secondary circuits were then completed to the other end of
the resistance. The voltage across this resistance measures the required
current difference if winding polarities are correct.
Comparisons have also been made of calculated primary current
using equation (5-12) and measured primary current. It is found that
calculated current is lower than measured current by from four to 15 per
cent for typical operating conditions. The principal reason for this
discrepancy is that the method of combining primary current components is
only approximate.
Another aspect of unbalanced operation is the effect of primary
resistance, which tends to distort the flux wave shape. During one core
test, external primary resistance of the order of the magnetizing impedance
was added, but optimum core gaps are practically the same as with winding
resistance alone, for the same RMS winding voltages and unbalanced magneti-
zation.
Optimum Excitation and Flux Density
Part of a recent paper' is devoted to the development of criteria
for selecting an optimum flux density for transformers without unbalanced
direct current. The analytic approach used was to find the flux density
which would yield maximum volt-ampere output from a given transformer, as
primary voltage was varied After the optimum density, currents and voltages
are found for a given transformer, the wire sizes and turns can then be ad-
justed so that the required voltages are obtained. However, this procedure
is assumed in order to obtain analytic expressions for finding the optimum
density. These equations can be used to evaluate a design. An attempt has
hAwn mute to apply the sane methods to transformers with unbalanced direct
current. While it is probable that qualitatively-similar criteria exist as
for the balanced types, preliminary- work indicates that further efforts in
this direction are not warranted. Certain interesting relations are briefly
outlined.
Assuming that there is some optimum flux density, the RMS volt-
mere product of the secondary, W = I_, will vary little over a range
of A-C densities B near the optimum dengitF. It can also be assumed that
the direct component of secondary current Tre (and therefore the average un-
balanced magnetomotive force HDP) is proporTIonal to BM secondary current
I. Since the number of turns Is considered constant in an example, A-C
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+war ??????
?
nr.se gr". * ^ ? ?.?-? ? ?? ?'
TEST
CORE
INDUCTANCE
FIG. 5-2 CIRCUIT FOR MAGNETIC TESTS,
REQUIRING A LARGE INDUCTANCE
RMS
TEST
CORE
1111111
? AUXILIARY
VMS A 11,1101CAMIO11
II
1111111411111611"
BATTERY -Tr,-
1_11
INSNIff*MMNIIMMONEWO?WWwW*WW*IMNIMMNFORIMIWNIIMMI
RMS DC
FIG. 5-3 CIRCUIT FOR MAGNETIC TESTS,
USING AN AUXILIARY TRANSFORMER
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???- ? VP,IN 11.--0.
factors, the data given for magnetic materials in following sections cannot be
applied to magnetic amplifier problems. Magnetic amplifier data are often
given in terms of voltages, current, impedances and winding parameters. It is
believed that such data would be more general and readily applicable if quanti-
ties such an flux density, magnetic field strength and excitation in volt-am-
peres were used instead.
Test Results and Design Curves
The variables which have been studied experimentally to compile data
for design use are A-C incremental flux density B, average magnetic field
strength 1Ine0 length of non-magnetic op, grade of core material and thickness,
core geomeify and frequency of the power supply. Considefable data have re-
cently been made available by Battelle Memorial Institute?, However, one im-
portant variable not considered was the non-magnetic gap, and the values of un-
balanced magnetic field strength are limited to fcur oersteds.
Four cores were selected as representative of geometry, size, laei-
nation thickness and grade of material which are predominantly used in small
electronic power transformers. In using the circuit of Fig. 5-30 it would be
desirable to measure core lose directly with the wattmeter. However, the
window areas of typical small cores is not sufficient to accommodate the large
wire sites in the A-C winding that would make winding losses negligible* This
is a disadvantage which could be overcome by using a such smaller ratio of core
cross section to window area. It im less likely that this difficulty would be
encountered on much larger cores, because flux density is then limited by core
lees rather than by exciting current. With the typical small cores selected,
it is easy to measure winding resistance and to calculate winding loss, This
is subtracted from total input looses to obtain core lees, It is desirable to
use a low power factor type wattmeter for magnetic measurements. The one used
for these tests was a Weston Model 310, Form 2.
Descriptions of the four cores and graphical results are given in
Appendix R. These data are considered to be typical, but since only One
sample of each was tested, the variations which would exist among cores of the
same type and construction are not known. However, the relative characteristics
should be the same. Figures 1-1 to R-10 give excitation (volt amperes per
pound) and core loss (watts per pound) for the four cores at typical A-C flux
densities. The abscissa Hpc is defined by equation (5-1). The parameter is
the effective per cent non-magnetic gap, or the ratio mg/mi times 100. The
term my includes the appropriate weighting fector from Table 5-1, and is there-
fore Anal to the given factor plus the sum of the actual gap lengths. The
eorrection factor is particularly important for relatively small cores. Typi-
cal excitation data at one density, such as Fig. R-1, shcw the effect of the
gap. For a particular value of average magnetic field strength limo several
values of excitation can be obtained with various rape. Similarly, typical
core loss data at one density are given, such as in Fig. R-3, and the mag-
nitude of the gap also has an effect upon core loss.
Results of the tests have been studied to find if the gap which
gives minimum excitation also yields minimum core loss. If the values of
non-magnetic gap for minimum core loss and minimum excitation are 4ppreciably
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different, then both should be considered in selecting a joint. In general,
there is a fair correlation of conditions for minimum core loss and minimum
excitation current. That is, minimum core loss and excitation, at the various
values of density B and magnetisation Hix, are many obtained with the same,
or almost the same effective gap. There is better correlation between the
conditions for minimum total loss and minium excitation current. Total input
loss in these tests is the sum of core loss and primary winding loss. Since
core proportions and winding saes in the experimental transformers are typical
of those that might be used in production units, it is indicated that designing
for minimum excitation will tend to yield minimum total losses, even though
core losses are not quite at the minimum in all oases.
In accordance with the foregoing discussion, it is desirable to se-
lect a non-magnetic gap which yields minimum excitation. Therefore, the de-
sign conditions are determined by the envelopes of the curves for excitation
at each flux density. From the data for a large range of flux densities,
two design curves have been derived for each of the four cores as given in
Fig. 13-1 to 13-8. Each design curve for excitation permits the determination
of excitation (the ordinate) and non-magnetic gap from two independent quanti-
ties, flux density B (the abscissa) and magnetic field strength nix (the para-
meter). The appropriate values of effective gap are marked off on the curves.
The design curves for finding core loss also yield this quantity as a function
of density and magnetic field strength. The core loss values given are those
for the per cent gap which yields minimum excitation. The fact that this does
not always correspond to the condition for minimum core lose makes some of the
core loss design curves appear to be somewhat erraic.
Qualitatively, it can be seen from the design curves that non-mag-
natio gap Is likely to be 1 nriletatafi when I-lily dansity 4. 41terwairs4.4a
.A.usi
and field strength is high. Approximate empirical equations have been ob-
tained to relate the three variables: per cent effective gap, flux density
and magnetic field strength. For each of the four cores tested there is an
equation of the form
% gap m P HDC 4' 112 (54)
where PI Qs and R are parameters, which have the values given it -,pendix E.
Observation of the wave shapes of field strength as a function of
time and of B-H loops on an oscilloscope shows that the core performance is
491 selsammont with tho anglris prananfAvi amrlier. 4in 4niftrafmn ^4. Ito nril_
magnetic gap makes the wave shape of the excitation current more nearly
sinusoidal, and decreases the peak-to-peak value of H or current. A onm-
parison of B-H curves shows that an increase in gap decreases the slope of the
loop for small HI and also decreases the maximum H in the saturation region.
Comparisons of Data
Test results for cores No. 1, 31 and 4 have been compared with the
results recently obtained by Battelle Memorial Institute6. These comparisons
are restricted to the conditions of minimum gap in the magnetic circuits and
to low values of maenetizing force Hdc, belowfour and two oersteds for the
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NO, ...????????? ? 1.?
1
USW
60-cycle and 1400-cycle tests, respectively. In view of material variability,
the comparison of results can be considered good.
Battelle gives test results for three wound cores of 14 mil oriented
material tested at 60 cycles, comparable to No. 1. The cores represented
relatively good, average and poor oharacteristics of a number of samples.
&citation and core loss resulos Obtained for core No. I were within or close
to the range of values from the Battelle tests. Core No. 3 was compared with
a wound core of five mil, oriented material tested at hoo cycles by Battelle.
Losses of core No. 3 were found to be somewhat lower, but values for excita-
tion are close.
Data are given by Battelle for a core of four all laminations.
Comparison of excitation values with the results for core No. 4 shows ex-
cellent agreement. Win= differences are only ten per cent. Core loss
values check well up to incremental flux densitlec of 70 kilolines, but from
80 to 100 kilclines: the losses of No. 4 average about 20 per cent lower,
which is not an abnormal variation.
It may sometimes be desirable to use data for non-gapped cores to
estimate the performance of cores with gaps. Since core loss is affected
very little by small gaps, core loss data for the proper magnetisation and
density should give a reasonable value. Hoiever, the excitation values of
non-gapped cores may be up to 40 per cent higher than those of a gapped core
at the same magnetisation and A-C or incremental flux density.
Properties of a Core Joint
From the tests, it has been fcund that core loos morally increases
as unbalanced magnetisation Him increases, for a certain incremental flux
density B. With fixed B and Hie and an increasing gap, the core loss varia-
tion is at first unpredictable. Some tests show an initial decrease in loos
while others shoe An increase in lose. As the gap becomes fairly large, that
is, considerably greater than the values for minimum excitation, the core loss
tends to increase with gap length.
Increase in core loss for these conditions seem to be attributable
only to flux-fringing losses at the non-magnetic gap. For a non-gapped core,
the losses increase with increasing R. Since Hpc is an average of the meg-
netomotive force around the core, an Increase in gap length means that actual ;
magnetomotiya force in the steel must decrease, if itc is held constant.
Therefore, it might be expected that core loss would decrease with an increase
in gap, for constant B and Hric. Since this is not what is found by test for
large gaps, fringing of the flux at the gap is believed to cause the increase.
Flux entering a lamination perpendicular to the plane of the lamination can
induce such higher eddy-currents than when entering parallel to the plane of
the lamination.
Several 60-cycle tests haw been made on core No. 1 (wound-type) to
investigate joint losses. It is well known that fringing is greater from a
joint not surrounded by a winding than from a joint beneath a winding. To
find the effect of joint location on losses and excitation, one joint of core
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,
No. I was ground down so that the gap could be located entirely in one care
leg. Testa were than made with the winding structure located on the same
leg as the gap, and on the leg opposite from the gap. Gap sizes of 0.0054,
0.0108 and 0.0216 inch were tried. Excitation and losses were measured for
each of these gaps, and for the winding located on the same and opposite legs
from the aap? at several values of incremental density and unbalanced magnet-
isation.
It is found that excitation is lower by 15-20 per cent for the
0.0216 inch gap, when the gap is on the leg opposite the winding. This
indicates greater triaging when the gap is outside of the winding, or a
greater effective flux cross-sectional area, and therefore a higher mag-
netising inductance. Losses are found to be 10-20 per cent lower when the
gap is on the leg opposite from the winding. This is evidently caused by a
reduction of density in a large part of the core path outside of the winding.
The core gap increases the reluctance of the outer part of the magnetic
circuit so much that considerable flux may pass through long non-magnetic
paths. The increase in total losses which might be expected with higher
fringing loons when the gap is on the outside, is therefore overbalanced by
the reduction in density outside of the winding.
To find if core loss could be decreased by reducing the fringing
flux, a copper Shield was placed around the core gap outside of the winding.
This shield consisted to two turns of a thin copper sheet 1-1/2 inches wide,
insulated between turns and from the core. Such a shield tends to confine
the flux, because of the magnetomotive farces arising from eddy-currents
in the plans of the eonducting sheet. It was found that the shield has no
measurable effect an losses or excitation. This result might be attributed
to long leakage-flux paths completely outside the core and shield, as well
as to fringing beneath the shield, since some separation between shield
anti core is unavoidable. In addition there are some eddy-current losses
in such a shield.
Even though losses and excitation of a core are lass when the gap
is outside of the winding, it is normally better practice to place the gap
inside when large gaps are used. With the gap outside, the higher stray
fields can cause local heating in structural parts such as the case, or
can cause noise in signal circuits. However, the effects of joints on
core loss are small for the relatively small sizes of non-magnetic gap which
are found to give minimum excitation. Therefore, the gap can best be pro-
vided in the easiest manner for a particular core. A wound core with two
butt joints should have spacers in each joint to give the suitable total
gaps grinding one joint is not justifiable. Similarly, laminations may be
stacked with spacers placed where the butt joints normally occur.
Rectifier
The application of the data and analysis to the half-wave recti-
fier supply transformer will be considered. In a full-wave rectifier circuit,
the current in each half of the secondary has a direct-current component,
but the total D-C ampere turns of the two halves is zero in +him
LIAAV... Ideal nmea.
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IP*
There may be 90/68 unbalance due to dissimilar rectifier characteristics,
and there may be an unbalance due to dissymmetrical location of the two
halves of the secondary windings, but these effects are usually negligible,
particularly in small transformers. In large transformers, elimination of
any dissymmetry is very desirable. In the event that a transformer has two
different .aecondaries which are each to supply a half-wave rectifier, then
terminal connections should be made so that the net unbalance effecting the
core is the difference, rather than the sum of the two unbalancing magneto-
motive forces.
The half-wave rectifier supply transformer connection, shown in
Fig. 5.4, is almost always mentioned briefly in discussions of rectifier
circuits, but its analysis and design problems have received very little
attention. The half-wave rectifier supply is used in relatively few, but
nevertheless important applications. Among these are electronic power
supplies -- particularly for bias power, battery-charging circuits and high-
potential sources such as those in electrostatic dust precipitators.
The design or evaluation of transformers used in half-wave power is
similar to balanced types in that size depends upon rating, density in the
core and current densities in the windings. In order to obtain the smallest
size, it is necessary to use the highest flux and current densities that
heating or other limitations will permit. Winding wire sizes should be
chosen according to the root-mean-square (RMS) currents which determine losses
and therefore heating. Secondary MS current is a function of the secondary
voltage, trantformer impedances and the output circuit. Primary RMS current
is principally a function of secondary current and excitation current. With
unbalanced magnetization, the excitation current is not the same as no-load
current, as it is, approximately, in balanced transformers. The problem in
core design is to select the highest flux density in order to approach one
of the two possible limits, either core loss or excitation volt amperes.,
Both of these quantities are a function of load current, flux density and
OA "Ana +grow
.A6 .7 ?
In order to design a transformer with a core of suitable cross-
sectional area and window size and with windings of proper cross section
and turns, it is necessary to have information on core characteristics
under unbalanced conditions and to calculate winding currents and voltages
for a given load circuit. The necessarv data on magnetic materials have been
presented infoilowing chapters or in Appendix E, and following sections show
how this information can be applied to the transformer. Secondary current
may be calculated by well-known methods, but primary current presents more
of a problem. The correct turns ratio must then be used in order to obtain
specified winding voltages.
Two typical load circuits have been shown in Fig. 5-4, the resist-
ance load, and a resistance load with capacitance filter. The latter circuit
is also equivalent to the battery-charging circuit. It will be noted that
an inductance-input filter is absent. Such a filter is used in other types
of rectifiers to obtain an almost steady output current and voltage. This
effect cannot be obtained with the half-wave circuit. With a sinusoidal
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4. 11"1111r yr... I -- 4/. !
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FIG. 5-4 BASIC HALF-WAVE RECTIFIER CIRCUITS
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SEC. CURRENT
AVERAGE CURRENT' loc
TIME
(4) SECONDARY CURRENT WITH RESISTANCE LOAD
NIIIII?1110111
AVERAGE CURRENT' loc
(b)SECONDARY CURRENT WITH CAPACITANCE INPUT LOAD
TOTAL PRIMARY CURIWIT
LIN OF 1 ffika elIRRENT
PRIMARY COMPONENT
I/2A
I \NC\ if
A\
TIME
APPLIED VOLTAGE
AVG. FLUX
P? PRIMARY EXCITING
CURRENT
ORE FLUX
(c) PHASE RELATIONS OF CURRENTS, VOLTAGE AND FLUX
Fla. 5 ? 5 WAVE SHAPES IN HALF- WAVE RECTIFIER
SUPPLY TRANSFORMER
-- -
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? td0
voltage input to the primary, the secondary current for the resistance load
will be half-wave pulses of undirectional current. as Shown in Fig. 54a.
With the capacitance-input filter, the current consists of sharply-peaked
pulses every cycle, as in Fig. 5-5b. For, this filter, as far a battery
charger, cement only flows during the interval when the output voltage ex-
ceeds the voltage of the capacitance, With an inductance-input filter,
8ee171.5 Shows that the peak magnitude of current is reduced over that of
the 14kaiefame lead, and that time of conductance becomes greater than one-
half cycle. The average output ate rent is reduced, depending on the else of
the inductance. If it were possible to draw a steady, ripple-free current
with a large inductance, then the rectifier could be removed. Obviously,
this would not work. When suitable parameters are used, the two output
circuits of Fig. 544 are equivalent to more complex filter circuits, insofar
as the transformer is affected.
For the resistance load the wave-shape of secondary current is
fixed, while for the capacitance-input load, wave Shape depends upon the
product of load resistance, capacitance and frequency, and upon the series
resistance up to the load, including the winding, rectifier and leads. One
problem is to find the relation of average load currenT"to RMS currents in
the windings. When the output of the rectifier is simply a resistance as in
Fig. 5-5a, an ideal rectifier permits conduction for. exactly half of each
cycle, and the currant is in phase with the secondary voltage. The average
D-C current is found to be 0.318 times the peak current. Since the RMS value
of this wave shape is 0.500 times peak current, the ratio of secondary RMS
current to direct current is 0.500/0.318 m 1.57. Therefore the secondary
winding will heat as though it carried 1.57 times the value of average load
current. The ratio of voltages mut also be determined. Since load voltage
wave shape is similar to load current, average load voltage is 0.318 times
the peak value. The secondary RI6 voltage is 0.707 times its peak, so that
the ratio of secondary-MB to average load voltage is 0.707/0.318 ei 2.22.
With the capacitance input circuit, the peak of the current occurs
I n time Slightly before the peak of the voltage because the difference be-
tween secondary and capacitor voltages is greater when secondary 'altar is
increasing toward, rather than decreasing from the peak value. The ratio
of secondary RMS current to load direct current may be found from rather
involved analysis, or use may be made of curves given by Schade14. The
ratios are given directly as a function of circuit resistance and of load
eamiettelee divided by filter reactance - WC% or 2n times frequency times
capacitance ttmes load resistance. For reference, some values from Schade's
curves have been adapted and listed in Table 11-1 for the ratio of secondary
RMS current to load direct current.
Table 13-2 also gives the ratio of peak secondary currant to load
direct current, a quant#y useful for selecting a rectifier of proper peak
current rating,. Table 11.1 [Avon the ratio nfMB
wialaymoum4j VV.Lirage 40
average load voltage.
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Transformer uen oormer nents
Consideration of the different frequency components of currents
and voltages leads to a relatively simple method for finding the primary
current and the,magnetic characteristics of the transformer with unbalanced
magnetization. Although there is a direct-currant component in the secondary
caused by the rectifier, there can be no steady-state, DeC voltage in the
primary, because the supply is assumed to be sinusoidal, and beams an in-
duced DeC voltage would require that the core flat increase continuously in
one direction. Since there will be some resistance in the primary winding
and connected supply, any unidirectional transient current will decay to
zero. If a zero-resistance supply and electing were possible, then a primary
direct current would also be possible. However, further consideration is
limited to the practical steady-state condition.
The principle of super position is the basis for a very useful
method for analyzing linear circuits. If all impedances are linear, then
the currents and voltages may be found by solving for the eontributione re-
sulting from each voltage or current source, and then adding these.
Similarly, super position may be used for analysing separately the voltages
and currents due to each harmonic frequency of any one source, and then
adding these components for each instant of time.
In the circuit consisting of a transformer supplying a half-wave
rectifier, there are in general two nonlinear elements, the rectifier in the
secondary circuit and the impedance corresponding to the excitation required
to establish a varying flux in the care. An ideal rectifier may be con-
sidered as a voltage source instead of an impedance. As such, the rectifier
has zero impedance during forward conduction, and is equivalent to a voltage
equal and opposite to the impressed voltage .during nonebondection. Thus
when considered as a voltage source, the rectifier supplies a half-sine wave
with magnitude corresponding to the secondary voltage during the non-conducting
half cycles. This voltage function consists of an average or D-C component,
a fundamental-frequency component which is approximately half of the secondary
voltage, and of higher even-harmonic voltages. If, then, the magnetizing
impedance of theptransformer were linear, the equivalent circuit of the
transformer consists of linear impedances and two voltage sources, the
voltage applied to the prirary and the rectifier voltage. The solution for
currents and voltages can then be obtaih64 by solving the individual equiv-
alent circuits shown in Fig. 5-6. Fig. 5e6a is a circuit for fundamental-
frequency currents; 5-6b is a circuit for harmonic frequencies; and 5-6c
is a Ovec-4t for 44us component:
The component circuits Fig. 5-6 would be applicable in case the
magnetic core material were operated in regions of induction B and magnetizing
force H where the relation between these two is practically linear. The
analysis would also apply for an air-cored transformer. Primary and
secondary resistances are assumed to be relatively small, so that the harmonic
voltage in Fig. 5-6h will ha impressed almost entirely arrngA the load
resistance RL. Similarly, the D-C voltage in Fig. 5-6c will almost all
appear across the load resistance. However, the direct current which flows
in this circuit provides an unbalanced magnetizing force on the core which
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*it*. 11111.1111' S '.????? ???
11) FUNDAMENTAL - FREQUENCY CIRCUIT
(b) HARMONIC?FREQUENCIES CIRCUIT
(c) OC COMPONENT CoRCuiT
FIG. 5-6 EQUIVALENT CIRCUITS OF COMPONENT
VOLTAGES WITH LINEAR IMPEDANCES.
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.41P111 1W.^. 4 ???? ???- ? -.444
? Warr
(a) FUNDAMENTAL? FREQUENCY AND DC COMPONENTS CIRCUIT
04 HARMONIC' FREQUENCIES CIRCUIT
FIG. 5-7 EQUIVALENT CIRCUITS OF 03 MPON'ENT
VOLTAGES WITH NON?LINEAR MAGNETIZING
INDUCTANCE.
RL
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Ar...4
is not represented by a voltage drop in the circuit.
Nett, the effect of a nonlinear magnetising impedance can be con-
sidered. The principle of super position prohibits separation of the current
and voltage components associated with a nonlinear impedance. However,
currents and voltages of harmonic frequencies across the magnetising is-
pianos 11. are very small, as can be deduced &along. 5-6b. Therefore it
is possible, when winding resistances are relatively small, to analyse the
circuit as in Fig, Here the fundamental frequency and D-C components
are together in one circuit. The equivalent rectifier voltage in Fig. 5-7a
consists of ftuidiusental-frequency and D-C components only.
These equivalent circuits are an aid in showing how the electrical
quantities affect the operation of the *ore. If the applied voltage is
nearly sinusoidal then the core flue ittU also be nearly sinusoidal. The
other effect upon the core is that of the direct-current component in the
secondary which is determined by the magnitude of the D-C voltage component
and the secondary circuit resistance. The magnitude of the DC magnetising
force resulting from this current depends upon the nuiber of secondary turns
and upon the core geometry, according to equation (5-1).
Primary Orrent
The significance of the equivalent-circuit analysis is that all
alternating components of secondary ampere turns are equal to the load
component of primary ampere turns. The sun of this load component and the
excitation component is the primary current. The A-C excitation current
funotion of time plus the secondary direct-current component determines the
total seignetomotive force 'Mich is related to the mare flux function by the
magnetisation cum of the materiel. The primary component of load current
for a half-wave rectifier with a resistance load is shown in Fig. 5-5o as a
half eine-wave function without an *image component. It is next necessary
to establish the excitation component in terms of phase and qualitative form.
SAM@ the peaks of the flux function lag the peaks of the applied voltage by
one quarter cycle by definition, the peaky of the excitation component must
also lag the voltage peaks by one quarter cycle or po electrical degrees.
It must be found which peak of the excitation current is sharper
because of the saturation effect. TO do this, the primary load component
of lig. 54c can be considered for the moment as two currants, one exactly
like the secondary current, including D-C component, plus a constant negative
part equal to the average of the other. If this second negative part were
absent, then average core flux would be Iwo, because the et= of the first
part and secondary current would provide no unbalanced magnetmotive force.
The fact that the hypothetical second part is negative indicates that
saturation tends to oocur during the negative half cycles of the flux and
exoltatim current, as shown in Fig. 54c. we reasoning establishes the
qualitative form of excitation current and the digetnemoot of the average
flue as vim in the figure. Next, the sum of the lead and excitation
components gives the time function of total primary current. For very small
flux densities the primary current becomes very similar to the given load
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component.
It should be anpreciated that an ideal core material having definite
permeability cannot be assumed in an analysis such as this, because the
presence of the unbalance in the secondary would yield an infinite flux.
Therefore, an excitation component cannot be eliminated in the consideration
of an ideal material. However excitation current could be made small compared
to the primary load component of current if the A-C density wore ao smell
that the cyclic variation in magnetic field strength (and corresponding
ampere turns) were relatively small compared to load-current ampere turns.
These conditions require a magnetic material with less than infinite per-
meability.
The qualitative shape of primary current has now been established,
and next it is necessary to find methods for calculating the RMS magnitude
which determines the sise of wire needed for the winding. One method for
finding primary current is by graphical addition of the components as in
Fig. $-5c, followed by computation of the RMS value from the resultant time
function, that is, by squaring the function, taking the time average and then
the square root of the average. However, this procedure would be very time
consuming for a design computation. A better method is based upon elementary
A-C circuit algebra. In general, both excitation and load components of
primary current are non-sinusoidal. If the magMbude and phase of all
frequency parts of each component were known, thin the value of primary
current could be readily determined. The resultant of each frequency might
be found by combining the parts of the same frequency as phasors. Finally,
the total current is determined by adding in quadrature the contributions
at all different frequencies. These calculations can be made using and
obtaining RMS values of current.
The excitation and load components of primary current have funda-
mental-frequency components which are almost in quadrature, or one quarter
cycle out of phase. If in addition the two components were sinusoidal,
or if only one were sinusoidal and the other non-sinusoidal, or if the two
components contained different higher harmonics, or if the corresponding
harmonics in the components were in time quadrature, then the RMS values of
the two components could be combined in quadrature to obtain accurately the
total RMS primary current. Although none of these conditions is satisfied
in general, the principles suggest combination of the two components in
emnrivaa+Atvoa efh+.10411 ATI AnnrAvimwElevin l?f priMary current, evnti 4,
this is a suitable procedure.
r. y
For a two-winding transformer having a turns ratio of unity, the
HMS load component of primary current is defined as the alternating parts
of the secondary current function, which is simply the secondary current with
the D-C component removed. Since the 115 value of secondary current is
wranisualv the quadrature stim of D-C And All A-n nrap"nian+-a; it fnilnsin ThAt
2- I 2
PL s DC
(5-10)
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IF-. we- ?
where I a RMS load component of primary current,
pL
Is HMS secondary current,
I average secondary current.
DC
For the case of an unfiltered output resistance (the first load circuit of
Fig. 5-4, the secondary MS current is 1.57 Inn, and the primary component
of load current, from 5-10, is 1.21 In,. TheNfore primary current may be
lees than secondary current, but the Minion of excitation in practical
designs will maks it greater.
Total primary input can be calculated by summing in-phase and
quadrature volt-ampere components. The input component of output volt-
amperes is secondary voltage times the load component of primary current.
Vr-mir 2
Wa * Vs 110.12V - I
s a DC
(5-11)
Other real paver components are the winding losses and core losses
The magnetising component of excitation power is "
w . ' where Vex is the excitation volt-amperes given by
the curves. Leakage reactance is neglected, so that the difference between
primary and secondary terminal voltages (with unity turns ratio) is due to
resistance drops in the windings. Approximate primary current is approximate
input volt amperes divided by primary voltage 'WI,.
a va ? tr.
P P
where W In approximate total primary volt amperes,
rp
VP at primary voltage.
(5-12)
A more refined method than equation (5-1 is not justifiable in
view of the variable nature of excitation among similar cores. However,
the results obtained with the equation tend to be a few per cent low. A
reason for this is that both 11..1. and W.x have higher harmonic components of
the same frequency which Are AVV00+4..T7 added in quadrature regardless of
HUAI 'phase. An inspection of Fig. 5-5c shows that the second harmonics of
the two components are actually in phase (of the phase +12 cos 2&)t), so that
the approximate calculation might be expected to give a low result.
Load Tests
During the magnetic tests which have been described, only A4.4.
44.1.10UU
current flowed in the secondary winding of the test transformers. In order
to check these results, several tests were made on )Was No. 1 and 3
loaded with a half-wave rectifier. The optimum values for the non-magnetic
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gap were found to check; that is, the same gap gives minimum primary current
during load tests and minimum excitation during the no-load or core tests for
corresponding A-C flux density and unbalanced magnetisation.
BeH curves for the load tests were found to be similar to those
for the core tests. The density B was applied to the vertical plates of an
oscilloscope using induced voltage from a core winding fed through an
integrating circuit. The magnetising force H is proportional to the
difference of primary and secondary currents. One primary and one secondary
transformer lead were connected together and to one and of a small resistance.
The primary and secondary circuits were then completed to the other and of
the resistance. The voltage across this resistance measures the required
current difference if winding polarities are correct.
Comparisons have also been made of calculated primary current
using equation (5-12) and measured primary current. It is found that
calculated current is lower than measured current by from four to 15 per
cent for typical operating conditions. The principal reason for this
discrepancy is that the method of combining primary current components is
only approximate.
Another aspect of unbalanced operation is the effect of primary
resistance, which tends to distort the flux wave shape. During one core
test, external primary resistance of the order of the magnetising impedance
was added, but optimum core gaps are practically the same as with winding
reeistance alone, for the same RMS winding voltages and unbalanced magneti-
zation.
SAltij,TELExcitation and Flux Density
O.&
Part of a recent paper16 is devoted to the development of criteria
for selecting an optimum flux density for transformers without unbalanced
direct current. The analytic approach used was to find the flux density
which would yield maximum volt-ampere output from a given transformer, as
primary voltage was varied After the optimum density, currents and voltages
are found for a given transformer, the wire sizes and turns can than be ad-
justed so that the required voltages are obtained. However, this procedure
is assumed in order to obtain analytic expressions for finding the optimum
density. These equations can be used to evaluate a design. An attempt has
been made to apply the same methods to transformers with unbalanced direct
current. While it is probable that qualitatively-similar criteria exist as
for the balanced types, preliminary work indicates that further efforts in
this direction are not warranted. Certain interesting relations are briefly
outlined.
Atsumine that there is some optimum flux density, the RMS volt-
were product of the secondary, Wr - Vs Is, will vary little over a range
of A-C densities B neer the optimum density. It can also be assumed that
the direct component of secondary current Inr (and therefore the average un-
balanced magnetomotive force Hy) is proportIonal to .13M secondary current
Is. Since the number of turns /s considered constant in an example, A-C
ARHOUg
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w...wwww? ? W
?
??? w
flux density is proportional to NHS voltage Vs. Therefore, if Wr w vs is
is constant over a range of A-C densities, Ias Inn and Hnn are
all inversely proportional to AC density B.' Thrdesign'Eurves for primary
excitation volt-aaperesW. versus density 8 with the parameter Hnn have been
studied to find how V 'Vies with Bt subject to the condition Olt B is
inversely proportionarto ? Such functions are readily derived point by
point and are found to be less steep than the given curves for itm.
versus B at a constant Hne. Although not a precise linear relation, '^
excitation volt-amperes rex are roughly proportional to AC density B.
It is possible to derive equations for the uaalLwArd transformer
which are similar to equations (7) and (10) of the reference'. However m
the above discussion indicates that the exponent n4 defined by Wary ? B"
is roughly equal unity. In view of this, the reference equation117) Ind
(10 show that the optimum is roughly independent of the selected AC
density B. Therefore, in the absence of a more concrete guide, it is
recommended that designs be made so that excitation volt-amperes are in the
range of 110 to 80 per cent of the secondary HNS volt-ampere product.
Simple designs indicate that such a balance between excitation
and load volt-amperes for a transformer with unbalanced direct current is
obtained when the selected A-C fluxIl.iensity is about ten per cent lower
than the density which would be used for a unit without the unbalance. Since
desirable values for A-C density and per cent excitation are functions of
unbalanced magnetization Hpc as defined by equation (5-1), some sta4y has been
given to the effects of size and proportions on H. Total winding ampere
turns are proportional to window area times currefit density times winding
space factor. This indicates that, for constant currpnt density and space
factor, Hnn is proportional to window area divided by length of the magnetic
circuit. 'In a given size and rating, Hpc can be reduced somewhat by in-
creasing core cross section and reducing window area, a change which results
in a higher proportion of core volume to winding volume.
Next, consider the effect of increasing size and rating. holding
all geometric proportions fixed. The fact the Hnn is proportional to an
area (window area) divided by a length means tharHne would increase
linearly with size if current density and space factor are constant. However
it can be shown that to hold winding losses per unit of winding exposed
surface area constant because of temperature-rise limitations, current
density should be reduced, and changed inversely as the square root of
linear size. The combined effect including geometric factors and current
density indicates that HI, is directly proportional to square root of
Unser size. Therefore Sbalanced magnetomotive force will tend to be
higher in largei transformers.
gtation and Turns Ratio
In transformers carrying sinusoidal currents, corrections for
voltage drops can be made using the HMS current and resistance for each
winding (and the leakage-reactance, if appreciable). When sem-Mary current
or voltage Nave shapes differ appreciably from sinusoidal forms, the usual
methods will yield voltage ratios which are excessively in error. This
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? ???? ?????? Ir.-. I -? -? ? ? ? -?-?
prolasehes been met in tests on model transformers with unbalanced direct
current, which usually have complex current wave Shapes.
To find a sufficiently accurate relation between primary and
secondary voltages, an analysis has been made which is based upon an
assumed sinusoidal applied primary voltage. If the secondary current is
not sinusoidal, secondary voltage must likewise be nonsinusoidal unless the
transformer has sero equivalent series impedance. Secondary RMS voltage may
be defined as an exact function of its several components.
Tee
Vsf2 Vih2 4. VeDc2 RMS volts
(543)
where V ? RMS fundamental volts,
sf
V a HMS harmonic frequency volts,
sh
Vse voltage due to direct current.
The term Via, is composed of the second and Ligher harmonics, all of which
add in quaaPature to yield V.
Next, equations may be written for the secondary voltage components
in terms of the respective current components and impedances. These are ob-
tains(' by treating each of the three components of Vs independently.
V
v - I R
of n sf
V ? I R
sh sh
Rop
(5-10
(5-15)
(5-10
Idlers VP 0 primary voltage
n 0 turns ratio
1
R 0 transformer equivalent series resistance referred
to the secondary, ohms
R ? secondary resistance, !ohms.
To include the effects of leakage reactance, tot41 impedance 7, could be
substituted in equations (5-14) and (5-15) for R , but it would be necessary
to consider the terms of the equations as phasors rather than as magnitudes.
The calculation of secondary IS load voltage V from equation* (5-13) to
(5-16) can be considered as surcefsive operatio& on the no-load secondary
voltage 5/n. First a term 1.4. R is subtracted algebraically, then two
other te s are added successfiely in quadrature. However, in transformers
the voltage drop terms are always small compared to V /i. Only the term
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I ? I
subtracted directly, according to (5-14) =dm an appreciable change in
Vtiethe addition of the quadrature terns can be neglected. It follows
t is closely equal to Vete, and that the difference between V and Vis
&spina only upon the voltagelPatrop of the fundamental-frequency t
of secondary current through the transform* equivalent resistance R.
The next wales is finding the fundamental-frequency current
magnitude from the RKS current value. This depends upon the type of load
circuit. Tar the case of a half-wave rectifier and meastance Ladd without
a capacitance filter, the currant is a half-sine leave, and the RNS valve
of the fundamental component is 70.7 per cent of the total INS secondary
current. Another important ratio for this case is that of the secondary
RNS current to its D6C component, which is 1.57. Regulation is
Bag 14.11
, R 0.707 IsR
Lvu s --v.? 100 ? 100
s
0.707 Is2 RI
in trio
100 . 100
(5.17)
where We is winding losses, watts,
W im secondary RIC volts times RMS amperes.
A capacitance filter is commoay used across the resistance load
of a half-wave rectifier. This tends to increase the ratio of secondary
RMS current to D-C component above 1.571 a typical value is 2.0. /he
current wave shape with a filter becomes more peaked and current flows less
than half of the entire period. Therefore the ratio of secondary NIS
fundamental current to total INS current will be less than 0.707, about
0.5 for the typical case, a value checked try tests of a model transformer.
The foregoing discussion shows that the previous equation for per
cent regulation should be multiplied by some factor less than one: The tiro
esamples given, without and with a filter, Show ham an estimate can be made.
It is observed that EMS fundamental current is more dependent on the D-C
component than on the total secondary current. Therefore it is suggested
that the following factor be used in (547) in place of the quamtikr 0.707.
Correction Factor gm
If 1.1 Inc LI
alelirlikrINEM
A's' "DC
(5-18)
The ratio I A is determined from Table 5-2 as a function of the circuit
or DC
parameters.
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*0 ? ? ?????
Procedure for a Transformer with Unbalanced tisation
The first step in the design of a transformer with unbalanced
direct current is determining the equivalent secondary volt-ampere rating.
Secondary RNS current is the D-C load current required, times the proper
ratio of Table 134. If series resistance, load resistance, and filter
capacitance are not known, a ratio of 2.0 can be considered typical. Similar-
ly secondary RMS voltage is found as the D-C load voltage tines the appropriate
ratio of Table 13-3, or it may be specifilad for the transformer designer. If
circuit conditions are unknown, a value of 1.1 is typical. Then the product
of RP S current and RNS voltage is defined as equivalent secondary rating.
If secondaries with balanced loads are present, the ratings of these are
to be added.
The design procedure is then carried out similarly to that for
the balanced transformer except that the flux density from Table 11-2
should be decreased up to about 10 or 15 per cent depending upon whether there
are additional secondaries supplying balanced loads. The maxima reduction
is used when only one secondary with unbalanced direct current is, present,
but higher values of flux density are permissible when secondaries with
balanced loads are present. The care loss and excitation are found in order
to ascertain whether the flux density is reasonable. This requires the use
of the design curves, Fig. 134 through 40-8. The appropriate unbalanced
magnetising force Hnm, for use with the design curves is calculated in the
following manner. The mean length of the magnetic circuit mi is
mi Is a 4 inches, (2-7)
where a so constant from Fig. 11-3 or 11.5,
is characteristic linear dimension from nomograph,
Fig. 11.7
The approximate secondary turns N5, is calculated from
K16 Vs
turns
f F B 4g
where K 81 constant from Fig. 11.3, 114, or
A
V it secondary RNS voltage in volts,
f ix frequency in cycles per second,
Fi P core space factor,
B = flux density in kilolines per square inch.
The approxitate unbalancedmagnetizing force Rix is then
(2.3Is)
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???????????111,0 .1/
? ? ...T., at..., a
.05 Ns
HiC? average oereteds,
4 Mi
(5-19)
where n mean length of magnetic circuit in inches,
Ix a average load current in amperes.
(lote: the cAstant, .1195 .10112.54, so that mi can be inches).
Then the core loss, excitation, and nonmagnetic gap are obtained from the
design curves (Fig. 13-1 to 13.8).
The next modification of the design procedure is in the calcula-
tion of the primary current. The primary oolip-wwit of load volt-amperes
4 is calculated from
Wiz "1 v8 /I5 - 1=2 volt amperes, (5-13.)
where Is gs secondary APIS current in amperes,
I es average load current in amperes.
DC
The
2 primary current I is then obtained from (5-12), neglecting
W., in comparison with Waw2, andrincluding the ratings of additional
ettcondaries Wr2, mbore AINPlicable?
In ? 1
tI tre y N 4' T. Vir2+ + W + W )- + W
c ex amperes (5-20)
P
The value obtained for Iv, should then be increased 10 per cent for a trans-
former with one seconder, which supplies imbalanced direct current. If
secondaries with balanced loads are present, a smaller per cent increase
Should be used, proportional to the fraction of the unbalanced winding
rating to the total rating of an secondaries.
The correction of the turns to account for regulation follows the
nermal procedure with the exception that the correction for regulation is
made in accordance with equation (5-17). Therefore the expressions for
winLi', g turns far the primary and seoondary are:
IT .707 W
P P V (5-21)
.707 It
N r (1 + .2"r: ) turns,
where NA calculated turns per volt.
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Where a capacitance filter is used, the factor 0.707 is replaced by the
correction factor of (5-18). The design is then completed in the usual
manner, including design checks. When the voltage ratio is clucked, the
following expression should be used,
VI) a n + 1.1 I? (R. 4. Rpii2)] volts.
(5-22)
The design summary and calculation of temperature rise are the same as for
the transformer with balanced loads.
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'
? ?????
VI. CURRENT-LIMINO TRANSFORMERS
Some transformer loads have a vezy low initial resistance when
power is applied, but a higher resistance after the load has heated. For
such loads it is often necessary to limit initial current in some manner.
One way of accomplishing this is to apply a reduced initial voltage, but
the most common method is to design the traneforser such that it has a
high equivalent series or leakage reactance. such transformers are prin-
cipally used for tube filaments although there are other possible applications.
Among these might be a curreint-ilmiting rectifier supply to limit current
when charging batteries, or a current limiting supply to restrict damage in
a circuit in the event of a abort circuit. Since the main application of
current-limiting transformers is for a filament supply, these will be dis-
cussed specifically, with the understanding that the same principles would
apply to a current-limiting rectifier supply.
!nuirements and Construction
Materials used for electronic tube filaments have a high positive-
resistance temperature coefficient. The cold-filament resistance may be
low enough to result in an initial current which is many times rated current.
In tubes with small filaments having short thermal time constants and relative-
ly low rated currents, the initial current has little if any detrimental
effect. However, the current for large filaments must be limited to prevent
damage to the filament or cathode resulting from thermal changes and mag-
netic forces. The resistance of a cold tungsten filament is aoproximately
nne-tenth of its resistance when hot. Usually the electronic-equipment
engineer will specify complete requirements for the transformer engineer.
However the latter should be aware of the possible current-limiting require-
ment whenever the rated filament current is greater than about twenty amperes.
A typical requirement is that the cold-filament starting current be limited
to 150 or 200 per cent of the rated current.
A current limiting transformer provides current-limiting action
as the result of high-leakage reactance. It is feasible to mks a design
using air-spaced coils to provide the leakage path, but this is likely to
present problems to the electronic equipment manufacturer. An air-spaced,
high leakage-reactance design may be unsatisfactory if the leakage flux
path is greatly affected by the location of other components of ferro-
magnetic materials in the vicinity of the transformer. Not only will the
stray field of magnetic flux be affected by components located near the
transformer, but this stray field may interfere with the operation of other
equipment as well.
A much more satisfactory design can be made by providing a low-
reluctance, leakage flux path in the magnetic circuit which will confine
the flux to a rather definite path. The use of a magnetic shunt as shown
in Fig. 6-1 is 'the usual lamer of providing the leakage-flux path. With
no secondary load, the magnetic flux path of least reluctance is through
the secondary v.4..nding, so that very little of the flux passes through the
shunts, thus providing nearly the same open circuit secondary voltage as
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??????????????
MAGNETIC
SHUNTS
i????? ? ??? ??????? ??.-???
MAGNETIC
SHUNT
CI) HIGH ? LEAKAGE REACTANCE b) HIGH LEAKAGE REACT'ANCE
SIMPLE-TYPE TRANSFORMER
*HELL -TYPE TRANGrORMER
? WO
FIG. 6 -1 EXAMPLES OF HIGH- LEAKAGE REACTANCE TRANSFORMERS.
-6O
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??? ^^- ? ? ???? ....Roc- ? V
? ? ?
? ??????? -r'-- ? . --
without the shunts. As load an the secondary winding is increased, the
secondary ampere turns oppose the flux induced by the primary winding, and
part of the flux induced by the primary follows the magnetic shunt path.
Consequently, the secondary voltage will drop since secondary voltage is
proporticreal to flux linking the secondary winding.
The actual physical design is little different from conventional
transferrers except for the Shunt structures The secondary coil for a low
voltage output is frequently wound with strip copper. The strip copper,
when used, may be the toll width of the secondary coil leas necessary margins.
Strip copper is usually used in thicknesses of from .010 to .032 inches. The
total height of the copper in each turn is built up to the desired thickness
with enough strips to carry the rated current. Usually no allowance is made
in the current rating of either primary or secondary condtctor cross section
for the current at cold-filament starting, because this is only an in-
frequent transient condition, and the thermal capacity of the transformer will
take care of this current for the short-time starting period.
Teets and inspection for a high-reactance filament transformer
Include measurement of winding resistances high potential test, open-circuit
ratio test, measurement of insulation resistance, and inspection of
mechanical details. In addition, two other tests must be made. A load test
must be made to assure that the transformer will supply rated voltage at
rated current. One commonly-used specification requires that the transformer
supply rated current at rated voltage with a tolerance on the rated voltage
of plus or minus three per cent. The other is a load test using a load equal
the cold filament starting resistance %4:0 check the cold-filament initial
current. A short-circuit test is frequently substituted since the cold-
filament initial current and the short-circuit current are nearly the same.
To design a current-limiting transformer, the desired leakage
reactancs must be determined from the &wit' conditions. Once the lgtelenne
reactance is known, the leakage flux may be deduced. Hence, for apy given
flux density in the primary portion of the core, the flux density in the
secondary portion of the core may be calculated. By using this secondfry
flux density together with the rated secondary output, the design procedure
becomes similar to that for an ordinary filament transformer. Firstex-
pressions will be derived for the leakage reactance and no-load voltage.
With the aid of these expressions, the ratio of flux density in the secondary
portion to that in the primary portion can be readily obtained.
Leakae Reactance and No-load Voltad
The quantities that are usually specified for the current-limiting
transformer are:
V m primary voltage,
Vs m rated secondary voltage,
Is = rated secondary current,
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?11
fr
???
p m ratio of short-circuit current to rated secondary current.
When the transformer is delivering rated current at rated secondary voltage
to a resistive load, the relationship among quantities shown in the equiva-
lent circuit of Fig. 6-2 is:
1. as Vr?Or + R)2 + (1 1)2 volts, (6-1)
V
n a 8 a
where n NP /0 m ratio of primary turns to secondary turns,
?
2 + Rs Is equivalent winding resistance referred
to the secondary,
X m leakage reactance referred to the secondary.
When the load resistance is very small, such as that presented
by the cold resistance of vacuum-tube filaments, the secondary current is
very nearly the short-circuit current of the transformer. For this condition,
the flux density in the shunt is much higher than during the rated load
condition. The reluctance of the shunt path is increased at the higher flux
density, and the leakage reactance is reduced. If reluctance of the leakage
flux path were due entirely to the non-magnetic portions, or if steel
permeability were constant, there would be no such change in reactance. In
order to account for this variation in leakage reactance, the following ratio
is introduced.
reactance at short circuit
q graiara-FiginaFgat
(6-2)
A typical value of q is .8 or .9. Higher values are representative when
shunt flux density during short circuit is not very high compared to
saturation density for the material.
The relationship of voltages during short circuit, similar to
equation (6-1), is
Vpjn m PIs
R2 4. (q X)2
volts.
Eliminating leakage reactance X, or primary voltage V from (6-1)
and (6-3) gives the following equations.
Vp/n pq
2
4. Is -2
n (1-1 2
/4)
Vs(Vs + 2Is R)
V
2 2
p q -1
(6-3)
volts, (6-14)
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???????????11110 "Nilo
rum. ?vir-na
EQUIVALENT CIRCUIT OF A TRANSFORMER WITH
QUANTITIES REFERRED TO THE SECONDARY SIDE.
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al????????????pro, .gpo... ? . wow. ??????? VW, ? V, r
X
?nor -mrliS %gr.^.
? Neglecting R, anproximate expressions for the no-load voltage and
leakage reactance are:
/n
P q
V
I VP2 c12 - 1
volts,
Ohms.
(6-5)
(6-10
(6.7)
The relationship between the flux density in the portion of the
core which is surrounded iv the primary winding and the primary voltage is
s 4.44 f BP Ai Fi Np 10-5 volts,
? (6-8)
where N m number of primary turns,
B flux density in portion of core surrounded by the
primary winding in kilolines per square inch,
m induced primary voltage,
Ai m core croes-teetional area in square inches,
F m core space factor,
f frequency in cycles per second.
relationship for the secondary is
4.44 f Bs Ai Fi I% 104 volts,
where N = number of secondary turns,
= flux density in portion of core surrounded by the
.11.1101.410
4
II ,
1
1
I
Secondary winding in kilolines per square inch,
= secondary voltage induced as a result of flux Bs.
The ratio 0- equation (6-8) to (6-9) is
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? ....P.o.e... V.
4
6
I
B E N
a ep
rrT
P P
Since n Vie, equation (6-10) becomes
Be
nan
rwr
?
(6-10)
(64.3.)
Referring to Fig. 6-2, it is apparent that B. and 1161 may be approximated
by and V if the winding resistances are fieglectrid. Then
Bs
? Vs
B 1,7 kilolines per square inch,
(6-12)
where Vpifn is given by equation (6-6). Equation (6-12) indicates that
for short-circuit conditions Bs 0, and for open-circuit conditions
Bs Bp' approximations for quantities in the actual transformer.
ta:ftelltAm
Another design problem is the calculation of the proper gap in
the magnetic shunt path. The actual gap as determined from trial and
test is usually different than that calculated. This is partly attributed
to fringing effects of the flux path around the gap. An examination of
some core and shunt structures reveals that much of the apparent error in
"" length is the result of imperfections in lamination dimensions and
stacking workmanship. The normal dimensional tolerances and stacking
irregularities add up to more than the allowable gap tolerance. Success
in efforts to improve the accuracy of gap calculations depends on the
precision maintained in the manufacturing. The use of trials for determin-
ing the final gap dimension is predominant in manufacturing. The improvement
of manufacturing mathada neemanstry to al 4isti turEA +.1?401 At Mir be imnrActtnable
The actual shunt air gap is fixed, but an effective air gap can
be defined as a length depending upon the total reluctance of the shunt
flux path. Leakage reactance is inversely proportional to such an effective
gap. Since the ratio of leakage reactance at short circuit to leakage
reactance during load is defined as q,
mg
(6-13)
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II
1
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???????? "inn "Ir.,. I ????? ? ??
1
where m a effective gap at rated load, inches,
I.
1
m
BC 0 effective gap at Short circuit, inches.
g
The effective gap length may be calculated using the principle that the
total magnetomotive force Around a closed path is sero. During abort
circuit, it is assumed that the total magnetomotive force around the
secondary appears across the shunt flux path, and therefore across the
effective gap.
.4 R Ns (p VT Is) a Hg so (2?54 Mig so)
where H ? magnetic field intensity in the gap during
Hg ec short circultpin oersteds.
?
(64.14)
Since for a non-magnetic material, magnetic field intensity equals flux
density, Bg sc may be substituted for Hg sc. Changing unite for density,
and solving for effective short-circuit gap, gives
1.52N p1
m, el 1 inches (645)
geeg sc
where Bg sc is the flux density in the gap during abort circuit
in kilolines per square inch.
load should be closer than the
Combining equations (643) and
4,52 p q NS IS
103 Bg sc
The effective gap during rated
above to the actual gap length.
I,
ko..14),
(6-16)
For a shell-type core, where two shunts are required; each garint
should have the gap length given by Eq. (6-16). The flux density in the
gap Bg Sc' corresponds to the short-circuit condition and may be calculated
by assuming that all the primary flux is carried by the shunt during this
condition. A correction factor to account for fringing of the flmt does
not appear to be warranted, to judge from test results and calculations.
A reactance to give the correct load and short-circuit condition can usually
be achieved by altering the thickness of the shunt through adding or sub-
tracting a few of the shunt laminations, or by changing the length of the
gap.
Design Procedure
The design of a current-limiting transformer follows the design
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? 'OP' OM. _4v? a T ? ?
S.
procedure for an ordinary filament transformer after the addition of several
important modifications. These modifications have been introduced into the
design procedure Walking use of the results whiGh uere derived in the
previous two sections.
the transformer rating should be based on the secondary full load
output, using the semmehnlrimatege and current during full load.
The minding dissipation is found in the normal manner, although
the exposedwilmitng surface area, 8., is increased slight4 (over the one
winding which would fill the same dadaw without the Shunt) because of
separation of primary and secondary. Nevertheless the surface area of a
winding which fills the window can be used consietent4 in the calculations,
and this practice is justifiable from thermal considerations.
Due to the presence of the shunt and the need for additional
winding margins adjacent to the shunt, the window area available for windings
is greatly reduced. The place factor for a transformer using a Aunt, F,1
may be estimated from the space factor for a unit without a shunt. The "
winding space factor for a current-limiting transformer is
(6-17)
F.; s .1570 ,
where Fc is the copper space factor from 14. (2-20).
The factor .6 is used for a scrapless lamination, and the most suitable
value is nearer to .5 for units less than 50 volt.AmmAimea, For a 1W:station
with larger windows than the scrapless type, the factor is usually somewhat
greater than .6.
The flax donsitir in the Felon of the core surrounded by the
primly minding is selected using Mks 11-2 as a guide. The secondary
flux density when the transformer is carrying full load is then approximately
Vs
B Bp vp-74- kilolines per square inch, (6-12)
pqlfe
?11thfre. V in eig
P' 2 2
volts.
p 'I
The scale manes should be calculated
KO
F ir
?
c c
and rc---
inla
p ce of,
(64)
The characteristic linear dimension is then found using the scale values
and the secondary flux density B.0 since the transformer rating is based
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,
a. ? ? ? i? e ? ? ?
, . .
ilea! *a.
on the secondary full-load output. In checking the primary and secondary
flux densities to determine that allowable core loss and excitation are not
exceeded, half of the core weight should be used with each flux density.
The calculations involving the core dimensions follow the normal
procedure. However, some changes are required in the winding calculations.
Calculation of conductor weight should be omitted because the shunts occupy
only a part of the window area and equation (2-30) is no longer valid. The
primary current should not be based on Eq. (2-32), since the leakage re-
actance cannot be neglected. Instead the expression for calculating the
primary current is:
IP V
I ?
r + Vre + Wd2 + (Vex + 182 42 amperes f6-18)
ill II I I I I I II I I I I I I I MI I I I I I I NI I I I I I I I I I I I I I I I LI I MI I I I I II I I Ili
where W rated secondary output in volt-amperes,
W ? winding looses in watts,
se core losses in watts (neglecting Shunt losses),
Wexu excitation volt-amperes.
The leakage reactance volt-amperes, from Eq. (6-7) are:
VI
Is 2X so
- 1
The primary and secondary wire sizes may then be readily found.
(6-19)
The determination of winding turns involves a correction for
transformer impedance in two steps. Nominal values for turns per volt
are obtained for both primary and secondary. The fact that these are
different indicates the correction for leakage reactance ?. Then a correction
for winding resistance drops are made in the usual ways that is by adding
turns to the secondary and subtracting turns from the primary. The nominal
primary and secondary turns per volt are given by the following:
and
105
1:12- 14.114 f fi Bp
105
r- 711717171r.
? (6.20)
(6-21)
where B is the chosen primary flux density, and Bs is the calculated
secondary flux density according to Eq. (6-12).
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In determining the winding layout, space must be provided for the
mmgnetic shunt or shuntsidepending upon the core type. Because the flux
in the shunt is at a maximum only during short circuit, the shunt cross-
sectional area need not be as high as that of the reminder of the core. It
is suggested that shunt area be at least two-thirds that of the core, and
more, if necessary, such that shunt flux density during short circuit is
over higher than 130 kilolimis per square inch, KA shunt densities are
to be avoided in cases where the ratio p is below about 1.3, so that changes
in leakage reactance can be kept amall.
The proper cross-sectional area of shunt may be obtained by varying
Aunt thickness in the direction parallel to the coil axes or to a lesser
extent, by varying length in the direction through the window. Normally the
latter dimension will be the same as the core stack. For a simple-type core,
shad thickness is about (2/3)L or more.
Subtracting the thickness of the shunt from the window length gives
the apace remaining for windings and margins. Usually the shunt will not be
exactly in the .center of the window. By moving it off center, the winding
space may be used more efficiently. With these considerations taken into
account, the winding layout follows the pattern of the general design method.
After the winding layout is completed, the actual winding resistances
should be calculated. First calculate the mean length of turn of each winding
(length of the inside turn of the winding x times the build-up of the
winding). Resistance equals resistance per unit length (corrected to
operating temperature from Fig. 11.9times mean length of turn times number
of turns. Once the winding resistances are determined, the design should be
checked by calculating the primary voltage in order to ascertain that the
turns ratio is correct. Rewriting Eq. (6-1) in a slightly different manner
gives an expression for the primary voltage,
volts. (6-22)
The turns ratio should be adjusted if the calculated primary voltage differs
appreciably from the specified voltage. The winding resistances need not be
re-calculated if the turns are altered, since the change in resistance will
be small.
As shown in Fig. 6-1, the gap is ordinarily divided into two parts,
one on eadh side of the shunt, so that fringing is minimised and it is
easier to force the shunt into position. The total non-magnetic gap
associated with a shunt used in a simple-type transformer, or with each
shunt used in a shell-type transformer, is
h.52 p q Ns Is
mg= nowerimo. A .2
Bg sc 10'
inttha
(6..16)
where B is the flux density in the gap during short circuit--
g-Rf ? h
in bilnlinon per savall v. inc...
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VII. CURRENT-LIMITING TRANSFORMERS WITH UNBALANCED MAGNETIZATION
This type of transformer has: (1) a high-leakage reactance whirl is
usually obtained by using a magnetic shunt, and (2) an unbalanced magneti-
zation component of the core caused by direct current flowing in the
secondary winding. Both of these characteristics have been studied separately.
The design method for a current-limiting transformer with unbalanced magneti-
sation is developed by combining the two procedures and by accounting for
certain new problems.
Deirign Procedure
The design procedure for a current-limiting transformer with un-
balanced magnetisation follows the basic procedure as presented for a
filament transformers with few modifications. Only the deviations required
to adapt the procedure to a current-limiting transformer with unbalanced
magnetisation are presented here.
An equivalent rating for the transformer is based on RMS secondary
voltage and current. These are related to load voltage and current, filter
capacitance, circuit resistance and frequency in the same manner as for
transformers with only unbalanced magnetization. For a resistive load, the
secondary RMS current is obtained by multiplying the average load current
by 1.57; whereas for a capacitance-filtered load, a ratio from Table 13-1
should be used. An inductance-input filter is seldom used with a half-wave
rectifier. When no filter is used, the secondary PAS voltage equals 2.22
times the sum of the average load voltage plus rectifier forward voltage drop
and any other circuit resistance voltage drops. When a capacitance-input
filter is used, the secondary DB voltage is obtained by multiplying the
average load voltage by a ratio from Table 13-3.
Since window space must be provided for the magnetic shunt, the
winding space factor is reduced in the same manner as for the current-
limiting transformer supplying a balanced load. The ratio of the leakage
reactance at short circuit to that at rated current is expressed by the
factor q, which has a typical value of 0.8.
The flux density in the secondary portion of the core is calculated
from the primary flux density in the same manner as for the current-limiting
transformer with a balanced load. The selected primary flux density Should be
about 10 to 15 per cent lower than that which would be used for transformers
without unbalance in order to obtain designs with reasorab1 values of
excitation in comparison with rating.
The design curves presented in Fig. 13-1 through 13-8 are used to
determine core loss and excitation as functions of flux density and un-
balanced magnetization. Unbalanced magnetizing force is different in the
primary and secondary portions of the core. If the value given by equation
(5-19) is defined as HDc, then measurements and analysis indicate that the
unbalanced magnetizing force in the primary portion of the core is about
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r.
Rpop m .7 Rix average oersteds, (7-1)
The unbalanced magnetising force in the secondary portion of the
core is about
Rilos ? 1.3 Rric average oersteds. (7-2)
These equations are readily justified qualitatively by comparing
a core before and after the insertion of the shunt, foragiven value of
unbalancing 0-0 ampere turns. Before the shunt is inserted, the direct
component of field strength will be about the same all around the care path.
Mk the Shunt in place the reluctance of the magnetic circuit as seen
from the secondary winding will be decreased, so that average (in time)
secondary flu and will be increased. Also the Shunt will certainly
reduce the average .41-tomotive force across the primary part of the core,
93 that average primary flux and R nnp will be decreased. However these
statements cannot be used as a sing; basis for quantitative analysis be-
cause nonlinear relations of the magnetic quantities prohibit separate
consideration of A4 and D-C components.
A gap in the secondary portion of the core will often be indicated
by the design curves because of the relatively low flux density and high
unbalancsd magnetising force in the secondary portion. Sometimes a gap will
also be indicated for the primary portion. The type of core construction
will decide whether it is possible to employ the exact gaps. The designer
should attempt to use the value of gap indicated by the design curves.
To calculate the primary current, the leakage reactance volt-amperes
must be determined. The leakage reactance is
X
Vat
Ink2 q2 - 1
( 7- 3 )
where Vsf RIC fundamental component of secondary voltage,
Isf--RMS
Omftelloomehm+101
_ ^^MMOWW401+ ^44 arab^
.541.1~41. Arrf~e~a~41.11ynstwrant
p st ratio of short-circuit current to rated current,
q m ratio of leakage reactance at Short circuit to
leakage reactance at rated current.
Er4....t4-.n (7=3) is s4mallar to (6-7), which Is .Ehg, awnranninn for the lpakapp
reactance of an ordinary current-limiting transformer. It is obtained in an
analogous manner by considering only the fundamental components in the voltage
equations. The MS fundamental secondary voltage, Vsf, is the major component
in the transformer 11116 secondary voltage, and therefore Vs may be used with
little error. The RAS fundamental secondary current, Ibr, may be assumed
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equal to 1.1 times Inr according to the discussion in Chapter V. The expression
for leakage reactancrbecomes
V
X is .
ohms. (7-4)
1.1 I EC p2 g2 .
The reactive power absorbed by the transformer leakage reactance is
defined as leakage-reactance volt-amperes, and is approximately equal to
2 2.
X (Is - I
Only the alternating-current components of the secondary current
contribute to the leakage reactance volt-amperes.
The primary current may be calculated frgm
IP
(7-5)
mVI(wI, Wc Wi) 1(1.2 - =i]x
1.1 2 r 2
where WPL is primary component of load voltage-amperes
according to equation (5-11),
W at winding loss in watts,
amperes,
(7-6)
Wilscore loss in watts (neglecting shunt losses),
W - excitation in volt-amperes.
ex
X leakage reactance in ohms referred to secondary winding.
The calculation of turns per volt is made in the same manner as for
an ordinary current-limiting transformer. The difference between primary and
secondary turns per volt accounts for the leakage-reactance voltage drop.
The corrections for winding-resistance voltage drops are made by adjusting the
turns in the same way as for a transformer with unbalanced magnetization only.
When the transformer design is completed, the voltage ratio should be checked.
In accordance with the reasoning given in Chapter V, only the fundamental-
frequency components should be considered. From the equivalent circuit for
the fundamental-frequency components, the primary voltage is
Ir
,
21 2 2
A,
VP Ti + isf (Rs + Rijn.] IT T1 volts $ (7-7)
"sf
where Vsf = HMS fundamental secondary voltage,
Isf 11. RMS fundamental secondary current,
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R ? secondary resistance,
R1in2 ? primary resistance referred to secondary,
? leakage reactance referred to secondary Wilding.
When apprcadmate relationships are substituted for fUndamental components,
equation (7-7) becomes
2
V
+ 1.1 Ipc CRE, + Rp/ei] + (1.1 Ive 1)2 volts (7-8)
If the calculated primary voltage differs appreciably from the specified
voltage, the turns are altered, since the change in resistance will be small.
?
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VIII. VIBRATOR-SUPPLY TRANSFORMER
The design of a transformer for a vibrator supply is only a part
of the more general problem presented by the entire supply circuit. The
transformer, vibrator, and timing capacitor must be integrated so as to
achieve a satisfactory power supply. EMOhasis is placed here on the re-
quirements and design of the transformers sincea study of the complete
supply19i;quit is beyond the scope of this projed. Recourse to the refer-
ences, ' in particular the Vibrator Data Bookir of P. R. Mallory and
Company, will provide the designer via additional information. Material of
a general nature is given by Connelly and Distin19, whereas Evans2? presents
a detailed and mathematical treatment of vibrator-suPply circuits. Vibrator
power supplies normally do not exceed a rating of 50 to 60 watts at 300 to
WO volts DC output. Dixey and Wilnan21 discuss ratings greater than 50
watts, and moral trends in vibrator power supply developments are reported
by Mitchell".
A typical vibrator supply circuit with contact-driving coil omitted
is given in Fig. 8-1. The capacitor Shown, called the timing capacitor or
buffer capacitor, is used across either one or both the windings of the
transformer. Capacitance is necessary to prolong contact life and to de-
crease stress on transformer insulation. Numerous circuits are used, but as
far as transformer operation is concerned, most circuits perform similarly
to Fig. 8-1. The middle contact is vibrated by a relay coil which can be
incorporated into the circuit in many ways. As the mildle contact meets one
of the others, battery voltage minus circuit drop is applied across half of
the primary winding. When the contact reverses, voltage is applied across the
other half of winding in an opposite direction. The result is an alternating
voltage induced across the entire primary, and therefore across the secondary.
A second set of vibrator contacts, operated by the same relay, is
sometimes placed in the secondary to yield a reztifiAd output, the so-called
self-rectifying type of circuit. When only one pair of stationary contacts
is used as in Fig. 8-1, the vibrator is termed an interrupter type. In this
case, a rectified output may be obtained by placing either a metallic or
tube rectifier across the transformer secondary. For a properly adjusted
vibrator, the self-rectifying type is the more efficient. The contact
travel time, usually referred to as the "off-contact" time, ranges from 15 to
30 per cent of a complete cycle. Expressed another way; the "time efficiency"
which is the ratio of vibrator contacting time to half a period is normalll,
between 0.7 and 0.85.
The frequency of operation is generally 115 cycles per second,
although some vibrators have been made for 250 and 1300 cycles. The obvious
advantage of a reduction in transformer size as a result of using a frequency
greater than 115 cycles does not always result in an overall improvement
because of the influence of other factors. The driving power for the
vibrator coil increases with the third power of the frequency. This effect
is compensated for by using a permanent magnet which, however, increases the
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FIG, 9-I VIBRATOR, TIMING CAPACITOR, AND TRANSFORMER
'CORE FLUX
I'
r?k%
11,? VOLTAGE
1 aro'
I -
1+1
FIG. t2
-2
ARMOUR
1 Lwawasasortmatlia
-.WAVE SHAPE OF TRANSFORMER II1PuT.VOLTAGE AND FLUX
SHOWING EFFECT OF TIMING CAPACITANCE
r or r oo r oft II am
mm am mg am Nir fit
r 1%/111161104All TO01111.8
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d.*F !LI !MA!!
ttuteinyiiiya etc ?gel:Imes: etray
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v. ???? vovv "Vv.... ? V
?
vibrator cost. Manufacturing costs are further increased since adjustment of
a vibrator which operates at a higher frequency is more critical. The time
efficiency decreases with an increase in frequency since a finite amount of
"off-contact" time is necessary to avoid destructive arcing. Larger and more
expensive filters are required since the vibrator is operating in a frequency
range which is more likely to cause interference with communication equipment.
Furthermore, contact life would be shortened at a higher frequency as a result
of the greater number of operations per unit time.
Flux Density
The vibrator contacts are usually made from tungsten. As the
contacts wear, the time efficiency decreases, Which greatly affects the
waveform and hence the transformer characteristics. To avoid contact
deterioration, the normal practice is to design the transformer with a
relatively low flux density so as to reduce the exciting current:n=1.41litre
additional protection of the contacts is required, Dixey and Wi
suggest inserting a choke in the transformer secondary and Kiltie23
describes a vibrator circuit for reducipg contact current to zero before
opening occurs. Others, such as Allenat and Hunt25,also have considered the
problem of reducing contact deterioration.
Starting of a vibrator is especially critical, since it is during
this time that the contacts may be completely destroyed. When the battery is
connected, the flux density after the first contact closure may exceed the
normal maximum flux density if the residual magnetization of the transformer
core is of an adverse polarity. Even more significant is the fact that while
the vibrator is coming up to normal operating speed, the exciting current on
successive half cycles may be different due to unequal contact closures. As
a result, during the initial seven or eight cycles, the transformer may be
subjected to a uni-directional component of magnetization. All these factors
may produce an extremely high flux density and a high exciting current.
Table 19-1 gives suggested flux densities which should result in
satisfactory contact life. The flux densities= given are for the maximum
anticipated voltage. The supply voltage is usually a battery which may be
in various states of charge. Table 19-2 gives typical operating voltage
ranges corresponding to the nominal voltages. For economic reasons, vibrator-
supply transformers are most often designed with 214 gage (.025 Inch thick)
non-oriented, silicon steel of approximately AISI M-22 grade. Better grades
of steel are sometimes used in order to operate the transformer at higher
flux densities and at the same time avoid an excessive exciting current.
The same advantage is obtained by using wound cores of oriented etee1.26
In order to reduce the saturating effects and limit the exciting
current during starting, a gap in the transformer core is sometimes used.
However, this practice is ordinarily not recommended since it results in a
large steady-state exciting current. Another way by which the exciting
current may be limited is by inserting resistance in series with the battery
or primary winding. This has a self-regulating effect, since the voltage
across the primary is reduced when the transformer draws a large exciting
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.11. Wee
current. For this reason some manufacturers prefer to place the primary
winding over the secondary winding to increase the mean length of turn.
Methods have been devised whereby a relay automatically Inserts resistance
only during the starting period. A variable resistance which is reduced
to sero after starting often is necessary, especially when the supply voltage
exceeds 12 volts.
The principal reason that starting is more difficult with higher
supply voltages is that arcing at the vibrator contacts is much more severe.
For tungsten contacts an arcing voltage in excess of 14 or 16 volts makes
it difficult to interrupt the current. For this reason the currents which
the vibrator contacts can adequately handle at the higher supply voltages
must be reduced so as to insure that exciting current, especially during
starting, does not become excessive. When series resistance is not used
with 24 and 32 volt vibrator supplies, the design flux densities should be
somewhat less than those given by Table 19-1. Capacitance across each of
the contacts is effective in extinguishing the arc, but it is not recommended
since it greatly reduces contact life. However, a modification of this
idea is used, since for 24 and 32 volt vibrators, it is customary to place
some capacitance across the entire primary winding. A portion of the timing
capacitance is usually used for this purpose.
ab...2.1t.m.y.NLEae Relationship
When a transformer is supplied by a battery and vibrator without
using a timing capacitor, the idealised wave shape for primary voltage is an
alternating series of rectangular pulses. When a timing capacitor of proper
value is used, the wave shape is in most cases similar to that shown in
Fig. 8.2. The main function of the timing capacitance is to supply the
transformer exciting current during the contact-off periods. Otherwise
there would be a rapid collapse of the flux as the contacts opened, resulting
in high induced voltages and destructive arcing at the contacts. The wave
shape of the core flux also shown in Fig. 8-2 is mildly determined from
UU0
applied voltage wave shape by use of the basic equation of induction,
v N 16.5 volts, (8-1)
where v = instantaneous voltage,
N ? number of turns across which
voltage is applied,
cf= core flux in kilolines.
Since previously derived equations relating core flux and voltage
are intended for a sinusoidal input, they are not applicable for the vibrator
transformer. There is a more general equation found by integrating the basic
equation of induction. This gives,
/12
d0
v dt
it:2
(8-2)
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If the times ti and to are chosen such that t1 is the time at which voltage
is sero and inereasing, and to is time at WhiCh voltage is sero and de-
creasing, and there is no voltage sero between, then the right side of (8-2)
has a =dm= value. The value of the right side is proportional to the
average voltage during the period ti to tt, times the time, 4040. The
left side of the equation can be readily integrated, and the risult is
105
- g' (t2 - ti) Tan (8-3)
Since tines are chosen fOr which the right-siie term is MaXiMUR, then the
left term must also be a alligtalMs such that go is a positive peak and 011 is
a negative poWk. If there is no bias flux, aid applied voltage has the
property of half-wave memetry about sero (successive half waves are mirrored
images about the time axis), then (02 01) ? 2 Oin, where peak flux On is
measured from sero. The conditions Tor tae times are such that
(to - tad is one-half cycle equal 2r. where f is frequency. Substituting in
(8:3) gtves
105 Veme
7 Om a itr? 21PY (8-4)
v ? 4 f N 012 10-5 volts. (84)
tag
This is a basic equation independent of voltage wave shape, except for the
restriction to half-wave symmetry. Effective or EMS voltage is average
voltage times the form factor. For flux can be substituted net area times
density, and (84) becomes
V ? 4 fx f N Fi B Ai 10'5 BMS volts, (8-6)
where fx voltage-wave form factor,
F core space factor,
B ?
flux amity in kilolines per sq. in.,
Ai core cross section in square inches.
For a sinusoidal wave shape, form factor is 1.11, and. (8-6) is
the familiar relation for that case. For vibrator-supply transformers, the
form factor varies because of changes in wave !tape. The principal reason
for wave shape change is contact wear which increases the "contact-off" time.
Different types of loads also greatly influence =Ito To obtain some
idea of the form factor associated with a vibrator, a simplified wave shape
consisting of an alternating series of rectangular pulses separated by the
time required for contact travel will be considered, The IrdS voltage V of
such a rectangular wave is related to its maximum value V by
V ? VM \r7B14S volts,
ARMOUR RESSARCH FOUNDATION OF ILLINOIS INSTITUTE
(8-7)
yrera cirt1 t'S et V
ry ??? ??? ???? ?
? ??
.4
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''" ?
?????????? a
where T si the ratio of vibrator contacting
time to half a period, between
0.7 and 0.85.
Similarly, the average value Vavg is
V'avg T volts.
Hence, voltage form factor is
V1
avg
For the normal range of T, f, is between 1.19 and 1.08. It ahould be
noticed that these values brIcket 1.11, which is the form factor for a
sinusoidal wave shape.
Cre 1488 and Exciting
The core loss of a vibrator-supply transformer at a fixed flux
density will depend upon the form factor of the applied voltage wave.
Using the somewhat artificial approach of dividing core loss into "hysteresis"
and "eddy-current" losses, the following expression for core loss may be
written for any wave shape of flux,
1 ? P B' +Q V2,
where PI n, and Q are approximately constants,
B is maximum flux density,
V is BM volts of a winding.
(8-10)
Than since V Ix fx Vavg and since Vavg is proportional to flux density
B, (8-10) may be:rewritten
W gs P"Bn + B)2.
Equation (8-11) OhNR that for A firad flax derAitve the core loss of a
vibrator-supply transformer will be the same as that for a transformer
supplied by a sinusoidal voltage, provided f is 1.11. Since it has been
previously shown that the voltage form facto F is usually close to 1.11,
the core loss characteristics taken for an applied sinusoidal voltage may
be used with a reasonable degree of accuracy.
Excitation paver is unlike that of other transformers, because here
it is real power dissipated. Opening of vibrator contacts prevents excitation
power from returning to the source. The value of this power is the average
voltage-current product. Excitation volt-amperes may be roughly estimated
(8-u)
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????? lanar Tir???? a ? ? ? ? ? 1
as average battery voltage times the current corresponding to themaximmm
flux density, or may be taken directly from material characteristics in
volt-amperes per pound. It might seem that average volt-amperes should be
half of this, since current is initially zero at the beginning of each half
cycle. However, during a half-cycle of voltage, flux changes from negative
maximum to positive maxima and there must be a corresponding change in
exciting current. Since initial current during each voltage half cycle is
zero, the peak exciting current should correspond to twice the usual value
for maximum flux density. For the circuit of Fig. 8-1 the heating effect of
excitation current in each half of the primary is the same as though each
half carried .707 of thP total. Therefore the resulting excitation input
to both windings is 1./11h where W is the excitation required on the
basis of core weight and manmum flux amity. Total primary input, in-
cluding load component, excitation and winding losses, is
W ? W +1 4111 W + W volt-amperes,
rp r ax c
(8-12)
where W m load component,
W Is excitation as found from core weight and flux density,
W st winding losses.
Timing Capacitance
If the timing capacitor were not present, the core flux would drop
to its residual value during the interval that is required for the moving
vibrator contact to travel from one stationary contact to the other. By
placing a timing capacitor across either the primary or the secondary of the
transformer, the energy stored in the capacitor during one contact closure
controls the flux in the core until subsequent closure with the other
stationary contact.
Consider the transformer, capacitor, and vibrator contact arrange-
ment shown in Fig. 8-1. During closure of the moving contact with the upper
contact, half the primary is energized. As a result of the induced voltage
in the other half of the primary, the capacitor is charged to a voltage
equal to almost twice the batter) voltage. When the contacts open, the
timing capacitor and the magnetizing inductance of the transformer comprise
a !tee oscillatory circuit. During each "contact-off" time, it would be
desirable to have the voltage across the transformer primary Change from
twice battery voltage of one polarity to twice battery voltage of the
opposite polarity. In this way, the voltage across the primary would equal
the voltage which would be applied when the contacts meet. In other words,
a total change of approximately four times battery voltage is required across
the primary, and hence also across the timing capacitance, during each
contact-travel time. The timing capacitance must supply the transformer
exciting current during this period, so the charge required is approximately
equal to the peak value of the exciting current multiplied by the contact-
travel time. If T is defined as the ratio of vibrator contacting time to
half a period, then from Fig. 8-2 it is seen that each contact-travel time
ARMOUR iiSCARCN FOUNDATION 01: ILLINOIS INSTITUTE
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E
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Ter LI ILI eh I et E. ?I
I is r? %I' WI,
.4 ,
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???????.- ???
-ergo ir-.? ?
is (1-T0f second, where f is the vibrator frequency in cycles per second.
From the foregoing, an expression for the timing capacitance is
(1-T)/2f 6
C as Pa 10 microfarads. (8-13)
vhere = peak value of exciting current,
T is ratio of vibrator contacting time
to half a period,
f w vibrator frequency,
1110 so battery voltage.
TO obtain an expression for the peak value of exciting current, assume that
the excitation is the product of battery voltage times average no-load
i current. Since peak exciting current may be approximated as equal twice the
I average no-load current, equation (8-13) becomes,
(1-T) W 106
1 cn ......42L... microfarads, (8-1h)
i 4 f Eb
? ???
where W is excitation as found from
eX core weight and flux density.
The value of capacitance calculated by equation (8-14) should be
divided by 0.6 in accordance with recommended practice. This is done mainly
to give satisfactory operation when the time efficiency, T, decreases due
to contact wear. Furthermore, a larger capacitance helps starting and it is
less damaging to the contacts than not enough capacitance. Imuation (8=19
shove that the required timing capacitance varies with ?Magee in supply
voltage. Also, a higher supply voltage means a slight increase In vibrator
frequency and duration of contact-closure time. If the vibrator transformer
is operated with a flux density which does not prodtce appreciable satur-
ation under the highest input voltage, a timing capacitance can be selected
which provides satisfactory vibrator operation over the expected range of
input voltages. From the foregoing it is apparent that mary factors in-
fluence and alter the optimum value of timing capacitance. It is suggested
that the calculated value of timing caPacitance be used only as a rough
approximation, and that the most satisfactory-value be determined by viewing
the primary voltage wave shape on a cathode ray oscilloscope. When the
correct timing capacitance is used, the wave shape at no load should be
similar to Fig. 8-2.
The timing capacitor is usually placed on the secondary side since
a smaller size is required, capacitance being inversely proportional to the
turns squared. In applications where the input voltage exceeds 12 volts,
part of the timing capacitance should be placed on the primary side to
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?
alleviate arcing. With the timing capacitor on the secondary side, the
capacitor must have a much higher voltage rating so all of the gain due to re-
flecting the capacitance is not realized. A general rule is to use a
capacitor having a voltage rating about four times the secondary no-load
voltage corresponding to the highest anticipated input voltage. In general,
a resistor Should be placed in series with the capacitor when it is placed
on the secondary side. The purpose of the resistance is to damp oscillations
arising from the presence of the leakage reactance, and to limit during
contact make, the capacitor charging current which results from using too
large a timing capacitance. A resistor should never be used in series with
the portton of the timing capacitance on the primary side, since the
function of this capacitance is to alleviate arcing.
.V.1.12atcTTransirme.ationWith Unbalanced Magnetization
The undesirable effects of a high exciting current as the result of
unbalanced magnetization during vibrator starting have already been mentioned.
Because of these effects, half-wave rectification is normally not used on the
output of the customary circuit of Fig. 8-1. However, a satisfactory design
can be achieved when using a half-wave rectifier by designing the transformer
to operate with a somewhat lower flux density than would normally be used.
This problem is similar to the unbalanced magnetization of a transformer
supplied from a sinusoidal voltage. Particular attention must be given to
the magnitude of the exciting current to avoid damaging the contacts. A
gap in the core structure may in some cases be desirable in order to limit
the exciting current during starting. Also a gap may help to reduce the
excitation volt-amperes, as shown by the curves given in Chapter V.
Another circuit arrangement which results in unbalanced magneti-
zation is a non-center-tapped transformer together with a single-contact
vibrator. A single-contact vibrator may be obtained from a conventional
vibrator by connecting the two stationary contacts together. If the
secondary load is not rectified, the direct component of the primary current
will produce an unbalanced magnetization of the core. To obtain satisfactory
operation with this condition, a low flux density should be &insert, and an
attempt should be made to obtain a low residual magnetism, porsibly by the
use of a gap in the core structure. However, if the secondary load is
rectified, it may be possible to balance the secondary and primary ampere
turns so that a net unbalance magnetization of the core does not occur.
A small unbalanced magnetization of the core can occur in still
another way even though the circuit of Fig. 8-1 is used with a full wave
rectifier. This remits from the fact that with a 0W-1-type f.rsnetrilm..ion
the two halves of the primary (also applies to the secondary) will have a
different winding drop due to different mean lengths of turn when one half
is wound over the other half. This can be avoided by using a bifilar
winding, or by winding each half of the primary and secondary side by side
rather than by winding one nn top of the other.
Leakage Reactance and lending Lavout
The last mentioned scheme has the disadvantage that leakage
ARM0141/ IIFSFARci4 gniiNnAT!n!h! Or !LUIkle",!5 IHST:TUTC
- 82 -
et t tf
I IS Voir, 11,1% i?UO {g,
:1
? 7
ii
1
1
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reactance will very probably be increased. High leakage reactance is un-
desirable in a vibrator transformer since it causes high induced voltages
upon contact opening, and causes undesired oscillations with the timing
capacitor. To Obtain a low leakage reactance with the mentioned scheme, the
Primary and secondary windings should be subdivided into sufficiently many
parts so as to distribute each winding more effectively. With a scheme such
as this, the various coils must be externally connected so that those coils
which are carrying current at any particular time are adjacent to one another.
With a normal layer winding, the usual manner for reducing leakage reactance
is by inter-leaving portions of the primary and secondary. This type of
winding is the most effective for obtaining a low leakage reactance. Each
time the windingr are subdivided, the length of the leakage flux path is
greatly increased with only a slight increase in the cross sectional area of
the leakage flux path. However, as additional subdivisions are made the
advantage dimishes and the cost of the winding increases.
The manner in which the windings are placed on the core is even
more important from the leakage reactance standpoint for other arrangements.
For example, if a full-wave-rectifier load is supplied by a core-type trans-
former with both primary and secondary center tapped, half of the primary
and half of the secondary should be placed on one leg with the other two halves
on the other leg. Care nust be taken in making the external connections to
be sure that both the windings on any one leg are conducting at the sane time.
If a non-rectified load is supplied by a core-type transformer with primary
winding center tapped, the secondary should be split with half on each leg,
and the primary should be divided into four parts with two parts to each leg.
In this way, when either half of the primary is energized, an adjacent
section of the secondary is also conductingooproviding the external connections
are made properly. The general rule is to equalize primary and secondary
load ampere turns at each instant, for each leg of the core structure.
In addition to the special techniques already mentioned, the
windings of the vibrator transformer differ from those of conventional trans-
formers in a number of other ways. Additional insulation is often required
in order to avoid breakdown from the high induced voltages developed during
contact opening. Heavier insulation is also required to help support the
primary winding on low voltage designs, since only a few layers of rather
heavy wire are usually required. When heavy wire is used, the primary
winding is often placed over the secondary to facilitate winding and to take
advantage of the increase in resistance resulting from the greater mean
length of turn.
Because of the induced voltages developed during contact opening,
a great deal of high-frequency interference is presented by a vibrator-supply
circuit. To eliminate some of the interference, a copper shield is sometimes
placed between the primary and secondary windings and then grounded to the
core. When the use of a copper shield is not justified, some degree of
shielding can be obtained by "inverting" the secondary winding. This is
accomplished by bringing out all the leads for both halves of the secondary.
and then externally joining and grounding the farther outside and inside
leads of the secondary winding. This requires that additional insulation be
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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used between the middle two layers of the secondary, since the entire
secondary voltage appears here. When neither of these two special techniques
appear to be justified for eliminating high frequency interference, satis-
factory operation can often be achieved by simply encasing the entire
transformer and properly placing it and the vibrator with respect to the
frequency sensitive equipment. Other techniques employing additional circuit
components are usually used, but these will not be discussed since these are
not directly related to the transformer design.
Design Procedure
The transformer rating will in most cases be based on HMS voltages
and currents. However, for some low-voltage vibrator supplies, the primary
resistance drop may be great enough to necessitate a larger primary wire vise
together with a larger transformer. A check should be made at the completion
of the design to determine whether a revision is necessary.
The equivalent RMS seconds -y current is determined from the DC
load current and the filter requirements. If a vibrator transformer is
supplying a full-wave rectified load through an infinite inductance-input
filter, the RMS current in each half of the secondary would be .707 times
the DC load current, since each half of the secondary supplies half of the
load current. If a filter were not used, then the current in each half of
the secondary would flow for less than the entire half cycle as determined
by the time efficiency. For a rectangular wave, the DC load current should
be multiplied by .707/ Or. For T a .81, the multiplying factor becomes .786
which is the same as for a sine-wave. For a capacitance-filtered load, the
ratio depends on the amount of filtering. Since both eine and vibrator wave
shapes give the sane ratio for an infinite inductance-input filter, and for
no filter with a reasonable value of T, it is reasonable that the ratios of
RMS secondary current to DC load current given in Table l22, whichare for
sine waves, also be used for the vibrator transformer.
The equivalent RJ S voltage for the secondary winding is usually
specified; otherwise it may be estimated from the required DC 'kind voltage
plus estimated rectifier forward drop and other series resistance voltage
drops multiplied by 1.11 for an infinite inductance-input filter, or multi-
plied by 1/ Orrif a filter is not used; or DC load voltage multiplied by the
ratio from Table 12-4 for a capacitance-filtered load.
The total secondary rating is twice the rating of each half of the
winding, so the equivalent rating becomes
M = 2 I V /2 volt-amperes,
V9/2 (8-15)
where Is = secondary RMS current,
Vs = half the secondary EMS voltage.
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? ? Ilirlla 111 ??? ^^" ^^. ^
For exactness in using the nomograph, this rating should be multiplied by a
correction factor which depends on the form factor of the voltage wave.
Referring to equation (8-16), it is seen how the form factor enters in the
general relationship between MS voltage and flux density. It should be re-
called that the nomograph has been constructed for a sinusoidal wave shape.
However, since the farm factor for a vibrator wave shape is near to that for
a sine wave, in accordance with the discussion following equation (8-5), the
rating given by (8-15) can be used for the nomograpliwith negligible error.
The design method then follows the general design procedure for a filament
transformer with only slight changee.
? ??
The winding space factor Fc should be obtained from Fig. 11-2 in
the usual way, with each half of a center-tapped winding counted 'as a separate
minding. Construction of models indicates that this: procedure allows for the
miuction in winding space factor which, results from bringing out center
taps and the use of additional insulation to protect against induced voltages.
In the selection of flux density, a low value must be chosen for
the reasons listed previously. Table 19-1 gives suggested flux densities
corresponding to maxima anticipated voltage, and Table 19-2 Mows typical
voltage variations for the nominal voltage systems. The flux density to be
used in the design procedure is selected from Table 19-1, and then decreased
by the ratio of most probable operating voltage to maximum operating voltage.
Next, the characteristic linear dimension may be determined from the nomograph.
Core loss and excitation are then found. In general the core loss and exciting
volt-amperes which result from selecting the flux density in the foregoing
manner will be acceptable unless some special requirements must be met. In
determining the lamination size and stack from the characteristic linear
dimension, an attempt should be made to minimize the exciting current by
obtaining a low core weight. This means that a lamination with a large window
area per unit core cross-sectional area should be chosen, if available. Also
a low stack will reduce core weight for some types of laminations.
The next modification in the design procedure occurs in the cal-
culation of the RMS value of primary current. For a vibrator transformer
total primary input power is,
W =W +W +1.414W volt-amperes,
rp r c ex
where Wr is given by
Wrc and W are
ex
Eq. (8-15),
calculated in the design procedure.
(8-16)
The excitation volt-amperes are multiplied by the factor 1.4114 to account
for the heating effect of the exciting current which flows only during half
a period in each half of the primary. The primary HMS current for use in
calculating wire sizes, is half of the total primary power input divided by
the RMS voltage across half of the winding
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?11,-.111 -?? ? - ? ?? ??? ? 1 ? ????-?
amperes. (8-17)
An expression for the RIG voltage across half the primary winding, allowing
one volt for contact drop, follows from equation (8-7):
V /2 (Vb - Rio volts,
(8-18)
where Vb ? battery voltage.
After circular mils per ampere are found in the normal manner, the wire
sleep are calculated from the RIS primary current given by (8-17) and
from the RhS secondary current which was determined at the start of the
design.
The exact equation giving turns per volt is
105
mroZ ry,mAZ turns per volt,
4 a
(8-19)
where V RMS voltage,
fx ? form factor, ratio of RMS voltage to average voltage.
Since the form factor for a vibrator voltage wave approximates that for a
this wave, the standard expression may be used with reasonable accuracy.
The primary RhS voltage of half the winding is given by equation
(&-18), whereas that for the secondary was determined at the start of the
design. To calculate the total turns in each winding, the result must be
multiplied by two and then corrected for regulation in the normal marmer.
Finally the :findings should be laid out to see if the window is
properly filled, and other checks on the completed design made to find if
any critical limitation has been exceeded. Adequate insulation should be
used to insure against breakdown from high induced voltages.
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ri. CITAJ TRANSFORMER
Construction
This type of transformer is used to supply filament beater power in
a circuit where it is necessary to have a low-capacitance from the filament
circuit to ground. Frequent)" the transformer is operated such that the
secondary has a high voltage with respect to ground and to the primary,
although the voltage difference across the secondary is small. A low value
of capacitance can only be achieved by providing a large Oysical separation
between the secondary and other parts. Secondary supports should have a low
dielectric constant and should occupy as little space as practical. An open
transformer, with air comprising most of the space around the secondary, has
a laser capacitance than the same unit immersed in a compound or oil. The
presence of adjacent equipment raises the effective secondary capacitance.
Special construction or provision to meet low-capacitance re-
quirements is normally necessary for values up to 50 micro-micrefarads, and
perhaps even higher. Since capacitance is a function of sise as well as of
proportions, construction will depend on rating, frequency, temperature
rise and perhaps test voltage, since all of the quantities affect sise to some
degree. It has been found that conventional 60-cycle filament transformers
with ratings from about 28 to 250 volt-amperes have capacitance values rang-
ing upward from 100 micro-microtarads. This gives a rough guide to the values
for which special construction is required.
To obtain very low values of capacitance, in the order of 5 to 30
micro-ed.crofareds, an arrangement of core and coils as shown in Fig 9-1
can be used. Although no secondary support is sham, same scheme is necessary,
and the design of supports depends principally on shock and vibration which
the unit mat withstanO. Primary and secondary windings may be placed on the
same leg (as im rig 9-1) or on opposite lege of the care, bat ths former is
usually preferred because of the lower leakage reactance. In some cases
where the low-capacitance winding is operatedak.-...e..h.ish voltage with respect
to ground, the spacing necessary to obtain low capacitance is adequate to
withstand the voltage stress. A check should be made in every case. Since
nsulation strength usually depends on the length of the creepage pathothe
secondary mechanical supports should be designed for adequate creepage length.
To obtain intermediate values of capacitance, in the order of 50 to
100 sicro-vicrofarads, a construction very similar to that of conventional
filament transformers can be used, provided that margins and inter-coil in-
sulation are increased over normal values.
Calculation of Capacitance
The capacitance between electrodes of any shape is based upon the
simple capacitance relation for parallel plates. Extension of the basic
parallel-plate formula to complex shapes can be accomplished by dividing up
all of the space between the two electrodes into infinitely small sections to
which the parallel-plate formula can be pplied with negligible error. Then
the proper caibination of the infinitely small sections, in series and
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1
1
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?? "44, a -? -????? ? '? ?
FIG.9-I CORE AND WINDINGS OF LOW-CAF'ACITANCE TRANSFORMER
0
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. ? ,
parallel, yields the capacitance of a complex shape. In the report on Contra
No. Di-36-039 sc-5519 the capacitance between parallel plates with nig-
ligible fringing has been shown to be
micro-microfarads, (9-1
where K ? dielectric constant,
it PI area of the plates, sq. in.,
t separation of the plates, inches.
Equation (94) is given here to show that capacitance has the
dimension of lengthy in that dielectric constant I is dimensionless, area
A is a length squared and separation t is a length. Extension of this
principle to WV pair of co:01ex electrodes means that capacitance varies
linearly with sue for constant proportions.
Exact values of capacitance can be readily calculated for a few
simple geometric electrode shapes, such as parallel planes, parallel
cylinders and spheres. Many fairly intricate two-dimensional electrode
shapes can be handled by the method of complex variables to obtain exact
capacitance values. However the low-capacitance transformer presents a three-
dimensional configuration which is much too intricate to obtain exact values
kr analytical means, and even approximate calculations would be fairly in-
volved and subject to error. Therefore data have been compiled for the pur-
pose of developing an empirical formula for use in calculating capacitance.
Capacitance measurements have been made on four 60 cycle trans-
former development modals. Each of these had the secondary mounted on the
same leg as the primary, and supported by four wooden blocks which were
about the same length as the seccadary winding axial length. The primary'
was connected to the core, and capacitance was measured (using a General
Radio 716 C Capacitance Bridge) between secondary and core for three condi-
tions: with wooden blocks in place, with the secondary suspended by strings
and blocks removed, and with the secondary suspended around the core leg
opposite from the primary. Capacitance was measured at 1000 cycles. Cap-
acitance measurements and other data for these models, identified as 120 /31
041 and 0, are given in Table 9.1,
Extensive testa were made on model 12 to determine the effect of
moving the secondary winding around in the core window, but about the same
leg. It was found that capacitance is not sensitive to a change in the
position until clearance in any one direction is reduced to a small value.
The winding supplied with 12 was removed, and measurements were made using
single turns of wire and copper strips of different sizes. In addition a
core of the same cross section but with a smaller window area was constructed,
and measurements of capacitance between the core and single turns of wire
were made.
The data obtained from all tests were cowiled and studied to rim
an empirical formdla for capacitance. The form of the equation given in the
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,OP2 ? perimeter of secondary cross section neglecting
1
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Mort suPPlosout of Contract BA 36-039 ac-5519 in tried, and found to be
very satisfactory. The resulting equation is
01,35 it() acs
c nicrosed.crofarads (9-2)
In 41
ra.
2
where mos ? mean length of noonday turn, inches,
P perimeter of open care window space with primary
1 in place, epee 2( hit ? )13) of Pig 94
,
outside insulation, equal Igh + hi) of Fig 94,
ko ? correction factor for secondary supports and
dielectric between secondary and core,
In logaritha to Nspierian base, e.
s ?orn ns Nunes
ComPagr
ARMOUR
RESEARCH
4110.
FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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? ........???????? ? ???'"
TABLE ?-4. Data for Low-Get..._ance !Sodas
Wing at approx. 35 c rise, volt
soperes
Core type
Core cross section, inches
Wilda", inches
Primary builds inches
Mean length of magnetic iircuit,
inches
Prissily turns
Noon length of secondary turn,
m inches
Winding space factor, Fc
Iffective gap, pri to sec.
Axial length of sec. layer,
inches
Capacitance with blocks, C, micro-
microfarads
Capacitance without blocks, ssif
Capacitance without blocks, sec. on
opposite leg, mmf
Ratio at C6 Sec. on sane leg to sec.
on opposite log (without Modica)
ftas. Reactance at 60 cps, same
leg; ohms
Meas. Reactance, opps 1A44, ohms
Ratio of X, opp. leg to same leg
calculetad romtance same
h.
38.5
4.2 148
laminations
419x1.125
2.5x2.5
.13
12.9
.5x.5
ixl.5
.13
7.0
690 2070
12.0 6.5
.0385
.66
.375
0658
.35
.221
10.0 7.2
9.0 5.6
U. is.
1.13 1.30
32.9
73.8
2.24
30.2
Inuf
11.187
itz14
.25
20.0
433
15.7
.0512
1.5
.815
36
so'
.753g1
145K2
.38
9.5
552
8.75
.0563
.282
24.8 8.9
12.3 7.6
31.0 6.2
1.12 1.22
1. 0
*44,16,
384 35.9
2.18 2.53
133 16.4
13.0
314.6
2.66
14.2
41?11?11111?11Mir
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The factor k.
fact that the seconder,
estimated fro* the type
mounted adjacent to the
used for supporting the
????,? mewl I ..?
is a ratio greater than one which accounts for the
is not suspended in air. The factor k. can be
of construction, prolixity of equipmen% to be
transformer, and the dielectric constant of materials
secondary, as given in Table 9-2.
Table 94
DININCTRIC CONSTANTS
oramiworraistirliamostarsatiatiwarisso
Materiel
Air
40bestos pressed fibers
Bakelite
Oleos
Oil
Paper (dry)
Polystyrene
Porcelain
Wood
Dielectric Constant
1.0
40 - 250
14?5-5.5
5.141.9.9
2.2 -44
2.0-2.6
115057?7
41111111111111111
ANOMMONIIMISSI
The factor kis lower than the dielectric constant of the
-surrounding material Sra supports unless the entire space between the second-
ary and the core is occIpied by a solid or liquid dielectric. Tests made on
models of low-capacitance transformers provide a guide for selecting ke:
When wood blocks are used to support the secondary, capacitance is in-
creased about 20 per cent., so k_ is 1.2. Tests made with porcelain supports
also increased capacitance about 20 per cent. Table 9-2 lists the dielectric
constant of asbestos treated fibers, a material which is applicable for
2W60 operation. The fibers are pressed into a board-like "Aerial frtis
which blocks may be out for secondary supports. Because of its high dielectric
constant, measurements on model transformers using this material showed an
increase in capacitance of about 50 per cent over values obtained when the
secondary was supported in air With strings. Naturallyimaterials with low-
est dielectric constants are preferred for this type of transformer.
Table 9-1 shams that capacitance values obtained fram the trans-
former models with secondary suspended around the core leg opposite from the
primary are 12 to 30 per cent lower than the values for the secondary
suspended around the same leg encircled by the primary. From these data, an
average decrease of about 20 per cent can be expected for the same lanrth of
secondary mean tarn. However, if designs are made so that the secondary is
equidistant from primary and core, a secondary opposite from OA primary will
have a smaller mean turn than one on the same legs and consequent],y, an even
lower capacitance, according to equation (9-2).
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To mein& the applicability of equation (9-2), a plot of the
quantities salle and 1VP, was made on seallogaritla paper, with
ik
on the log It Stein noted that both of these ratios are diment
sionless the first being so because 0 is a length. The points gave a
straigheline relationship, laicals in accordance with the equation. The
transformer data obtained *Mout solid imports were used.
Since equation (9-2) checked measured capacitance when using small
sises of Are, one limiting configuration is accounted for. Another limiting
case is obtained when the secondary almost fills the window. As Pt approaches
Pao the denominator of (9-2) approaches sero? and capacitance 0 Wide to a
very high value for very mall spacings to primary and core. Values obtained
from (94) for smell secondary spacing have been compared with results of
the parallel-plate formes, and are found to agree well.
Leskole Reactance
Ons basic formula is used for practically all calculations of toff
stance or meows of coils and transformers. For a flux path in a non.
conducting material having relative permeability of unity, reactance or
leakage reactance is
x-
2044 2 A
ohms, (9'4)
10"
vhere f ? frequency, cycles per second,
0.19
irlriamaelwinding to which reactance is referred
A cross-sectional area of flux path, square inches,
h lenath of flux:path, inches.
A derivation and discussion of(9-3) has been given in Chapter II
of the final report for Contract DA 36=039 8045142: One 4unortant principle
is that reactance (or inductance) has the dimension of length, gime an. area
appears in the numerator and a length appears in the demmainator. This is
also a feature of the basic formmla for capacitance. The significance is that
reactance per turn squared (for constant frequency) is directly proportional
to linear Aso, if proportions of a transformer are fixed. It has also been
shown that for a non-Lliftvera isaanatic field, the geometric terms A and h de-
pend principally on those pats of the field where the flux is met donee.
In agy transformer, including the low-capacitance type; the greatest leakage
flux:density occurs betmeon primary and secondary windings. However a low-
capacitance transformer has a very complex magnetic field distribution which
makes impossible &precise calculation of leakage reactancef.
To obtain an empirical forvole, data obtained from the models of
Table 94 have been Atudied to find how equation (9-3) could be applied. The
equation recommended for reactance of low-capacitance units with concentric
windings is
?
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10
where m a mean length of secondary turN inches,
cs
0 effective magnetic separation of primary and secondary in
IBMTIqual to actual separation plus one third the sum
of primary and secondary radial builds,
h 0 axial length of secondary in inches, equal turns per
leyer times wire diameter
In table 9-1 are given motancos referred to the primary as cal-
culated from (9-3), measured reactances for primary and secondary windings
around the same core leg and for windings around opposite core legs. The
agreement between measured and calculated values is quite good except for
model 13. Values for reactance with windings on opposite legs are found to be
2.18 to 2.66 times the values for doncentric windings) the average is 2.4.
0
f112 cs
obits
"Veil" Mr.,.
(9-0
Tbs so-called measured values of reactance given in Table 94 were
actua34 calculated from short-circuit tests. The secondary winding is short*.
circuited thrall& an ammeter, and reduced voltage is applied to the primary.
Readings are taken of primary voltage and secondary current. It is also
necessary to measure resistances of both windings and of the ammeter. Leak-
age reactance referred to the primary can then be calculated from
m Isr
111111010NOI Rp 4' n2 (Re + Ra) r, vats (94)
P n
where V is applied primary volts,
Is a secondary short-circuit current, amperes,
Rp
0 primary resistance, ohms,
* secondary resistance, ohms,
-s
mg ammeter resistance, lams,
I mleakme reactance referred to the primary, ohms,
n turns ratio, primary to secondary.
Equation (9-5) is a quadrature sum of equivalent real and reactive
voltage drops witch yield the primary voltage. Although the model trans-
formers were designed for 60 cycles, the reactance of one unit was measured
at 400 cycles and a close check (3 per cent difference) of the 60-cycle
value was obtained.
The measured values of leakage reactance for all models was
checked by calculating primary voltage for load conditions, and comparing
with measured values. Such calculations can be made with the formula
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. -
VI.
V m (0 +.--:.- R + nI R )2 + (Is /02, (9-6)
p snipes
n
where Vs is secondary terminal voltage.
Calculated primary voltages from (9-6) were within five per cent of the
measured values. An interesting observation is that theiWyn) term in
(9-6) oontributes at most two per cent to the value of p voltage
Vn for these particular modeles when the winding' are concentric. The
agnificence of this is that the regulation of low-frequency, lowtempera-
ture-rise units depends almost faired); upon resistance drop in the windings,
particular); that of the secondary. The secondary resistance voltage drop is
typically four times that of the primary, due to the large mean length of
secondary turn. The leaksge-reactance drop term is more appreciable when
the windings are on opposite core legs. It is also higher at higher frequencies,
and should not be neglected. The effect of leakage reactance voltage drop
tends to be greater for higher temperature-rise units because all impedance
voltage drops in (9-6) increase in comparison with nVn. If a low-temperature
transformer were re-rated for a high rise by a change of materials, the
currents would be increased and turns ratio n would be decreased (by in-
creasing secondary turns) to maintain proper secondary voltage.
It should be noted that the empirical leakage reactance formula
(94) gives a value which is about one-fourth to one-third of that which
would be obtained from the basic formula (9-3), for which the tern A is
usually set equal to af30 (mean length of all turns times effective separation).
The result of (9-4) is not as low as one-fourth becausemo. is greater
than a.. It is apparent that (9-4) should not be applied to transformers
where the windings occupy most of the *Indus space. To obtain one formula
valid for both regular high-capacitance construction and low-capacitance units,
it would be necessary to multiply (9-4) by a dimensionless correction factor
based upon proportions of the configuration. 'YErrlilmWiamon practice
in the calculation of coil inductances which makes the reactance formula
(9-3) Applicable to apy vise or shape.
Capacitance and Leakage Reactance Checks
Measurements were mads on additional low-capacitance models to
compare square and circular configurations of the secondary windings and to
verify the annirical equations for capacitance and leakage reactance,:
One model identified as D5, consisted of model K3 with a new
secondary substituted for the previous one. The new secondary contains
twice as maw layers of wire and twice as many tarns per laiers giving
a total of four times the turns of the previous secondary. The same wire
size was used. Secondary capacitance was measured under various conditions
and was also calculated by equation (9-2). Results are as follows:
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Micro-
Microfarads
Capacitance - calculated, 8.5
without blocks
Capacitance - measured, 9.8
without blocks,
concentric windings
Capacitance - measured, 124
with blocks,
concentric 'windings
Capacitance - measured,
without blocks
windings on opposite
legs
The agreement between the calculated value of 8.5 and the measured value of
9.8 is coLsidered to be satisfactory, and within the accuracy limitations
of the empirical formula.
7.4
Another model identified as D3, consisted of a new secondary on
Model K4. The new secondary was madr in a square rather than in a circular
shape. It has the same number of turns, number of layers, turns per layer and
wire aise. The over-all else of the new secondary is such that the minimum
inside and outside dimensions are equal respectively to the inside and outside
diameters of the previous circular winding. Capacitance values were measured
and calculated for the square secondary's, and are compared with the circular
secondary as follows:
22E! Circular
Capacitance - calculated 16.7 13.5
without blocks
Capacitance - measured, 13.5
12
without blocks,
concentric windings
Capacitance - measured, 16.2 14.8
with blocks
concentric winding::
Capacitance - measured, 12.1 11.0
without blocks,
windings on
opposite legs
From these values it can be seen that capacitance of the circular winding
is less than that of the square by about 10 per cent for all measurements.
It is also interesting to note that the formula, although empirical, accounts
for the direction of change in capacitance from circular to square shape.
It might perhaps have been expected that the square secondary would have a
lower capacitance than the round because it has a somewhat greater average
separation from the core. The fact that this is not the case can be explained
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w.-_ -tr?-?
in a qualitative sumer by noting that the surface area of the circular
secondary considered as an electrode, is less than that of the square secondary.
It should also be noted that the circular secondary has a mean turn
of about 25 per cent less than the square, and would therefore have correspond-
ingly less secondary winding losses, an additional advantage.
Values of leakage reactance were measured and calculated for the
square secondary in the same manner as for the round secondary. Results at
60 cycles are as follows:
!..1 Circular
Calculated reactance, windings
concentric, ohms 20.5 16.4
Measured reactance, windings
concentric, ohms 17.5 14.2
Measured reactance, windings on
opposite legs, ohas 3762 35.9
Ratio of measured reactances,
opposite leg to concentric 2.13 2.53
These results show that the circular winding is preferable to the
square because of the lowered reactance obtained in every case. Therefore it
appears that the circular winding is preferable in all respects considered here,
and in addition, is easier to wind than the square shape. It is concluded that
the round secondary can be used to advantage except in designs where the primary
is almost square and spacing between secondary and primary is comparatively
small.
Regulation and Size
In the design of low-capacitance transformers, it is desIrable to
achieve minimum dee and weight in meeting the circuit requirements. The
relations between regulation and transformer sise have been studied to find
how a designer should be guided in obtaining these minimums. Another purpose
has been to find whether it is feasible to operate such a traneAser at high
values of temperature rise. The low-capacitance unit is characterised by
higher 0~4i:slant series impedance than conventional fil-isent trarliem.mornt
The secondary resistance is higher because of the long secondary turns, and
leakage reactance is higher because of the low reluctance of the leakage-
flux path.
It is a well-known principle that mazilaum power output from a
source is obtained when load resistance equals source impedance. Applied to
the low capacitance transformer, maiduzna power output occurs when
11211,1, " V (RP + n2R 12
s'
where RL load resistance
(9-7)
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V.
? .111,1111 ?
Although secondary 'tame of a given transformer would vary as the load
resistance changes, the seoondary wire else and turns could be varied to keep
secondary voltage and oontinctor volume constant for different values of power.
For most transformers limiting teiperature rise is reached long before power
output is increased to the theoretical maxims determined by (94). How-
ever, it mmy be found that operating sone low-capacitance transformers at
temperstures near maxim permissible values for the insulation materials would
result in having transformer impedance higher than load impedance. If this
wars it is possible to deliver the same load with lover transformer losses,
using the sane or less weight of secondary conductor. This is accosplished
changing secondary wire else and turns. This is a condition that should be
checked in low-capacitance designs.
The foregoing discussion has covered the effect of varying the power
output from a transformer of fixed weight. It remains to be shown how weight
varies with regulation for a fixed power output. Among the several designs
that might be made to meet certain requirements, one is a unit with low-
temperature rise and low regulation, and another is a unit with high-temperature
rise and high regulation. Regulation, which expresses the impedance voltage
drop from no load to full load is defined as
Regulation 611 fly 100 per cent, (9-8)
s
where V is applied primary voltage,
Vs In secondary terminal voltage at full load.
Of the two examples given, the transformer with high temperature
rise and high regulation has a smaller wire size than the other, but more sec-
ondary turns must be supplied to maintain specified secondary voltage. For
identical load requirements, the two examples have different values of turns ratio
no which enters into equation (9-8). It is desirable to find if the greater
number of turns of the first example yields a smaller or greater secondary
winding waight than thA *Amine' esimnlai in spite Of the saving in Ars she
To answer this question partially, consider that the nrimary turns of
a particular low capacitance unit with concentric windings are constant, such
that flux density is essentially constant. Actually leakage flux tends to re-
duce flux density in the portions of the core outside of the primary. Also
primary resistance voltage drop decreases flux flAnAity in all pArtA of the core,
but this impedance component is small compared to others present, so that the
effect on induced voltage is not appreciable.
Equation (9-6) is a general relation between transformer voltages.
An attempt has been made to find secondary 'eight as a function of regulation
accounting for all terms of (9-6), but the algebra is too formidable. Therefore
a admplified case may be considered as a qualitative guide. Primary resistance
and leakage reactance are neglected, since the tars iii R, is by far the Best
important in low-frequengy unite. Men induced secondary voltage is proportion-
al to secondary turns. Secondary resistance is proportional to turns and in-
versely proportional to vire cross-sectional area. For constant terminal
voltage and current, a voltage equation for the secondary is
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ire k2 smci
where k1 and k2 are constants
Ns s secondary turns, a variable
Aw a secondary wire cross-sectional area, a variable.
Solving for Ns gives
irs (9-10)
Narramorrisravorta
El? k2
I;
Now secondary conductor weight* for constant mean turns is proportional to
=ober at turns Uses wire area. Secondary weight* using (9-10), is
k3 vs Alit
Na. ? k3 A, - (9-U)
Knee weight becomes high for large wire Ass, A., a minimum my exist for
some smaller sire sue. Differentiating (941) iiitkrespect to to
d Nes2 As (kiAs k2) - kJ. A:
a.k...". _k3 v.
" Aw k2)
Equating this to sero gives a condition for minimum weights
k2WININTIMINS.~010
(9 -9 )
Substituting for k2 in (942) gives
%
kl Xs es To *
(9-12)
(9-13)
This shows Vast weight is obtained when regulation is 100 per cent,
or when the secondary terminal voltage is equal to half of the secondary in-
duced voltage.
The ;solution of the weight and regulation prohlm for the special
case elves the sane result as the condition for maximum payer from a transfaraer,
equation (94). It is suggested that this adidlaritir sight exist for the
moral case in mach primary resistance and leakage reactance were accounted
for.
The conclusion is that a transformer should not be designed for maxi- ,
air permissible temperature rise if the load resistance is less than the
treneormer equivalent series impedance referred to the secondary. Violation
of this principle results in higher transformer losses than necessary, and in
larger weight than neOessagre
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Modification of Basic Design Procedure
The design procedure for low-capacitance transformers is a modificam
tion of the basic method developed under Contract No. DA 36-039 SC-5519. The
basis for this special design method is an analysis of geometry and electrical
relations, with reliance upon dimensional principles and upon tests of
experimental models.
The design nomograph may be need for design of low-capacitance units
provided the various parameter, appearing on the nomograph scales are properly
selected. One of these is W0/Sc, defined as the ratio of winding losses to ax-
posed' wtading earface area. In a properly designed low-oapacitance transformer,
primary and secondary operate at roughly the same temperature, and most of the
winding losses occur in the secondary. Therefore, it is most isportant to
establish a suitable value for secondary losses in relation to sise and pro-
portions, This is done r, using the secondary dissipation per unit secondary
surface area in one nomograph scale factor. This ratio is calculated as:
1.25
CS AT
m ( ftwraiH watts per sq. in. (-14)
Sc,
where ifes di secondary winding losses, watts
S II secondary exposed surface area, sq. in.
es
AT in maximum permissible temperature rise, t
X a a parameter depending on aibient temperature.
Recommended values of the parameter X0 as determined from tests of
models, are given in Table 21-1 for open core and winding construction. With
the maximum permissible rise mid the given K, the value of IfJecs for use 'with
the nomograph is determined. Inspection of equation (9-14) Mows that too large
values of X are conservative, in that they tend to give an actual t.empersture
which is low. It is desirable that K be somewhat conservative so that actual
rise of a series of designs will average less than maximum permissible values,
simply to avoid too mapr rejects. Unpredictable variations in temperature rise
will always be present due to slight differences in design (which cannot reason-
ably be considered during design), manufacturing tolerances and errors in testing.
Another parameter which must be considered is the function of di-
mensionless geometric ratios, X0. The design nomograph is simply a means for
solving a general design equation. The design equation, as it applies to low-
capacitance urdA410 has been compared with the equation for common transformer
types. I comparison of terms and selection of constant based on model data give
.22
.
K - rrarre a
00 4'
VILIAG71.
F
C rro4 tra al4 lei rib rrwarr
w.a.saw-Lies COIJOAM factor, ratio of total wire cross-sectional
w
area to window area.
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Wading Apace rector
ewe factor is a very fundaxental quantity in the design of all types
of transfoniers, but in the low-capacitance type it hes a new significanee,
booms it helps determine secondary capacitance. In units share the winding
nearly fills the window, secondary capacitance can be reduced kr increasing
mender/ spacing, which in effect requires a lover winding space factor.
Roweveri there is no simple relation between space factor and capacitance be-
cause ()vaulter** is also a function at Asa. That is, for finid proportions,
capacitance is directly proportional to linear 14241, which in turn is a function
of rating, temperature and !roguing. Therefore, two transformers having
different ratings but the same capacitance have different sines and different
ships (determined kr Wave factor).
In order to deal with transformer else, it is necessary to obtain a
function of rating from which the effects of temperature use and frequency have
bow allseinated. This is done kr cam:.altift an equivalent volt-ampere rating
which is a measure of physical sise. This equivalent, based on 60 cycles fre-
quency and 40.0 rise has been shown (Contract DA 36-039 8C4519) to be
Vr
V(2-21)
r f % .76f AT %?.10
v.55..1 1.0.,
where f frequency, cycles per sec.,
AT= maxim= temperature rise, C.
The problems is to obtain apace factor IP as a function of equivalent
rating VI, and of secondary capacitance C. The stlrting place for each a
function is the capacitance formulas
1.35k
c co
C micro-microfarads, (9-2)
1
J.LI
2
? where mos w mean length of secondary turn, inches,
kc correction factor for secondary supports and any
dielectric between secondary and corei
1?1 a perimeter of remaining window space with primary
in place, inches,
F'2 0 perimeter of secondary cross section, around wire only,
inches.
19 equation (9-2) it is necessary to replace m?.. andFiAmo by functions
lr and Fe,. The derivation of these substitutias is brierly outlined.
re
To obtain a function for mcs, one relation needed is equivalent
rating in terms of geometry and space factor. This has been deduced from the
general transformer equation as it applies to low-capacitance transformers.
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?
?
e
kAi (F0A0
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3/4
(946)
where k al some constant,
Ai? core cross-sectional area,
Ac window area.
Another relation is needed to incorporate preferred transformer proportions. A
way of doing this is to require that core cross-sectional area be proportional
to total conductor cross-sectional area in the window. A suitable relation is
Ai ? 2.5 Folic
Nut; substituting for Ac in (9-16) according to (947) gives
"
VI* k Ai
?
?
where k is another constant.
(9-17)
(9-18)
From a study of transformer geometry only, it has been found that mean second-
ary turn is related to the areas and to space factor only.
( 2 + 4 fir; 2.8 Fc)
(9-19)
ripsaw, an epression for mcs is obtained by solving for Ai in (9-18) and sub-
stituting in (9-19).
w 2/7
"r
(2f is Pc+ 2.8 IV,
where k is another constant.
The ratio of Pi/ P2 in equation
winding space factor as
.66 1e16 F
In an effort to simplify the
closely equivalent to
.1
-2.6 sinh
x2
+ 1.3
(9-20
9-2) can be expressed in terms of
(921)
function, it was found that the ratio is very
Yre
/9
where sinh means hyperbolic sine.
This was obtained by expanding the denominator of (9-21) according to the bi-
nomial theorem.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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'
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.11.0. ? lerml 1111"."? I ?
?
JIM*
Therefore, trot equations (9110, (9-20), and (9-22), and by evaluation
of the constant using eppirieal data, one can obtain a copplicated but fairly
accurate relation among lc, Candi, 0
e
k01f1; 2/7
1.28 VT; in 2.6 slab (1n4n) (943)
. o e
.m.r....... _ ....
1 * 2 ifif + Lig Pc
c
blinding space factor F* is an =know quantity *Joh cannot be ex-
PliottAr found from (9-21); but rig 214 gives *plot of? vans the loft
side tern of (9-23). The fact that there are two possible values ofc for one
2/7A-
value of the ratio, ic**11 /V6 indicates that two designs mould give the re-
quired rating and capicitance. Of these, the higher?* 11111 yield the smaller
transformer. However, this snit may not have aufficialitiwindom creator in.
sciatica of the sectojarry, a factor to be checked in the design procedure.
Figaro 214 shove amnia= value for the ordinate or 032. This
Amu that then is a LIAAWI.i calpiaLtance which can be obtained for ow portion-
lar rating. If the calculated ordinate frau wattled rating and capacitance
exceeds We, then the conditions cannot be satisfied. This meadammiccours at
about?. 0 .051 corresponding to a ratio of porlaotors from equation (9-21),
of PIA: 0 5.50 For a certain rating, secondary capacitance viii be higher for
either ligher or lower space factors and ratios of perimeters. The almost
fist part of the carve Aare to varies hos about .03 to .07 is a region whore
deice of'et has little effect oncapacitance for a given equivalent rating.
Troia. t
Because desirable proportions of low-capacitance transformers vary
greatly vith requirements the geometric factors used in the basic design method
are not applicable. However, the definition of characteristic linear dimension
Is unchanged.
(24)
Eliminating first A0,
then 144 between equations (2-6) and (9-17) gives the
A
formless
_i*A 1137;
41412
V? c,
(9-24)
(9-25)
To obtain an estimate of total minding losses at an eari,y point in
the design of the-aveui4a-ngs, the following empirical equation can be used,
W ? 221- saw matte. (9-26)
Cs
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?
The forsola for circular mils per ampere whioh has been used in the basic pro-
ceihwe is satisfactory if the quantity, IWO X., (IA from (9-)5) is used in-
stead of lei Although the current density is 5asedwon secondary winding
t?esperatari rise, tests of modals show that reasonable values of primary rise
are obtained tor using spprodaately the same current density for the primary.
Nominal turns per volts should be calculated as in the basic procecture.
To correct for regulations it is recommended that nominal primary turns be un-
changed, but that nominal secondary turas be increased by the ratio We,.
This is a correction for resistance drops made entirely in secondary wimp,
cause most of the transformer equivalent series resistance is due to the
secondary, a direct result of the longer mean length of turn. No correction in
turns 'Wald be made at this point for voltage regulation duo to leakage-react-
ance voltage drop, because this factor is usually negligible.
Design Checks
After wire use, number of turns and physical leyout of the winding
have been determined, the design should be checked. Checks are of particular
Wimportance where values are critical or 'here quantities depend on rough
approcimattens. Insulation of the windings, especially from secondary to
primary and core, should be checked. For working (peak) voltage over 700
volts or .71114 the winding must be able to withstand a test voltage of
EV IL provW 4, 1 kilovolts, ANS,
T
where XVT a test kilovolts, RM86
XVw 0 working (peak) kilovolts.
(9-27)
411 Another important check is made to see that equivalent transformer
aeries impedance is less than load resistance. This requires calculation of
vioding resistances and of leakage reautanco.
A proper voltage ratio at the specified Iced is usually very impor-
tant. This can be checked by calculating the primary voltage which would yield
the required load conditions. Rpsistance and leakage reactance drops are
added to secondary voltage.
t /
Ito A, 42
Vp = VINYL; * n Is Rd2 4.17. volts (9-6)
where n = turas ratio, yWil,
ra = secondary volts'
I11 msecondary current, amperes,
R primary resistance, ohms,
Rs Is secondary resistance, ohms,
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? ???? ??? ? ???"??? 1111?1 11".... ? "P. "L'
I ? leakage reactance referred to the primary, elm.
A cheek of enroximate secondary temperature rise soy be mods ming
espotion (940 and the vsLimes el( from Table 214. Calealated secondary
losses are used far the tem If ?Approximate exposed sewed sty wean can
be fond from
8 is 2.5 an P2 sq?
es
(9-V)
ambers ?ean length of secondary tmrs, inches,
ace
P a perimeter of secondary cross sections around wire
2 only, imbue
The factor 1?5 is introdt bowman Pe is defined is net u large as the
effective heat-diseipating perimeter of the windizg.
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.....????????
X. INSTRUMENT TRANSFORMERS
Instrument transformers provide low voltages or low currents which are
proportional respectively to higher voltages or currents. The two types are
potential transformers which provide a low-voltage output, and current trans-
formers which provide a low-current output. These transformers are used for
measurement, protection and/or control of quantities in the higher-voltage or
higher-current circuit. The use of instrument transformers also avoids a direct
connection with high-voltage circuits and heavy, current-carrying conductors.
Therefore it is possible to measure electrical quantities with safety and to
connect to transformer secondaries meters or devices which have low-voltage or
current ratings.
Potential Transformers,
In the design of a potential transformer, it is necessary to keep
voltage-ratio and phase-angle errors within prescribed limits over the operating
range. These errors result from resistance and reactance voltage drops which
are functions of the load and exciting currents. At one particular load (load
is usually referred to as a burden of instrument transformers) the error in
voltage ratio may be compensated for by slightly increasing the secondary turns
or decreasing the primary turns. However errors will be obtained for primary
voltage or burdens different from the design values. Phase-angle errors cannot
be corrected or adjusting the turns ratio, but can only be minimised by special
design of the windings and core. Resistances are kept down by using sufficiently
large mire sues and by making the mean length of winding as short as possible.
The exciting current is minimised by using high-grade materials for the core
together with low flux densities, and by keeping the magnetic path as short
as possible. These requirements for reduction of errors may Appear to be con-
flicting. However, the errors in a given design can be reduced by an increase
in overall transformer sise.
of 115 %mitotic,
u---
rutamuLau torauguurmarer WOUSAAJ unvw a secondary rat4ng
In most lame= countries, the standard is 110 volts. Since the primary
voltage is usually quite high, adequate insulation must be used between the
primary and secondary utndings. Furthermore, since potential transformers are
frequently used with electric power distribution systems, overvoltages re-
sulting from faults, lightning discharges and switching may occur. Insulation
should be adequate to protect against unusual conditions,. The seeondAry is
usually wound next to the core. Core type or simple type construction with the
bindings arranged concentpieelirlis usuelly t4R100..
The design procedure for a potential transformer is the same as that
for a filament transformer. However the designer should be aware of the special
considerations which have been mentioned. Values of maximum primary voltages
should be specified. These include the voltage across the winding and the
maximum voltages to ground if one end of the primary is not at ground potential.
Then the highest working voltage is used to calculate winding apace factor.
Transformer power rating is the product of secondary voltage and secondary
current, which is the burden. The design can be calculated in the usual way
(as for filament transformers), and the final design should be checked to see
wheller or not ratio and illbnea-nnglaalma.
? ...its ,14.16 within limite. If not, then a
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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higher value oft should be selected, and the design repeated. In order to
keep the exciting current down, a high grade steel shwald be used for the core,
and a conservative or low flux density be selected. Omit calculation of core
dissipation per unit area and winding losses. Particular attention should be
given to cheeks at the completion of the design to insure that adequate in-
sulation has been used and that internal impedance drops are not great enough
to cause excessive voltage ratio and phase-angle errors over the specified
ranges of burden and primary voltage.
Oarrent Transformers
Internal losses and impedances also cause ratio and phase-angle errors
in current transformers. It is particularly important to keep flux density
and therefore excitation low in current transformers because exciting current
causes a deviation from the ideal ratio of primary and secondary currents, and
in additioN smiting *lariat is a nonlinear function of the primary lead-
current component. Current transformers must often operate within limited
errors over a large range of currents, such as to several times the rated
value of a circuit. One limitation on upper current values of the transformer
is set by saturation effects of the coreohich cause a radieal departure from
the nominal ratio of currents. Therefore, current transformers are designed
with low flux densities, which sq be necessary because of normal-load error
requirements or because of overcurrent ratio limits. For example, it mey be
specified that a transformer have a certain maximum error at rated current, and
that it will not saturate at 10 times rated current.
Magnetising and loos components of the exciting current may be limited
tly using high quality materials, thin laminations, and high egaliy joint, in
the core structure. **dal core materials are sometimes used which have
values of core loss much lass than for silicon stool. These special core
materials are alloys of 50 per cent nickel and 50 per cent iron, and nickel
alloys having small percentages of copper and molybdenum or chroad3a. If a
high degree of mum!' is not required, or if the current transformer is not
to be used to obtain the difference between several large quantities, a silicon
steel core nay be used with a flux density that enables operation to be well
below a point where excitation becomes appreciable. From the foregoing," it
is apparent that the application of the current transformer will determine
accuracy requirements.
The physical appearance and construction of current transformers is
quite different from most transformers since extremely large currents are
usually to be measured. Often only one primary turn is required. When this
is the case, the -core mig7 be tcroidamr shaped with A bar in the center or
simply a bole through which a conductor may be inserted. Since it is necessary
to open the heavy current carrying conductor in order to inert the transformer
with conventional current transformers, another type of construction whereby
the core nay be separated is sometimes used. An example of this type is the
typical elw-ontommter. Since butt gaps are present in the core, the
exciting current is increased. With this type of core or with a stacked core
it is not as eaay to achieve the same degree of accuracy as with a one-piece
Mmhislak
WW1 tabich the secondary windings are wound. A secondary current
of five amperes is standard for current tricastormers. WA& a ofte-tarnixteigtm
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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1
1
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taps are placed on the secondary winding. For current transformers where the
maximum current is less than several hundred amperes, a number of primaries
may be wound on one core together with a single secondary winding. The voltage
of the conductor of which the current is to be measured also influences con-
struotion. For examples insulating a high-voltage bar-type transformer is
readily accomplished by surrounding the bar with an insulating tube. For the
type which has a hole for the primary conductor, no additional insulation is
required provided the high-current conductor is adequately insulated,
The design procedure for a current transformer is similar to that
for a filament transformer. The transformer rating should be based on the
rated secondary current (usually five amperes) and the highest secondary
voltage which will be required for the impedance placed across the secondary.
Winding space factor may be reduced somewhat because of the insulation between
the primary and secondary and primary and core. If the core is of the wound
type, the geometric constants of Fig. 11-3 and 11-5 Aey be used. New geometric
constants may be estimated or calculated in the manner indicated in Chapter
II for other types. A low flux density should be selected. The value
depends upon the type of core material and accuracy required by the
transformer. Calculations of core exposed surface area, core dissipation,
winding exposed surface area, winding losses, and conductor weight can be
omitted.
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sum(ART OF DESIGN PROCEDURE AND TEMPERATURE RISE CALCUL/nal
This chapter includes the step-by-step design procedure as
developed on Contract No. DA-36-039 SC-5519, and in addition a method for
calculating transformer temperature rise as developed on Contract No.
Da-36439 SC-54710. The design procedure is applicable to designs for the
frequencies 25 to 2500 cycles per second, for ambient temperatures to 200?C,
and for operating temperatures to 200%. Thus the Bathed can be used in
producing designs for high ambient temperatures and low temperature rise, or
designs for low ambient temperatures and high temperature rise. In each case
the method should give a compact design having the minimum sue and weight
possible for the type of core chosen.
m!ely.st, poop Procedure
1) NgAlletise:
Frequency, voltages, secondary currents, rectifier filter
circuit (Where applicable), temporratures (ambient and rise),
regulation, grade of protection.
2) Chosen Quantities:
Type of core, grade and thickness of lamination, limits for
core loss and excitation, core rtack(ng ratio, typo of
construction (open, compound-filled, or oil-filled).
3) !moth Values:
a) Secondary rating Wr
gi V Ivolt-amperes,
r s s
where Vs secondary RMS voltage, volts,
I secondary MS current, amperes.
b) Allowable winding dissipation WiSc
Vic a (T) 1.25 watts per eq. in.,
(2-19) or Fig.
Macka-up Wes a winding losses, watts,
im winding exposed surface area, square inches,
*m
&La 1.04.0em Table 11-1,
AT 0 maximum permissible winding temperature rise, 'C.
Note: See Table D.-1A for most commonly-used conditions.
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c) Copper space factor Fo
Flo ? .08 log10 (WT.') F
W ?
(zzy .76 Ilf) ? 3
Wr
where W is equivalent rating based on 60 cycles and 140C rise,
Fr is factor from Fig. 11.2
f 0 frequency, cps.
AT ? maximum permissible winding temperature rise, 'C.
KW
) Nomograph scale A factor "
Aloe Ko from Fig. 13.-3, u=4, or 11-5,
f " given frequency,
ri 0 core space factor, as given by manufacturer,
le ? secondary rating, from 3a.
F W
e) Scale F factor
where
-
where F from 3c,
Wo from 3b,
? resistivity of conductor at design temperature,
the value from Fig. 11-6, increased by 2 per cent.
f) Select flux density B in kilolines per eq. in., from Table 11-2
g) Find characteristic linear dimension from nomograph, Pig.
11-7.
Note: The following steps h) and 1), can be omitted at this point
unless it is desired to obtain approximate core loss and
excitation. Then, following step 4, weight, core loss
and excitation would be obtained from manufacturer's data.
h) Core weight Mi
Mi a (K1 F 1.) 43 pounds,
114,
where K1 is from Fig. 11-3, u-4, or
F m core space factor, as given by manufacturer,
... steel dens mil
ity in e per cu. in., .276 for cold-
rolled, oriented silicon steel, and .272 for hot-
rolled, non-oriented silicon steel.
?1 is from 3g.
(infal! For standard laminations; weight is given by manufacturer's
catalogue)
(2-23)
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V
i) Core loss W1 and excitation W (to check flux density, B)
ex
Use core weight, material curves, and correction factors from
Table ll-3.
Use tible 11-4 as a guide for typical values of core loss
and excitation.
4) Core Dimensions:
a) Core exposed surface area Si
Si ? Ai $2 sq. in., (2-25)
where 12 is from Fig. 11-3, 11-4, or
$2 is from 3g.
b) Core dissilmtion per unit area Wi/Si
Use Wi from 31, and from
0) Core width (width x stack ? cross-sectional area)
L ? $ inches, (2-24)
where $ is from 3g,
1/$ is from Fig. 11-3, n44, or n-5.
d) Select a lamination haring a width close to the calculated value.
If a wound core is to be used, Skip this step and select a core
with an area product close to that obtained in he.
e) Calculate area product A0 Ai
A A so 414
o i
where Ac ? window area, sq. in.,
A4 ? gross core cross-sectional area, sq. In.
A
I) Calculate stack height, 6, for stacked cores
A A
c
aL inches;
where A A is found from he,
c i
A_= window area of the chosen lamination,
Lc = lamination width selected in 4d.
(2-6)
? ??
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410"???? ? ? ? ??? ??? ? ? ? ?????
5) Windini Calculations:
a) Winding exposed surface Sc
A02
So ? a3 sq. in.,
where K3 is from Fig. 11-3, 11-4, or 11-5,
4112 is from 3g.
b) Approximate winding losses Wo
Wc
Wo?
re? So watts
We
where iv is found from 31),
we
S is found from Sa.
W
c) Approximate per cent regulation ? ir 100,
where Wcs is from 54b,
Wrr is from 3a.
d) Conductor weight Mc
MO ? (K4 Fe OW
(2-26)
(2-27)
(2-28)
(2-30)
where Kt is from Fig. 11-3, 11-4, or 114,
4
Fc is winding space factor from 30,
C7 is conductor material density equal .321 lbs. per cu.
o in. for copper.
e) Circular mils per ampere
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Primary current Xp
..? Owlet 1111.-0 ? ". ? ?-?"...1.
Vi 0
where Vp
V
i
Vet ? winding losses, watts, fron
V' ? excitatdon volt-amperes, Iran 3i.
ex
Calculate wire sises in circular ails
-Cinman? wile
? given primary voltage
? secondary volt-mperes, from 3a,
? core loss, watts, from 31.,
implore
where circular ails per ampere is brat 5e.
aaperes j
Then select a wire for each winding fron Table 11-5.
Ii) Turns per volt /1/9'
105
7 al 4-31.77.--raci
? Ai 44 Alia
AIrv%I 110
f a frequency, cycles per second,
(2-32)
(2-33)
core pace factor, as given by manufacturer,
B * flux density in Wolimo per square inch, from 3.1,
A ? gross core cross-sectional area, sq. in.
) Calculate turns of each winding, correcting for regulation
Nominal turns tines voltage of the winding.
where
-17. is from 5k.
Correct for regulation by adding tens to secondaries and
subtracting Ur= from prim, using per cent regalatisrg
Iron Sc. In most cases secondary Urns are _Increased by
a traction equal one-half of the regulation, and prinny
turns are decreased by the sane fraction. However, exceptions
S EA siCit FOUNDATION OF ILLINOIS iriSiiTUTZ OE TECHNOLOGY
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ir-ed $ .* ??????
?
mey occur, such as when there is difficulty in providing an
integral number of turns for several windings. Calculate
any winding taps.
6) Maggai.A.P211.
a) Find 'winding width, equal window length minus margins
from Table 11-6.
bl) Find turns per layer from Table 11-5 and calculate
number of layers.
o) Choose a tube thickness from Table 11-7 and layer
insulation from Table 11-6. Check voltage stressos
if above 250 volts.
7) Check the Coil Build
?
Add 'bibs thickness, wire, layer insulation, wrappers, shield
(if any). The sum should be about 80 to 90 per cent of
window width.
8) Summarise the Design
List core material and dimensions, tube, winding wire sizes,
total turns, turns per layer, number of layers, taps, layer
insulation, wrappers, and shield data.
9) ........1(2mwkcd!gLOANLNIAetgEt!
a0 Calculate resistance of each winding, equal to resistance
per unit length (corrected to operating temperature from
Fig. 11-6), times mean length of turn, times number of
turns. Resistance also equals resistivity, times mean
length of turn, times number of turns, divided by wire
cross-sectional area.
) Calculate mean length of turn of each winding, which is
equal to the length of the inside turn of the winding,
plus pi times the build-up of that winding.
10)cl.....LofVoseRCheatio
Calculate primary voltage
n Pin + Is CR. + Rtobli volts
VP
where R and RL are obtained from 9.
p
Adjust the turns ratio if the calculated primary voltage
differs appreciably from the specified voltage.
ARMOUR RESEARCH FOUNDATION OF ILLimOIS INSTITUTE OF
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11) ecial..........__tE,...,?-CaltculaonsandChecks (When necessary
orwhen *value is close to limit)
a) Muting losses Ito
Vre st mot' =meat squared time resistance for each winding.
b) Conductor weigbt
MI equals length of conductor times pounds per unit length;
or, is length in inches times cross-sectiona1 area in
square inches times density (.321 lbs. per on. in.).
c) Ixposed winding surface area So
Add all outside coil WA and end surfaces except those
facing the core.
d) Calculate winding lose per unit exposed surface area,
using values from lla and 110.
e) rind core weight Ni from lamination handbook for appropriate
stack height. This is also
1111i ?aA1 Fi
where mi is mean length of magnetic circuit,
A ? gross core cross-sectional area,
(2-22)
Ii I. core space factor,
Si. ? care material density.
Use dimensions for actual core.
Check flur. density B in kilaineo per square inch, from (2-33)
105
B' 77?11"71711711171TT
g) Chock core loos and excitation, as in 3i.
arsposed care surface area S,
Add all outside edge and face surfaces of the core except
those in contact with the winding.
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Declassified in Part - Sanitized Copy
50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-9
? ',AM ? Vrut mr-ir J
bi4
) Core loss per unit exposed core surface 44:
ci
Divide Wi from Ug, by Si from 11h.
12) Emarison of,and Calculated Values
Compare values from the design method with the detailed checks
in step 32, when these are made.
13) calculation of Toparature Rise
See method in section following.
ARMOUR RESGARCHFOUNDATION
CF !I I IHOIS
"
%.# r
Ter?NO,LOGY
31,6
Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R00250019nnni_q
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
? ? ? ? ? ??????? ? -* ???? ?
TABLE 311-1
VALUES 07 X FOR APPROIDIATE TEMPERATURE-ESE EQUATION
;25
50
9:1
50
50
SO
50
65
65
65
65
65
65
75
75
75
75
75
85
85
85
115
125
125
125
125
125
200
200
200
200
cuu
200
60
200
boo
Soo
Soo
25
60
200
boo
2500
25
60
200
h00
800
2500
25
60
200
400
800
25 I
60
200
2500110
1
60200
I
400
800
2500
60
200
400
Oyu
2500
ggtizkr1 g/504ser 5gagex 4g5igsm Sg*4 54?8-t
92 107
95110
107 123.
119
129
131 1.51
06 100
90101$
101U?
212 129
122 139
1Z5 143
8396
87 :too
97 113
108125
in 138
914
85 98
951(X)
105 122
115 131
118 134
79 92
83 96
93 107
103 119
lio ioR
115 131
711 86
78 90
86 99
96 111.
103 119
107 123
63 73
66 75
73 85
81 94
68 .7u7i
104
ARMOUR RESEARCH FOUNDATION OF ILLINOIS
-117-
70
714
8%
98
307
no
68
72
83
10931
107
67
71
82
93
102
105
66
70
81
92
100
103
65
69
80
91
99
1,o2
63
66
76
98
58
61
70
or80
90
814 98
88 103
3.01 117
117 136
128w
131 1,52
81 914
86 100
99 10
128 lie
80 93
814 98
9813k
111 129
121 1111
225 11,6
79 93
83 97
97 33.3
U0 128
120139
LU LIU
78 92
82 96
96 112
109 127
111% 117
122 142
7992 8
76
3,13 131
1094 la
1 105
UT 136 1
80
85
98
322
121
1.04
107
.1.G14 I
69
73
96
58 69 80
62 71h 86
13 87 301
85 101 117
95 313 131
90 126 1314
56 67 78
60 71 83
71 814 97
83 98 Ilk
92 ED 120
95313,131
55 65 76
59 10 81
69 83 95
81 96 112
90 107 124
93 3.10 128
54 64 714
58 69 80
68 82 94
80 95 110
08 205 122
ma 1 04
7J. (
53 63 73
57 68 79
67 80 93
79 94 109
art 103 120
90 107 1214
50 60 70
54 611
Qs 76 88
7'5 89 1?3
83 99 10!;
85 1.01. 117
46 55 64
le 58 67
58 69 80
68 81 94
'
g A07 44
92
i
INSTITUTE OF TECHNOLODY
1
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R0025001-9-0001-9
111.111111111111111111.1
- Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
111111011N .
i...
Table 11p1A-Values of (AT/a)1.25 for Standard Co
Temp.
Rise
Deg C
1-
Ambient
Temp.
Deg C
____
?Ysqu'ina7
'* ape
Open
Ii=m06.
,ma=====
Compound
- -
Oil
core and coil
shsu
Simple
Core
Shell
Simple
Core
Shell
Simple
Core
40
110
115
115
65
65
85
85
-
60
400
60
400
0.476
0.358
1.95
1.46
0.384
0.294
1.52
1.19
0.322
0.247
1.26
0.975
0.50
0.352
1.95
1.36
0.438
0.278
1.55
1.10
0.333
0.232
1.26
0.895
0.625
0.417
2.45
1.12
0.50
0.333
1.95
1.31
0.416
0.278
1.62
1.10
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
????? ?????? ? T??.? rt 1111.-???? ? ????? T "T?TI
I
Table 11-2
SIXIOESTED Flail DENSITIES FOR SILICON STEELS AT URIC= MOINCIES
Material and
Core
?-"T
(Kilolines per square inch)
frequency - cycles per second
25 flo hoo Boo 1600 2530
Non-oriented
Steel, Stacked Core
Oriented Steel,
Stacked Core
85-100 80-98 60-95 45-65 25-45 18-35
95403 90-100 70-97 50-70 30-50 22.4o
Oriented Steel, 98-108 95.105 80-100 55.80 35-55 25.45
wound Con
Tab.11.1L1.
TYPICAL CCU LOSS AND EXCITATION OF TRANSFOMER CCM AS Plt:RCENT OF MEN
VALUES FOR SILICON SIM
saimmisswismilialawaremisse.
Material and Core
Non-oriented steel, stacked core
Oriented steel, stacked core
Oriented steel, wound core with two
butt joints
Core Loss
Percent
120-1140
130-160
lne
Excitation
Percent
150.300
3004000
Table 31-11
TYPICAL VALUES liDR MRS LOSS, EXCITATION, AND REGULATION
Rating,
ye22.1.11 frequency
lo
10
100
100
lu"00-5MX)
1000-5000
60
400
'I'
COU
Care loss,
te
10-20
3-6
4-8
Excitation,
;A-60
20.40
24-45
5-15
1-5
10 or less
Regulation,*
10-30
6.12
4-10
9_5
141
_3
* The data for regulation are confined to low temperature (Class A), low
reactance designs with unity power factor loads. In this report, regulation
is calcu3Atd using no-lmd and full-load voltages obtained with the windings
40. 4..11 1 okaA
a 10 InTaliptta auu&ao lei.P14.- a OF4JJ411.11.1160 41. 4.11.11.4. ..1110.11iIKIA, ?
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/09/06: CIA-RDP81-01043R0025001-96001-9
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
Table 114 - COPPER KU DATA
Oise
Ale
Area in
Circular
Mils
Diaiseter - Inches
it tome
Bona
Turns/inch
(1 Layer
Enamel)
0biss/100b ft.
at 20%
100% Cond.
Deeper
1000 ft
Aware
i Wire
1 lager
Snead
4 141,740
5 33,100
6 26,250
7 20,820
8 16,510
0
11 8:234 .0907
12 6 530 .0808
13 5ft, 178 *0720
107 .06
*203
*1819
.1620
.1443
.1285
*1305
.248
?333
.395
.1498
.628
.0927 4943
.0827 4842
.0738 4753
069 .0673
16 2:583 .0508 .0525 60539
17 2,048 .01453 .0469 .0482
18 1,6214 41403 .014.18 .0432
19 3,288 .03 9 .037 .0387 214
?
23. 810 .0285
22 624.4 .0253
23 509.5 .0226
2 0 0 .0201
10
11
12
1.260
1.588
2.003
2
126.4
100.2
79.5
63.4
50.d
269
39.77
15.68
12.
17
19
21
.0300 .0310
.0267 .0278
.0238 .0249
.0213 .0224
26 2514.1 .0159
27 201.5.0142
2e 159.8 .0126
29 126.7 .0113
30 100.5 .0100
31 79.50 .0089
32 63.21 .0080
33 50.13 .0071.
3 39.75 .0063
36
37
38
39
41
42
1.4?
25.00 .0050
19.83 .00145
15.72 .0040
12.147_.0035
7,04/7 .0011
7.84 .0028
6.22 .0025
4093 .00222
3.91 .00196
.0170
.0153
.0136
.0122
.0109
.0100
.0088
.0078
.0070
2
netroif
INVX1
.0050
.0045
.0040
fr
0M.15
.0031
.0028
.00237
.00213
.0180
.0161
.0145 67
.0130 75
.0116
.0105
.0095
.0085
.007
.0067
nntn
30
314
39
7.82
6.20
4.92
3.90
.0055
.0050
.0043
AN'S!
OVV0/10
4036
4032
4041.1141111116
12.80
16.14
20.36
2.67
a.47
64.90
81.83
2.45
1.911
1.54
1.22
94 130.1
1014 1644
117 206.9
131 260.9
146 329.0
162
Lii. 2ow
183 523.1
204 649.6
227 8i 8
296
326
38/4
416
.769
.610
.0484
.384
.241
.1913
?1517
.1203
.09514
.0757
.0600
.0476
1 -111.00199
?
...1.?4,
1,323 .02)74
1,668
2,103 .011493
0 tee NI 1 Ali
a 1...wiL .......-,
??
46 2.46 .00157 .00169
47 1.95 .00140 .00151
148 1.55 .00124 .00135
19 1.e227o0nli07 .00121
50 -.973.00986 .00108
ARMOUR RESEAMT
4111011?11.011
4111011WOOM
0104111.0,11.
6111.101110410
ded.101????????
4111?1110?611111
538
603
674
7142
830
14217
5,320
6,710
1.4n
?iv*"
1.0 670
39
.00745
.00590
.00468
.00371
.00294
Alldir???? ?
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
1
1
1 60
I
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
?????
Table 114
WM INSULATION AND MARGINS FOR MECHANICAL STRENGTH
AVG
1046
17-19
20-21
2244
2547
28-31
324.33
34-38
3941
424414
10.0
7.0
5.0
3.5
2.2
1.5
as.)
1.0
.7
.5
411111.00100111111110111111111110111101.1111101111111111!
Nargarii
each enek, incises
5/32
1/8
?
I.
?
Table u-7
TUBE THICKNESS FOR MECHANICAL STRENGTH
.1111?111111111111111.111101111110110
4.11111MIMONNIft
Ammlleat glove
DimegmLlaltEL,
&WWI, 4. LM.
mils of paper
4?11104.
1
to 1/2 10-20
1/2 to 5/8 15-30 I
5/8 to 3/4 17-3$
1
7/8 to 1
1 -up 30-50
25-45
A to 7/8 2o-ho
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
1
1
1 60
I
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
?????
Table 114
WM INSULATION AND MARGINS FOR MECHANICAL STRENGTH
AVG
1046
17-19
20-21
2244
2547
28-31
324.33
34-38
3941
424414
10.0
7.0
5.0
3.5
2.2
1.5
as.)
1.0
.7
.5
411111.00100111111110111111111110111101.1111101111111111!
Nargarii
each enek, incises
5/32
1/8
?
I.
?
Table u-7
TUBE THICKNESS FOR MECHANICAL STRENGTH
.1111?111111111111111.111101111110110
4.11111MIMONNIft
Ammlleat glove
DimegmLlaltEL,
&WWI, 4. LM.
mils of paper
4?11104.
1
to 1/2 10-20
1/2 to 5/8 15-30 I
5/8 to 3/4 17-3$
1
7/8 to 1
1 -up 30-50
25-45
A to 7/8 2o-ho
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
1
1
1 60
I
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
?????
Table 114
WM INSULATION AND MARGINS FOR MECHANICAL STRENGTH
AVG
1046
17-19
20-21
2244
2547
28-31
324.33
34-38
3941
424414
10.0
7.0
5.0
3.5
2.2
1.5
as.)
1.0
.7
.5
411111.00100111111110111111111110111101.1111101111111111!
Nargarii
each enek, incises
5/32
1/8
?
I.
?
Table u-7
TUBE THICKNESS FOR MECHANICAL STRENGTH
.1111?111111111111111.111101111110110
4.11111MIMONNIft
Ammlleat glove
DimegmLlaltEL,
&WWI, 4. LM.
mils of paper
4?11104.
1
to 1/2 10-20
1/2 to 5/8 15-30 I
5/8 to 3/4 17-3$
1
7/8 to 1
1 -up 30-50
25-45
A to 7/8 2o-ho
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
CORE
SKETCH
AND
DESCRIPTION
El
Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/09/06 CIA-RDP81-01043R002500190001-9
F1 G. 11-3 CONSTANTS FOR DESIGN
..., _ ....
/.................7
A
(
E.
..11161
r
.
,
Er:
z
...,
gq
...
,_...
..11411
....
I
L I
LI Lk,
WV L 11361t
Ith I
L
41'04L
S
L
SIMPLE TYPE
SHELL. TYPE
SCRAPLESS E - I SNELL TYPE
CORE TYPE
(TYPICAL.
PROPORTIONS)
(AVERAGE
PROPORTIONS)
VERAGE PROPORTIONS)
S
1
1
2
2 k 3
s
?
1 1.5 12.25
6.25
1.667
0.750
1.12511.50
1.87512.25
4.5
675
10.12
0.633
0.080
1.077
0.970
0.902
0.854O.81'7
..687
.6 21
;561
6.42
5.137
6.45
5.82.
5.42
5-13
4.90
8-35
7.55
6.82
6.42
6.24
6.00 ?
6.36
6.84
7.32
7.82
4.37
4.57
4.97
1.00
1.162
1.155
1.411
1.832
I.82E
2.00
.472
.578
.707
1.00
0.860
0.886
0:706
0.612
0.54
0.500r 2.12
1.732
1.414
16.9
12.22
13.02
10.61
9.20
8.23
7.51 29.5
25.8
23.1
16.9
21 .7
23.1
24.0
25.3
26.6
28.0 10.17
10.08
10.44
0.616
0.661
0.630
a 649
0.675
0.690.72O
.560
.554
.552
6.42
6.84
7.45
8.23
0.86
9.35
9.80 3.94
4.37
4-82
16.9
21.7
I 23.1
24.0
25.3
26.8
28.0 10.17
10.08
10.44
16.9
12.22
13.02
10.61
9.20
8.23
7.51 29.5
25.8
23.1
6.42
5.3.7
5.20
4.49
4. 19
4.01
3.91 9.27
7.12
7.03
785
842
803
826.
860
886
917 712
705
703
-1
22,500
19,370
19,480
15
13 = ?
1231C
11,250 47,7
I?800
All.
-
c,,i+i7art r.rInv Anoroved for Release @50-Yr 2013/09/06 CIA-RDP81-01043R002500190001-9
CORE
SKETCH
AND
DESCRIPTION
El
Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/09/06 CIA-RDP81-01043R002500190001-9
F1 G. 11-3 CONSTANTS FOR DESIGN
..., _ ....
/.................7
A
(
E.
..11161
r
.
,
Er:
z
...,
gq
...
,_...
..11411
....
I
L I
LI Lk,
WV L 11361t
Ith I
L
41'04L
S
L
SIMPLE TYPE
SHELL. TYPE
SCRAPLESS E - I SNELL TYPE
CORE TYPE
(TYPICAL.
PROPORTIONS)
(AVERAGE
PROPORTIONS)
VERAGE PROPORTIONS)
S
1
1
2
2 k 3
s
?
1 1.5 12.25
6.25
1.667
0.750
1.12511.50
1.87512.25
4.5
675
10.12
0.633
0.080
1.077
0.970
0.902
0.854O.81'7
..687
.6 21
;561
6.42
5.137
6.45
5.82.
5.42
5-13
4.90
8-35
7.55
6.82
6.42
6.24
6.00 ?
6.36
6.84
7.32
7.82
4.37
4.57
4.97
1.00
1.162
1.155
1.411
1.832
I.82E
2.00
.472
.578
.707
1.00
0.860
0.886
0:706
0.612
0.54
0.500r 2.12
1.732
1.414
16.9
12.22
13.02
10.61
9.20
8.23
7.51 29.5
25.8
23.1
16.9
21 .7
23.1
24.0
25.3
26.6
28.0 10.17
10.08
10.44
0.616
0.661
0.630
a 649
0.675
0.690.72O
.560
.554
.552
6.42
6.84
7.45
8.23
0.86
9.35
9.80 3.94
4.37
4-82
16.9
21.7
I 23.1
24.0
25.3
26.8
28.0 10.17
10.08
10.44
16.9
12.22
13.02
10.61
9.20
8.23
7.51 29.5
25.8
23.1
6.42
5.3.7
5.20
4.49
4. 19
4.01
3.91 9.27
7.12
7.03
785
842
803
826.
860
886
917 712
705
703
-1
22,500
19,370
19,480
15
13 = ?
1231C
11,250 47,7
I?800
All.
-
c,,i+i7art r.rInv Anoroved for Release @50-Yr 2013/09/06 CIA-RDP81-01043R002500190001-9
FIG. -5 CONSTANTS FOR CORES WITH SCRAPLESS Ut LAMINA7IONS
s
SI!'IPLE TYPE WITH SCRAPLESS
UI LAMINATIONS
1.0
3. 0
7G0
1.5
4.5
.639
9.12 8.26
5.43 5. 62
.579 .713
1.74 143
23:2 20.3
17.9 17.8
225
6.75
.620
7,44
5.98
.866
1.16
17.9
18.2
1.0
3.0
760
CORE TYPE
'.5
4.5
.689
2.25
6.75
.840
9.12
423
579
1.74
26.6
12.7
8.26
4.53
.713
?.44
5.01
.866
1.43 116
23.6 21.6
12.8 13.3
KO .630 .629
IK1 5.28 5.89
Ka 17,9 17.8
.623
6.44
18.2
526
5.26
12.7
.521
5.69
12.8
K 3 23.2 20.3
K4 9.46 804
K5 1314 802
Ks 59,900 31,600
17. 9
694
795
2 6,00 0
iiiiIIM11111111111111111111111111111111111
26.6
7.36
659
K 398900
23.5
6.40
662k
.516
6.44
13.3
21.6
5.81
660
31p00 26poo
6-1-0006 I- 009Z001?170 I- 0
FIG. -5 CONSTANTS FOR CORES WITH SCRAPLESS Ut LAMINA7IONS
s
SI!'IPLE TYPE WITH SCRAPLESS
UI LAMINATIONS
1.0
3. 0
7G0
1.5
4.5
.639
9.12 8.26
5.43 5. 62
.579 .713
1.74 143
23:2 20.3
17.9 17.8
225
6.75
.620
7,44
5.98
.866
1.16
17.9
18.2
1.0
3.0
760
CORE TYPE
'.5
4.5
.689
2.25
6.75
.840
9.12
423
579
1.74
26.6
12.7
8.26
4.53
.713
?.44
5.01
.866
1.43 116
23.6 21.6
12.8 13.3
KO .630 .629
IK1 5.28 5.89
Ka 17,9 17.8
.623
6.44
18.2
526
5.26
12.7
.521
5.69
12.8
K 3 23.2 20.3
K4 9.46 804
K5 1314 802
Ks 59,900 31,600
17. 9
694
795
2 6,00 0
iiiiIIM11111111111111111111111111111111111
26.6
7.36
659
K 398900
23.5
6.40
662k
.516
6.44
13.3
21.6
5.81
660
31p00 26poo
6-1-0006 I- 009Z001?170 I- 0
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410
FIG. 114-1 POWER TRANSFORMER NOMOGRAPH
DRAW A LIN FROM SCALE A TO SCALE F
NARKING MTERSECTION ON SCALE C. DRAW
LINE FROM TINS POINT TO SCALE O.
INTERSECTION ON SCALE 0 GIVES
,
.192]
os
D5
.04
03
.02 --
1
DJ
Ko Wr
Fit
2
2.5
3
4
5
6
9
to
15
40
50
60
Fr- 70
;T.-. 80
? 90
(00
150
200
SCALE B
??:
ft
f
SCALE C
61
SCALE 0
(VI)
10
SCALE F
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1
1
1:
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????
Calculation of Tesperature Rise
MO design of a power traniformer is complete without either a
calculation of its winding temperature rise, or a cosparison with previously
manufactured transformers to make sure that temperature rise will not be
excessive. The design method includes maximum temperature rise as a required
specification. Equation 2-19 introduces temperature rise into the design
calculations as one of the main factors determining size. The parameter, X,
from Table 11-1, is an average based on past experience with standard types
of construction.
The method of calculating temperature rise presented here is based
on an analysis of the heat sources within a transformer and the paths by
which this heat flows to the ambient (Contract No. DA-36-039 SC-500). AY
making some simplifying assumptions, the heat flow diagram of Fig. 11-8 can
be applied to any standard type of power transformer. The heat generated by
core and coil losses flows to the surface of the core and coil respectively,
and for open types of construction, it is then transmitted directly to the
surrounding medium. For encased types of construction, it flows from the
coil and core surfaces, across the impregnant, oil or compound, to the case.
From the case surface, the heat is transmitted by convection and radiation
to the surrounding medium. Conduction of heat from the case can also occur
through the transformer mounting. However, conduction losses are usually
small, and in any event, the transformer designer seldom has control over
mounting conditions.
There are three transformer temperature gradients that are important.
As shown on Fig. 11-8, these are the surface gradient, the impregnant
gradient, 04mm, and the coil gradient, Ow, Each is inderilhaent of the other,
but is depdaNnt on the type of construdion, and on the transformer losses.
For an open type transformer, Quip is zero.
1) Surface Temperature
The following equations are used to calculate the surface rise
over the ambient:
(Wic 4.i)
f g rgil-15:-T
9 F degrees C
surf sur T-c--E;)
hc m 3.75 x 101.3 'surf'0.22
(Sc + s1)0.17 P
3.70 x 10-3
hr e *surf
watts
we
in2
(amb)MT c-1(R) 2 Nr
Tar)
watts
(uA)
(1-2)
(11-3) or
Fig. 11-9
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6-1-0006 1-009Z001?170 1-0-1-8dC1I-V10 90/60/?1,0Z JA-09
eseeiej .101. panaidd /Woo pazwues - 'Jed pawssepac
e.1,1
OP
3f1001VNV
EIMINOASNVHI
COIL HOT SPOT
1-. n
n 0
ce, 2)Z
7 00 CONDUCTION BETWEEN
mc
on NAA/ 100.
-I
? .i?
CORE AND COIL
an.. NANO
67
F Z
ore
mm
AVERAGE
TRANSFORMER SURFACE
AVERAGE CASE SURFACE
I
I
I
x I. 8
I?
11 1 0 11
Cb ow
O Z
< a
O IP 4> C
C i -4
Z
4. 4 -44 .4, ? ...O. 11111.416.
AMBIENT
6-1-00061-009ZOM?1701-0-1-8dCll-V10 90/60/? I-0Z JA-09 ? eSeeiei .104 panaiddv Ado paz!l!ueS u! PeWsseloaCI
6-1-0006 1-009Z001?170 1-0-1-8dC1I-V10 90/60/?1,0Z JA-09
eseeiej .101. panaidd /Woo pazwues - 'Jed pawssepac
e.1,1
OP
3f1001VNV
EIMINOASNVHI
COIL HOT SPOT
1-. n
n 0
ce, 2)Z
7 00 CONDUCTION BETWEEN
mc
on NAA/ 100.
-I
? .i?
CORE AND COIL
an.. NANO
67
F Z
ore
mm
AVERAGE
TRANSFORMER SURFACE
AVERAGE CASE SURFACE
I
I
I
x I. 8
I?
11 1 0 11
Cb ow
O Z
< a
O IP 4> C
C i -4
Z
4. 4 -44 .4, ? ...O. 11111.416.
AMBIENT
6-1-00061-009ZOM?1701-0-1-8dCll-V10 90/60/? I-0Z JA-09 ? eSeeiei .104 panaiddv Ado paz!l!ueS u! PeWsseloaCI
Declassified in Part - Sanitized Copy A
where Wc
Wi
S
Si
proved for Release @50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
11,0 .111r."...
? ,??????
= winding loss, watts,
m core loss, watts,
0 exposed coil surface, square inches.
? exposed core surface, square inches,
? air pressure in atmospheres,
watts
h ? coefficient of free convection, sq. fn. W'
watts
hr 0 coefficient of radiation,
Tsurf ?absolute temperature of surface, *Kelvin (eC+273),
? absolute temperature of ambient, 'Kelvin,
amb
0 emissivity of surface,
Fella 0 farm factor of surface.
It will be noted that ho and hr used in equation (11-1) to calculate 0surf'
are themselves functions of One. This necessitates a trial procedure,
whereby an assumed 0 f is used to find holy which in turn are need
to calculate One. If the calculated value is not close to the assumed
value, then the calculation should be repeated.
In an attempt to eliminate all further trials beyond the second,
a guide has been devised* for selecting the second assumed value. This
guide, believed to be sufficiently accurate if the first calculated value
is less than the first assumed value, is
gsurf ?Nassumed+e9Qcalc.
where
(11-4)
0surf is value to be used for the second trial,
gassumed
0 is
ciao
is initially assumed value,
the result of the first calculation.
Figure 11-10 gives the ratio of () to %ale the correction factor to be
applied to ?cox, as a function of 0assumed to Ocalc. Equation (11-4)
defines the curve only above (1.1). The accuracy of the function of Fig.
11-10 belay (1.1) has not been well confirmed. The first assumption for
Osurf(which is gassumed) should be somewhat over half, such as 64 per cent,
of the maximum permissible winding temperature rise, so that the
Fig. 11-10 will be greater than 1.0.
ahaci AAA
* MY. I. Remis of the Signal Corps suggested this guide.
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nf
4111**0+
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6-1-00061-009ZOOIC1701-0-1-8dCll-V10 90/60/C1-0Z -1A-09 ? eSeeiei .104 panaidd /Woo pazWueS u! PeWssepaa
CCI -
(hum (FINAL VALUE)
Ow, OST GALC. VALUE)
1100
IOW
0/.41
110,0
?
?
6-1-00061-009ZOnIC1701-0-1-8dCll-V10 90/60/C1-0Z -1A-09 ? eSeeiei Joj panaiddv Ado Pezq!ueS u! PeWsseloeCI
Sanitized Copy Approved for Release
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? MP'. vo?-?? ? ?-?? ???? ?-?- ? ? ? -?????
The following tables give values for e and F 1.
Table 11.8 - EMISSIVITY OF SURFACES
Surface
oil paint (any color)
enamel (any color)
varnish
black lacquer
aluminum paint
dull sheet steel
Emissiviti
0.92 - 0.96
0488 0.91
0.88 ... 0.91
0.80 0.95
0.27 ... 0667
0.80
VINO
Table 11.9 - SURFACE FORM FACTORS
Tree of Transformer
Open (shell or core)
Potted
Oil-filled
In using Table 11.8, the value of emissivity to choose within the range for
any particular surface, depends upon the glossiness of the surface. Dull
surfaces have a higher emmirkrity.
2) Gradient Across Impregnant
a. Compound-filled transformersi
/4averagemwaoa. ?amnarntmr* drop, 0 across the compound of a
potted transformer can be expressed as:
Oi +?
Gimp Es Pimp ; c degrees C,
WAVOAU
..UsWOM
(11 - 5 )
in average thickness of compound. 441u140.,
S m average area of compound, square inches,
k m thermal conductivity of compound, Twatts
in. ee
F m correlation factor.
imp
Thea average compound area is defined as the mathematical average of the
case surface area and the transformer area.
1
S -1- (Scam+ SC +5i) square inches.
(11-6)
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11$
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I.
1
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? an 'OEM ? Irv. "Ir.-.
1. ????
The average compound thickness nis is defined as the difference between the
radii of two spheres whose areas are equal to the surface areas of the case
and of the transformer.
An empirical value for limp is 1.75. This applies to transformers potted
in rectangular cases such as the MIL T-27 series. Typical values for the
conductivity of potting compounds are given in Table 1140.
Table 11-10
ram =mum OF POTTING COMM
44.
bitunin
bitunin - 45% silica
bitunin 55% silica
watts/in.?C
.008
.015
.016
b. Encapsulated Units:
Transformers sealed in plastic compounds fall into the same class
as compound-filled units. If the final shape is rectangular, an 74mn gg 1.75
would apply. If the transformer is coated with a =ifs= thiclamervof
gastic,r01.0, and sequels the actual thickness.
c. Oil Filled Transformers:
Accurately predicting the temperature gradient across the oil in
a small oil-filled transformer is Te27 tumult. In any specific trans-
former it is difficult to determine the percentage of heat being transferred
through the oil by convection and that transferred by conduction.
However, there are equations giving appmxichmate results. If previous data
are available for a particular transformer the oil gradient may be found
from the following equation:
m C +1.25 degrees C, (13.-8)
where
W m copper loss, watts,
if core loss, watts,
4
C = constant.
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_-
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Declassified in Part - Sanitized Cop
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ow,
yr.* -ar?-?,. I -- ?.
The constant, CI is found by substituting previous data into equation 11-8.
The following empirical equation may be used for a transformer
filled with an organic insulating oil such as %moo C" (Westinghouse):
0 IN 130 (We + Wi).78 degrees CI (11-9)
S s oil area from equation (11-6)
it in oil thickness from equation (11-7)
3) Gradients Across the Coil
a, Coil hot spot:
For the usual case, the hot spot of a coil is located in the center
of the coil cross section. The gradient from average transformer surface
temperature to hot-spot temperature may be found frms the following:
0 F Wx ( m )7 decrees CI (11-10)
h 0
where
0 im coil hot spot to transformer surface gradient, degrees C
copper loss, watts,
0 -
m m distance from coil surface to hot spot (assumed to be 1/2
coil build), inches,
k m coil conductivity, wattelin.?C,
c exposed coil surface area, square irAbAn,
F, x, 7 are parameters dependent on construction.
Typical experimental values for F, x and 7 are to be found in Table 11-11.
Table 11-11
COIL GRADIENT PARAKETKRS
TYPe
open
potted
oil
AMMO
1.2 .85 1.4
.32 1.0 2.0
.32 1.0 ' 2.0
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4......?????????? ? 111.?
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.? -sow ??11.S. '111?1111 ??????? ? ? ? ???? ? ?? ? ,f
The thermal conductivity of layer woOd coil is gins by
R+1
kmk( mr-rr.,)
k ? coil conductivity,
(u-u.)
R ? ratio of bare wire diameter to total insulation thickness
per layer,
watts
k ? thermal conductivity of composite insulation,
The total insulation thickness used for R means the interlayer
insulation thickness plus twice the mire radial insulation thickness. The
thermal conductivity of the composite insulation refers to an insulation
which is equivalent to the interlayer insulation, plus the impregnant, plus
any voids. A typical valuastaki for a varnish impregnated coil with kraft
paper insulation is .003 EiFIE.A.
b. Average Winding Rise
Temperature distribution throughout a winding is such that the
average minding rise over the transformer surface temperature is directly
related to the hot spot rise, depending on the location within the coil of
the particular winding.
Ow ? Ch degrees C,
Ow ? average winding rise over the trnasformer surface
temperature, degrees C,
C ? constant.
If m is the distance measured radially from the first layer of
a coil to the surface, Table 11-12 gives values for the constant, C,
depending on winding position within the coil.
Table 11-12
AVEPAriE tirlartruri RISE PAHORTER
mar&
0Qpen
0-50
50 - 100
0-25
25 - 50
-
75 . 100
natant,
Potted Oil-Filled
.90 .90 .80
.80 .65 .60
.80 .80 .67
.97 .97 .93
.99 .92 .86
-..
.62 .1j2 .35
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4) Summary
To find the temperature rise of agy particular part of a transformer,
it is necessary to add up the gradients from the ambient to the part for
mhich the rise is required. Adding the ambient temperature to the rise gives
actual operating temperature.
For example, the hot spot rise over ambient equals:
m ?surf * Gimp *
The hot spot temperature equals'
Th m Taab * ?surf * Qimp * ?IC
If the primary of a particular transformer occupies the first
half of the mil, its average temperature is
Tpri m TaMb * Qswrf * Gimp * Qh. (11-15)
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.1
.1
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?
=Moil iQuittunis
W
is
Fair?
aL
8 i?
mi
tr
? ? ? ? a 3
ri.6i.
411111111POMMUNIMMIIIIIIIIMMI,
Core loa abound
Wi
PONNIMP
111 0.16. 117if
Wax
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? ? ....wow ? w
Or. ??? a ? ? ". w ? ? ?
Table U-13 (Cont'd)
DEIGN MATIONS
+ wo + w
03(
Layers in primary
Layers in secondary
Coil Build:
Tube
layers of wire (
layer of paper (
Mpper
layers of wire (
layers of paper ( )
WIPPer
Build
N 4. vp(3. - Tr-
N we
v(i+
V 5 Wr
Winding length
Primary turns per layer
Secondary turns per layer
N r
# I V 4. (R R /1121
Pi p
"s -
wwwwwWWWW.
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? ????????!..1 -WV W
=atm= eacuunots
?3.75 3t 10
.22 .1414
0
surf
4, 8
Ii
vicase S 1/0
8+ Si
w 111
? x 11 Tomb 11
("Efrari (lar)
sun
Fort
0
calculated
%ROA')
(wit, wi)1.25
:L
Tr:Tvir
T +0 C
Tavg sec rm surf+ imp s h
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..,???????? ? "MO." Virg, Nr-.. "4".. ??? -???
XII. DESIGN PROCEDURES PREVIOUSLY FRESI4TE0
The three types of transformers considered in this chapter were
analysed in the final report for the previous Contract, No. DA-36-039 HC.5519.
In order to stake this report as inclusive as possible, abstracts of the de-
sign procedures for filament transformers, autotriaisformers, and rectifier-
supply transformers are presented in this chapter.
Filament Transformers
The design of filament transformers is carried out following the
procedure given in Chapter XI. Temperature ride may also be calculated
according to the method given. Normal-tiype filament transformers, isolation
transformers, or mq, single-phase type where each output winding carries
sinusoidal ...rrent, and where sinusoidal voltage is supplied across the
primary may be designed. Current-limiting filament transformers are con-
sidered in another chapter.
Autotransformers
To apply the procedure in the design of an autotransformer, an
equivalent two-winding transformer rating must be determined from the auto-
transformer rating. This equivalent transformer becomes the autotransformer
merely by proper inter-connection of windings. The rating of the equivalent
two-winding transformer is
(vV v W volt-amperes,
(12-1)
where W 111 rating of sutotransformer,
ra
v
'2 ?smaller sutotransformer voltage,
(V1 + v2) a larger autotransformer voltage.
The voltages of the equivalent twouomindire transformer are Vi and Vo When
the autotransformer increases the input voltage, the primary'voltalof the
equivalent two winding transformer is Vo s Vi, and the secondary voltage of
the equivalent two-winding transformer is Vs s Vi " (V' v2) - V20 When
the autotransformer decreases the input voltage, then Vio Vi and-Vn w V2.
Similarly I and 12 (in the windinge with voltages V.. Ad V, respectively)
,mommimil111 are the baa current components in the equivalent two winding transformer.
However load current to the high voltage winding of the autotransformer is
and load current to the low voltage winding is 12. Thus neglecting
losses and excitation, the volt-amperes of the two-vinding equivalent trans-
former are
lir a V1/1 a V212J
and for the autotransformer as connected, are
Wra (Vi + V2) a V2(1.1 t
(12-2)
(12-3)
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???? ????? ,???
ma. ? ...vs. ?IIP?1 '?ir."" ? ?
From equation (12-1), it is seen that if the voltage ratio of an
autotransformer ware two, the equivalent two-winding transformer has a nominal
rating equal half that of the autotrargformer. The advantage in reduced
physical she and reduced equivalent rating for a certain output rating, as
obtained with an antotransformer, decreases as the voltage transformation
ratio increases. This can readily be seen from equation (12-1), in that the
ratio iterthtspproaches =IV for large ratios of (T1 ? 1,02. Ce the other
hand, w s voltage ratio is vary close to unity the ratioWrt becomes
very mall, and the cams turns would consist of comparatively . wire
relative to the 1/1 winding. The rating Yr to be used in the design should be
increased to accomodate no-load current if the voltage ratio of the ante-
transformer is very close to uatti, such as within 25 per cent. When the
voltage transformation ratio is close to two, the current is almost the same
in all turns of the transformer, and one winding, tapped near the center turn,
satisfies the requirements.
Secondary current is:
Is a 1r opereed
s
(12-4)
If a tap is to be made on an autotransformer winding, the tap wire size must
be large enough to carry the rated output current (rather than a winding cur-
rent) of the autotransformer.
Primary current is:
1 1its Vir LS a * 2,2 2 2
vwr
e^ a
? weres? (2-32)
When exciting current flaws through the entire wilding, extra con-
ductor area may be required in both primary and secondary of the equivalent
two-ivinding transformer. If the low-voltage winding were the primary, than
only the lower half of the autotransformar winding carries the exciting cur-
rent.
ltth the exception of exciting current considerations, the design
method for an autotransformer (by my of the equivalent two-winding trans-
former) is the same as that for a filament transformer. Choice of winding
apace factor should be made using the equivalent rating W, and the highest
working voltage of the actual autotransformer,
Rectifier-Npply Transformers
Cnly rectifier transformers for balanced operation will be con-
sidered. The treatment of unbalanced operation, such as with a half-wave
rectifier, is presented in another chapter. The design precedure for recti-
fier-supply transformers is precisely that given in Chapter XI with the fol-
lowing suppiementa.
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????
+11....0?111.1.
1) Specifications should include type of rectifier and filter.
2) lir as Vs Is, secondary RMS volt-amperes.
Vs is RNS volts across the entire secondary. For the full-wave
rectifier, Vs is two times the factor of Table 12-1 (or Table 124) times
DC load voltage. For the bridge type, Vs is one times the factor of
Table 12-1 (or 124) times load voltage. Add secondary circuit voltage drop
to D-C load voltage when using Table 12-1.
Is is INS secondary current. For the full-wave rectifier, I is the
factor of Table 12-1 (or Table 12-2) times DC load current. For the bridge
type Is is the factor of Table 12-1 times load current, but for capacitance-
input filter, Is is 1.414 times the factor of Table 12-2 times D-C load
current.
It is 0010011 practice for a designer to be given specified values
of RNS secondary voltage and D-C load current. His work is easier if he is
given all transformer MS quantities.
3) Calculate primary current from equation (2-32) for the bridge-
type rectifier.
For the full-wave rectifier, calculate primary current from
AAUP
I
p r
(.707 * vi 4 110)2 w 2 . wi2
ex amperes. (12-5)
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1
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....,..??????
? .611?9?111 41?....? ? ?
N N N
A10A N N N CO 09 GIP
OM in in r4
? ? ? ? ? 4 0 ?
ri el el rI4 r; r4 r4
AA88 AA10
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r4 r4 ri r4
AA
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r4 ri r4 r4 r4
041 410%
g st ID; a 43
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AAR8 .17.A.A.gr.Sgia
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r-lrlr4r4r1 r4 rlr4r4r4
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aitri PP Z
42 b r &I VI . ?
1 cti ii? r4 5 5 44 14 Iwo
1: 2 o IC
I 000 inekFiLk I .0 o 0 I-1
a as vi
go 4
? op O' o o 43
xi
42 42 W1
l
ID 4,5
. - po 111 ID $4 Pi al 01 0
? ? r? P? / I i g? 1 r143 ? 43 V
1 0 0Ail 1^ )1 w i
d 0 ? " el r4
CA) 0 0
?
A A A 42 41 4) to ? r-1
42 b
^ a S
llCO... CO ri g ri
0.0o
bo
00 .5.1
I
?40 .?44'v V 6 ?ri U
b b F.. e ? ?
fp 0 vf 0 .
I !4?
014
4r4 CO P4
to 41) 14 TOW ft CI ftU)4r4. 2 It A
..., *
ARMOUR RESEARCH FOUNDATiON OF ?ILLINOIS INSTITUTE OF TECHNOLOGY
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?,?????? 4..ur "tr.. a
?
Table 12-2
RATIO OF RMS SECONDARY CUIRFNT TO AVERAGE LOAD CURRENT FOR
FULL-WAVE RRNIFIER
f?MNIUMM?1???
R 6 Series Res.
cLoad Res.
5
.0002
,001
.005
.05
.25
.790
.790
4,790
.790
,a90
.90
.90
.88
.85
.83
1.40
1.37
1.35
1.20
.95
2.30
2.00
1.68
1.21
98
2.80
2.25
1.74
1.23
1.00
Table 12-3
RATIO OF PEAK SECONDARY CURRENT TO AVERAOE LOAD CURRENT FOR
FULL-WAVE !mama
. Series Res.
".15r
c Load tee. *
st
? t111110111111111100.111111111111111115
1?01111MINIMINIMMINN7r1111/M11111111111111111.11111?UNIMIlI50
g0
allIMMOINIINOWIN
.0002
1.57
1.90
.001
1.57
1.85
.005
1.57
1.80
.05
1.57
1.80
.25
1.57
1.75
5.75 13.5
9.5
6.5
3.2
2.3
5.50
4.75
3.05
2.20
17.0
10.5
6.5
3.2
2.3
m-ul. la_L
Lawiam m4.c.-44
RATIO OF RMS SECONDARY VOLTAGE OF HALF TFelimoTNn TO AVERAGE LOAD VOLTAGE FOR
FULL-WAVE RECTIFIER
. Series Res.
ma Res.
1.0
Itatio
10
JLVVV
.005 1.13 1.06 479 .73
.02 1.1 1.07 .80 .78
.10 1.22 1.15 .95 .93
.25 1 ce 1 Ln
.1.0.02 .1.6moc 1.48 *Iola
.50 1.65 1.62 1.48 1.47
.72
.78
.93
1.0
1.47
R is total series resistance in one branch of rectifier circuit excluding
load resistance. This includes secondary resistance from center tap to
one end, resistance from end of winding to one side of the load, and
resistance from center tap to the other side of the load.
C is shunt capacitance across load.
f is supply frequency.
1.11111?JIML11.11/111J
ry r ra to rs yho %Or
LO: C te? ST TIFc14NOLOGY
-146-
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I
II 1
i1,1 1 1
I
I
;
I :
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
? "WM yr... ??? ???
WI. =SION PROCIOURE: TRIdiSFOHNIN WITH WIBALLIICED NAGNITIZATI(1
1) Specifications
Frequently, voltages, load and filter requirements, temperatures
(mettent and imudaum rise), grade of protection.
2) 0.1.11...t....oseies
Type of core grade and thickness of lamination, core space factor,
preferred stack ratio, type of construction. Factors to be con-
sidered in the choice of the type of care are extensively discussed
in the final mart for Contract DA 36-039 3C-55l9, Chapter VII.
3) EENEWOR!!!
Secondary MS current:
Is is average load current Ipx,multiplied by 1.57 if no filter
is used, or multiplied by a ratio frau Table 13-1 for a
capacitance-filtered load.
Secondary HMS voltage (minding eupplying rectifier):
V is average load voltage he plus rectifier average forward
drop and other circuit voltage drops vultiplied by 2.22
if no filter is used, or hc multiplied by the ratio frau
Table 13-3 for a capacitance-filtered load.
Equivalent secondary rating:
Wis = %In + 0 0 0 volt amperes,
where 142, etc. are the ratings of any additional secondary
vindings supplying balanced loads.
Winding dissipation:
1.25
(I) watts per sq. in., (2-19) or
Fig. n-a.
'Winding space factor:
r .o8 logio Wr 2-20)
Nomograph scale factors:
W F W
e
c"'" s
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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11
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
? 110,110 .0.???? 0 ? ? ???? -
Flux density:
Select flux density using a value from Table 11-2
decreased about 10 to 15 per cent according to the
percentage of the total secondary rating which is
supplying an unbalanced load.
Characteristic linear dimension:
Use nomograph, Fig. 11-7 to obtain 2.
Approximate core weight:
141. ? 11 Pi s
Mean length of magnetic circuit:
mi ? inches.
Approximate secondary turns:
s a 16 Vs
N 0 turns
f FiBk
Approximate unbalanced magnetizing force:
.1495N 'pc
IM ' average oersteds.
Core loss, excitation, and gap
Use design curves, Fig. 13-1 through 13-80
to calculate W, IL, and non-magnetic gap.
4) Core Dimensions
Area products
6.
A a
liamination leg width:
L 4 ..
" "e"Male...a aLl S
Window area:
(2-23)
(2-7)
(2-34)
(5-19)
Calculate A from lamination dimensions.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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'Orme -ar?mr a
Core orose-sectional, areas
Ai --rde.--11 eq. in.
Stack height
Ai
Stack ratio:
a is
?
inches.
Core exposed surface area:
A
? 1224 sq. in.
Core dissipation par unit area:
8 watts per sq. in.
5) Wixtdini Calculations
Winding exposed surface:
A 2
fk, ? L sq. in.
3
Approximate winding loses
W -- watts.
c
Conductor weight:
P c 13
ZIGiLk a
C C
Circular mils per ampere:
Primary component of load volt-area:
(2-25)
(2-26)
(2-27)
(2-30
(2-31)
s
(5-11)
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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If
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? ? .......???????? -""*.
Primary current:
1 I
I la ar Npief Vr2 * Wo WI) 2 =pares
P p
Increase In up to 10 per cent according to the mamber
of seooldaries which are mapplying unbalanced loads.
Wire sizes:
???.* ?hel.i. 111,1111 ?II I ?? ????? T ?
I.
(5-20)
Calculate from circular mils per ampere using primary and i
.
secondary EMS currents. 1 t
. 1
Turns per volts 1
I 105
ar ? raw turns per volt. (2-33) 0
Turns:
(1..
P P
N mv if (1.
?
.707%
.) turns.
.707W
L).
gwr
For capacitance filter, replace .707 by in equations (5-21).
(5-21)
6) WiningLqout,
Winding length:
Window length minus two margins.
Turns per layers
Appropriate turns per inch times winding lamtb4
Layers:
Appropriate turns divided by turns per layer.
7) Check of Coil Build
Choose tuba, layer inAniations and wrappers, and check build to
insure that it is between 80 and 90% of window width.
8) Sthamarr of Design
List core material, dimensions, weight, tube, winding vire sizes,
total turns, taps, turns per layer, number of layers, layer
insulation, wrappers, and shield data.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
- 15o -
1
IN7
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
3?"
t
1
I
1.11..1.1111?11?
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9 ?
Irma ?vor--* ? ???? ? ?
9) Check of Wading Resistances
Reststance equals resistance per unit length (corrected to
operating toperattuie fraa Fig. 11-6), times mean leaigth
of tarn, tines miser of Urns.
Keen length of turn equals length of inside Wm, plus
pi time buildily of winding.
10) Check of Voltage Ratio
Calculate primary wattages
v- n [V* + 1.1 ID (Rs Rin2?)
P C volts
where Re and Rp are obtained frail step 9.
Adjust the turns ratio if the calculated prism' voltage
differs appreciably from the specified voltage.
Ll geoid Calollations and Design Checks,
Apply when necessary
12 Calculation of Tasperattue Rise
Follow basic method.
040
III
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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????? ?????100 ? ? T.
? ?????? 'WINO ?ler,. ? -? ???? ?????????? ??? ??--??1 ? ?
.? ?
Tab.11.4:1,.?
RATIO OF DS SECONDARY CORM TO AVERAGE MINT FOR
IIALF-WAVZ RECTIFIER
R Series Res.
nc SgrwS17.
dawa"."1.1";1011
'Oa
.005
.05
.25
owomeMilail=0.0NOMMINITTIOMMONIIMOTrilmamileamm?MWOM?mmenisimilnirlift?ONIO
741a-""7760""'
1.58 1.80 2.75 4.00 4.50
2458 1?75 2.70 3.37 3.48
1.58 1.70 2?40 LW 2.45
1 1.6 1.0 1 2.00
;able 13-2
RATIO OF rEAK SECONDART CURRENT TO AVERME CURRENT FOR
NALF-WAVE RECTIFIER
Series Res
11 =Mrs Xi-- 1.0 .io31.0 Volt
5J 11.5 ii 34
.001 3.114 3.7 1140 19 21
4,005 3.14 3.6 9.5 13 13
4,05 3.14 3.6 6.1 6.3 6.3
Table 13..3
RATIO OF 8143 SECONDARY' VOLTAGE TO AVIRAGE LOAD VnTATAnE POE
HALMILVE RICTIFIER
???????111?????????
0?110?101?01111111001111111???1110111111MNIMINIMM?
a*?11101?? ?????????1~1??????01?1101001.NOWINIallle???
r eiklieries Res.
416wim
.02
.10
.25
.9a
?
1?V
100
464 I
2?18
2.45
345
3.3
wwar
1.91 .94
2.02 144
2.38 1.54
2.9 2.08
_
.83
1.09
1.49
2.02
11
4011, 40,W
Notes: R is total Series resistance in rectifier, circuit excluding load res-
istance. This includes transformer secondary resistance and res.
istande from ends of the winding to the filter capacitor.
C is Shunt capacitance across 1-"..
F is supply frequency .
If insufficient load. eireuit data are available,
used: V'il/V:Do a 1.); 18/1.6c a 2.
typical values may be
RCSEADri4 FOUNDATIO-N OF ILL!Nnt$ INSTITUTE OF 1ECiiii0LOGY
-152-
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I I
CORE:
STEEL:
I
WOUND,
BRAIN
I
TWO
- ORIENTED
BUTT
JOINTS
SILICON,
12
MILS
.................................
218,
AVERAGE
H
?
de
..
OERSTEDS
Jde
IS
-r
414?
c)
12
1
111
/ 4:51,e9
1
A
i?1
0.
4%
4
, .
.
v 1
.?LegroC24...........A.c40,1r.......+,.......t...........r?m
_...i
?os#:.4.27?01-
1
py...3..r. _,;i4,,H;c2?01
oleo
1 1
A
-.?...........---.
.
_
60 80 100 120
glirITATInN AND GAP FOR WOUND CORE. ---
DESIGN CURVES (60 CPS)
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
?353 ?
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Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
?
2.
I.
0
40
CORE:
STEEL:
WOUND,
GRAIN
TWO
-ORIENTED
BUTT
1
JOINTS
SILICON.
1
I 1
12
I
I
MILS
I 1
I
Hoc118,
AVERAGE
15
OERSTEDS
001
AA H0c s
0
; AlArr
k"%iHI
4...........................?
//zy
1 1
60 SO 100 120 140
A-C FLUX DENSITY - KILOLINES PER SO. IN.
-
FIG. 13-2 CORE LOSS OF WOUND CORE
DESIGNCURVES (60 CPS)
tig NOW=
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Declassified in Part -Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
140
CORE: LI LAMINATIONS
STEEL: NON-ORIENTED, AISI-M -IS 14 MILS
120
1
EXCITATION
issoinal
20
HOC z?1 I
.1 oio 444)
ru"--1 I Plt-
eaLl\I
40 60 80 100 120
A -C FLUX DENSITY KILOLINES PER SQ. IN.
FIG. 13-3 EXCITATION AND GAP FOR STACKED CORE-
DESIGN CURVES (60 cps)
ARMOUR ItSSSARCH FOUNDATION OF ILLINOIS INSTITUTS OF TICHNOLOS?
111
11111111111111?beclassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R0025001gnnm_q
? '
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CORE LOSS - WATTS PER POUND
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
.s
A
;IT
, ?????? ? ?????
.??? ????? ? ???gm Vella Mr...^. a * ??? ?????-? '?????.41
.6?1
CORE:
STEEL:
EI
NON
LAMINATIONS
-ORIENTED,
AISI
-M -
15, 14
MILS
Hoc 16
?
Hoc'

6
Hoer)
Illyry
Pr
OF
AaLi
r
1
LA
0
40 60 SO 100 120
A- C FLUX DENSITY - KILOLINES PER SO. IN.
FIG. 13-4 CORE LOSS OF STACKED CORE -
DESIGN CURVES (60 CPS)
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
ISO
140
120
0
X
3
0
a.
1I00
80
60
40
20
01 I
MN,
111/71111 1.11^".?
8 AVERAGE
OERSTEDS
CORE: WOUND, TWO Bun JOINTS
STEEL: ORIENTED, 5 MILS
rA
?.011? 401'
Z
i?-?? - -wow
fkitb
20 40 60
80
100
A - C FLUX DENSITY - KILDLINES PER SQ. IN.
FIG. 13-5 EXCITATION AND GAP FOR WOUND CORE
DESIGN CURVES (400 CPS)
UWE
?
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-9
a
0
a.
0
4
2
I.
I
CORE:
STEEL:
WOUND,
ORIENTED,
TWO BUTT
5
I
NILS
I
JOINTS
IMUIIIIIIIIII
11 11:laIMIIIIIMIIII
uI
IIIIIIIIIIIIIIMIIWAIAEIII
11111111111?1111111"?
HOcg8
allillIll1111111111111PPpfr
IA
"
A H
DC " Al A
OC: 0
NOW r`
41
A
20 40 60 so 100
'AC FLUX DENSITY - KILOLINES PER SO. IN.
FIG. 13- 6 CORE LOSS OF WOUND CORE --
DESIGN CURVES (400 CPS)
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Declassified in Part - Sanitized Copy Approved for Release
PER POUND
EXCITATION - VOLT AMPERES
340
320
300
280
260
240
220
200
IGO
ISO
140
120
!no
80
40
20
?
50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-9
`M. 'WM 1.1.?????? ????,' ???? ???????.??? ""????^..1/
gor=semarierrormwromorsirow=ruirsam=maliglimemerw
CORE: El LAMINATIONS
STEEL: ORIENTED s_ 4 MILS
(TRAN-COR 1-0)
atomormawatrorommanik
Hoe is
de AVERAGE
OERSTEDS
sio
0
20 40 60 80 100
AC FLUX DENSITY -KILOUNES PER SQ. IN.
120
FIG. 3-7 EXCITATION AND GAP FOR STACKED CORE-
DESIGN CURVES (400 CPS)
Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
0,11 www wwWwwWwwlww
If
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
14
12
ww?
waw wwww wekw 111r111 ww ? w ww, w ? ?we
wiemermagrararimmuummorommoomparowlemmempirairmon
CORE: EZ LAMINATIONS
STEEL: ORIENTED, 4 MILS
iTRAN?COR
TO;
`0111r1111111111111.11.11W
W We*
I
U)
4
0
0
4
HDC 818
AVERAGE OERSTEDS
1
7/17
Hoc s
20 40 60 80 100 120
A-C FLUX DENSITY - KILOLINES PER SQ
FIG. 13-8 CORE LOSS OF STACKED CORE?
DESIGN CURVES (400 CPS)
- 160 -
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Declassified in Part - Sanitized Copy Approved for Release
??? ??? ???? ?????
50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
???????? "WW1 mr?-?? I ^" ??? "*.? T ??????
XIV. EXAM& TRANSFORMER WITH UNBALANCID HAONEMATI(N
1) Specifications
Frequencv: 400 wales per second.
Ambient temperature: 05?C.
Maim: temperature rise: Wt.
Primary: 115 volts.
Secondary: 560 volts BA 1.0 ampere Wes 0.50 ampere DC,
half-maye rectifier AM capacitence4nput
Protection: Grade 2 (less resistant to adverse environmental acinditicas).
40 Cloven Quantities
Core: Bayless SI laminations.
Steel: Oriented silicon, 0.004 inch thick, (Armco Tran-Cor T-? grade).
Construction: Open core and coils.
(bre mpace factor: 0.9
Approximate stack ratios 1.5
3) Nomograph VaImes
Secondary RES voltage:
R- 560 volts Ms.
3imad16.7 sis current:
I 1.0 amperes MC
Equivalent secondary rating:
V m9 .1. T 0 (560)(1.0) 560 volt-ampere:4
r 9
Wilding dissipation:
(4...) 1195 (.110.5 )
1.25
11- 1.4 watts per sq. in.,
AT cUS.aaKjazatperatureriaeiz 'PC,
Ka 87 = constant from Table 11-10
ARMOUR RESEARCH FOUNDATION OF ILLINOIS IMeTITUTE OF TECHNOLOGY
i
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-161-
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Declassified in Part - Sanitized Copy A
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? ?????..??? n1.11, 111,111 41Ir... ? .^.
Winding space factor:
F w .08- Wr + F a a log 68 + .12 w .27
10 10
lir"783 ? 68 volt-amperes,
f irwm753
F w .12 se constant from Fig. 11-2,
f ? 400 froquency in voles per second.
Nomograph scale factors:
FW
IT-lc".
110 w 0.649 w constant from Fig. 11-3 or 11-4 corresponding to $
F ? 0.9 ow core space factor,
14)
? 1.01,
0 0.33)
m 14115 = resistivity, the roms firm Fig. 11-6 corresponding
to 1900,? increased 2 per cent.
Flux density:
Select 78 kilolines per square inch with the aid of Table 11-2.
Characteristic linear dimension:
4 1.0 from nomograph, Fig. 11-7.
Approximate core weight:
K.1 Fi S i 43 = (8 23)(.9)( 276)(1.0)3 2.04 pounds,
r w A_93
"1
constant from Fig. 11-3 or 11-4 corresponding to s
= .276 mi core steel dimity in lb. per sq. in.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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Approximate an length of magnetic circuit:
Ili ? a 4 (5.82)(1.0) 5.82 inches,
a ? 5.82 constant from Fig. 11-3 corresponding to s = 1.5.
Approximate secondary turns:
& V
et go 8
ne f F B 4
(1
(100)(.9)(78)(Lo)
? 318 turns,
K6 0 15,920 ? constant from Fig. 11-3 or 11-4 corresponding
to -
B so 78 61 flux density in kl. per sq. in.
Approximate unbalanced magnetising forces
?165 N
HDC 11.914342....8)( ? 13.5 average oersteds,
mi
IDC = 0.5 ? average load current in amperes.
Core loss, excitation, and gap:
For B = 78 kl per sq. in. and Ow
Core loss = 7.2 watts per lb. fro= Fig. 13=8,
Wiroi.katirin lAn TWIt?alencetre nog.
je/V041
Gap = AO from Fig. 13-7.
Wi (2.04)(7.2) w 15 watts (2.7,% of rating).
W = (2.04)(180 = 370 volt-amperes (66% of rating).
Effective gap = a (5.82) = .0075 inch.
4) Core Dimensions
Core exposed surface area:
Si = K22 = (24.0)(1.0)2 = 21j square inches,
lh, frAm re, 12-7i
K = 24.0 = constant from Fig. 11-3 or 11-4 corresponding to s =
2
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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mr,? ?????? ??????
? ???? ????
???? ? ? -1.? un- Mr'. ? ????? ..? r? ..????? ? ?. ? 41/4WAr,o
? Core dissipation per unit area:
Ti gi 15/24 0 .625 watts per square inch.
Lamination width:
L 0 4(0) ? (1.0)(47) ? .97 inch, use L ? 1.0 inch,
L/4 0 .97 ? constant from Fig. 11-3 corresponding to s 0 1.5.
Area product:
A Ai im 4 ? 1.0.
Window area:
Ac ? .75 square inch.
Core cross-sectional area:
14 1.0
Ai 0 0 ..mr a 1.33 square inches.
Stack height:
Ai 1.33 approximately 1-5/16w.
m 77. 0 ../7111 1.33 inches,
Stack ratio:
.t
1.33
"nr
1.33.
5) YalIELA115.21L4.12E1
Winding exposed surface atea:
2
S. 5$ 4 (10.61)(1.0)2 10.61 square inches,
c 3
1E3 10.61 st constant from Pig. 11-3 or A.s."'s4
11 I.
Approximate winding losses:
m S (W./S ) = (10.61)(1.4) in 14.8 watts.
?o c
AAVI,Onannnding tO 8 lig 105.
????0?41r dm .?
Conductor weight:
mFc 43 = (4.49)(.30)(.321)(1.0)3 a 0.433 lb.,
c 4
K4 4.49 se constant from Fig. 11-3 or 11-4 corresponding to s
a 0.321 a copper density in lb. per mi. 4"
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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Circular mils per amperes:
CN a
amp F -5
c
K., in 826 constant from Fig. u-3 or 11-4 corresponding toe a 1.5.
Primary component of load volt-amperes:
wpli s s
V VI 24. 11: 560 (1,0) (.5) ? 1885 volt-amperes.
11,1W ?-? ???????
? 1111111.10e . ?
(8210(.27) sm 388,
Primary current:
11 R + we +
P V
(1485 + 14 8 + 15)2 (370)2 se 6.0 Wow.
Primary wire else:
CM Is (388)(6.0) gs 2330. Use No. 17 N10 (2048 CM)
Secondary wire sise:
CH ? (388)(1.0) ? 388. Use No. 24 AWO (404 CI).
Turns per volt:
105
- ti,LL f
r?r- a
-?
105
14II ilk -??? ????- ? vow
Correction for resistance drop:
Reg a 1.41
isfiDC
Turns:
(1 ? 1/2 Reg)
N Vs 1/2 Reg)
s
se 0.604
at .01116.
(115)(.604)(.993) se 69 turns,
(560).(,6014)(1.007)= 340 turns.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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SO ..,?????????? ???"
111"1111 VIP". ? "
6) Winding Layout
Winding length equals window length minus two margins,
1.5. 2(.1563) 0 1.1874 inches.
Turns per Wars
Primary' (19)(1.1874) is 22.60 use 23 turns per layer,
Secondary: (42)(1.1874) w 49.8, use 49 turns per layer.
Layers*
Primary: 69/23 ? 3 layers,
Secondaryt 340/49 0 6.94, use 7 layers.
Tubes
.030 inch thick, 1-1/64 x 1-5/16 x 1-7/16 inches long.
Shields
.002 inch thick copper sheet.
7) Check of Coil Build
? .
Thickness - Inches
Tube .030
3 layers of No. 17 (3)(.0149) - iii
2 layers of high temp. insulation (2)(.009) ? .018
Wrapper of It II0 .009
Copper shield .002
*upper of high temp. inaulation
(7)(.0213) '
.wv,
7 layers of No. 24 .10
6 layers of high temp. insulation (6)(.009) so .054
Witmer of * " N .012
44.K.44.
8) Summary of Ilssista
Core:
Build go .424/.500 85%
Laminations scrapless El with center leg width of 1*,
Steels oriented silicon, (Armco Tran-Cor T-0 grade), .004 inch thick,
Stack: 1-5/16 inches,
Construction: butt joint.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
"I I
? ?
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? ? al. ? "Vt
' 4.,418 iv". ?
Dimensions: .030 inch thick, 14164 x 1-5/16 x 1-7/16 indhes long,
Material: suitable high-temperature insulation.
Primary winding - 115 volts, (next to core):
Inns sic: No. 17 AVG, high4emperature insulation
Turns per 1471r1 23,
Layers: 3,
?Urns: 69,
Layer irsulation: .009 inch, hub temperature insulation,
Wrapper: 409 inch, high temperature insulation
Shield - ground to core:
Material: one layer of .002 inch thick copper sheet,
Wrappers ?009 inch, high temperature insulation
Secondary minding - 560 volts RMS:
Wire eise: No. 24 MO, high temperature insulation
"swim per layer: 49,
Layers: 7,
da.....dammerammaill
AUIVUO0
Layer insulation: .006 inch, high temperature insulation,
Wrapper: .012 inch, high temperature insulation
9) Check of WinitUN; Resistance!
Resistance equals resistance per unit length (correct to operating
temperature from Mg. 11-6), times an length of ten, times
number or turns.
length of turn equals length of inside turn, plus pi times
build-up of minding.
*um
Primary:
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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????????????? IP"
5?0614)(1.3.3)
inubOit.87610 (5.40)(69) =
.261 ohne,
P ? 2(1.3125 + .06) + 2(1.0356+ .06) + ir ('159)- 5.40 inches.
a
Secondary:
(25.67). (1?13) (6.85)(340) 0 8.31 ohms,
Re el rI200b) (73758)
ace mi 2(1.3125 .06) + 2(1.0156 + .06) . 27(.209 + .102) ?
6.85 inches.
10) Check of Voltage Ratio
Primary voltage:
Vp n V + 1.1 Ipc (Rs + Ro/n2)
69
0 3m. 560 + (1.1)(.5)(14.65) 115 volts,
Rs + Rp/n2 ? 8.31 + .261 .(140)2 0 14.65 ohms.
(69)
11)ithoacseicivitLionsand.Diecks (none required)
12) Calculation of Temperature Rise
&ream temperature rise:
Wo+ vi
0
eurf surf (S +itho + h )
i
R 2 + I2 R ? (1.0)2(8.31) +(6.0)2(.261) is 17.73. watts,
we se pp
(-0(17071 + 19
W 15 watts,
10.61 *guars inches,
S = 24 square inches,
Fsurf = .9 = farm factor of surface from Table 11-9,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
?
itI
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??????????? ? ??
I
AI ANN ???A
? IA tawes ???? ?
?
?
3.75 x 1.6".22
3 gsgrf d
Cs ? )? Pas '22
3?75 x 66
o (104.61+24).1/ ?Was
ht ? (.0088)(.9) si .00792
Osurr is assumed to be 66?C,
%Oa a .1 ?assumed * .9 %ale
Coil hot spot temperature:
at a .85 .250 1.4
% Ir We 1/47) (1.2)(1.7.71) (aan x - 32"
m ? 1/2 (.5) ? .29) inch,
? ( .1) (66) + ( .9) (65.11) ? 65.5?C.
k 41,1) 0 ?003 (1'4,65) ? .0127,
R ? 6 (estimate for high temperature
Average winding temperatures:
Primary:
Tpri s Tamb * ()ourf * C gh
? 85 + 65.5 +
Secondary:
Ten Tamb + Gigue C Oh
85 + 65.5. (.8)(32.7
insulated wire).
voloni (AT 0 95?C)
? 176.7?C, (le or 91.7?C).
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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? 111,11 VP"... ? ?
XV. Design Procedure:vn.....L..tkgl..r.....Curziaimi?ansformers
I) kr..gleAla!
Frequency, voltages, secondary load and short-circuit currents,
temperatures (ambient and maximum rise), grade of protection.
2) Chosen Quantities
Type of core, grade and thickness of lamination =drum core
loss and excitation, core space factor, preferred stack
ratio, type of construction.
3) Nomograph Values
Rating based on secondary output:
W i? V I volt amperes.
r
Winding dissipation:
Am 1.25
C a I 44 watts/sq. in. (2-19) or
Fig. 11-1
Winding space factor:
F
where F sis .08 logri0 Wr + F.
J.
The factor .6 is for a scrapless lamination,
and is nearer to .5 for units less than
50 volt-Amperes.
For a non-scrapless lamination, the factor is
usually greater than ,4.
Nomograph scale values:
KW_ F If
0 c
fr-ir- and
1.f777-
(6-17)
(2-20)
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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'1 ?
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Flux density:
Select B using Table 11-2 as a guide.
V
Bs Bp Vpn kilolines per sq. in
V pq V.
where ..L.= ---mnsm*** volts,
VP2 c12-1 1
a
q
ratio of primary turns to
secondary turns,
short-circuit current
leakage reactance at short circuit
leakagereinancWaraZu'.."1?i'ren
.85 typically but is nearer to 1.0 if
shunt flux density during short
circuit is law.
Characteristic linear dimension:
Using Bs enter nomograph, Fig. 11-17 and obtain 4.
Approximate core weight:
Ni Ki F 43
i pounds.
(2-23)
Core loss and excitation:
Use material curves, correction factors (Table 11-3),
and half of the care weight with each flux density
C.% calwrilmtn V elisA TAr
"i ex'
4) Core Dimensions
Area product:
A_ Ai ?
41 1.
Lamination leg width:
L * 4
(2-6)
(2.24)
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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' ???????????/, "IPOP "41N.IN I
I, Window area:
A;
emir,. nal., ?
Calculate Ac from lamination dimensions.
Core cross-sectional area:
th
Ai 112 -T-- sq. in.
Stack height:
Ai
La
rOOPPINNION
inches
Stack ratio:
a
a
Coro exposed surface area:
8i 2 in X 42
Core dissipation per unit area:
/ Si watts per sq in.
5) Calculations for Windt=
Equivalent winding exposed surface:
se?K3 44 al. in.
Approximate winding loss:
. Ir... S. watts.
c
Circular Ails:per amperes
(2-25)
( 2. 26)
/ 4 1 t.,
(15 , 1 ....r........... ).
F ir c
, c n
7-3:-
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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von. ????
6)
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Primary current:
1
r--
P
? oar "el... ?KIV? 111.???? a e???? VP PP P?Pqmp. ? P.
Nr+ lc+ w1 01.41:
where
VI
Is
? lt ampere .
22
p q- 1
? .15?4
amperes, (6-18)
Wire sissy
Calculate from circular mils per ampere using
calculated primary current and rated secondary
load current.
Turns per volt:
105
Primary turns:
49-
Secondary turns:
turns per volt.
p
V (1 - c turns.
?
Is eat"? Vs
(6-19)
(6-20)
(6-21)
Total available winding length:
Window length minus (four nergizus (dimension
magnetic shunt thickness
Assume magnetic sliunt thickness (dimension parallel to coil
axis) to be at least (2/3) L for a simple-Vrpe core, and
(1/3) L for a shell-type core. In any case, the shunt
flux density thould not exceed 130 kilolines per square
Inch during short circuit. (Shunt flux density is equal
to the difference of primary flux and secondary flux
divided by the shunt net area.)
a ?? SEARCH, 11 II
ro se ???? ? . ? " el. tp4sTiTI,ETE OF 'T.ECtiollic:AotilY
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..?
Turns.per layers
Primary turns per layer equals turns per inch times 6
of 'finding length.
Secondary turns per layer equal turns per inch times .4
of winding length
Layers: 4
lP
Appropriate turns divided hy appropriate turns per layer.
7) Cheek of Coil Build
Choose tube, layer insulation, and wrappers,and check build of
both Primary' and secondary windings to insure that each is
80 to 90 per cent of window width.
To equalise builds, re-apportion the available winding length
between the primary and secoftUrywhom necessary.
8) 2!!!!Er of Desi
List core material, dimensions, weight, tube, winding wire
sixes, total turns, taps, turns per layer, number of
layers, layer insulation, wrappers, and shield data.
9) Check of Winding Resistance,
Resistance equals resistance per unit length (corrected to
operating temperature from Fig. 11-6, times mean length
of turn, times number of turns.
Mean length of turn equals length of inside turn, Plus Pi
times buiblow of winding.
ip) Chaitir
11
where R anda are obtained from step 9.
P
Adjust the turns ratio if the calculated primary
voltage dl.ffers appreciably from the specified
voltage.
it
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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111.?????
:
U)
11) and Design Meeks
ilagnetio shunt(s):
TiddrIMIMII (in the direction of long idndou dimension)
of aspette shunt(s) has previously been determined
In step 6)
d* of magnetic shunt(s) (in the direction pigpen-
&War to plane of witkiow) is approximately equal
to steak lesight of the aye, L.
Length of sagnetie shunt(s) is equal to window width
minus air pp.
An impression far the air gap associated with the sapetic
shunt, or with each shunt if there are two, is,
452pq11.1.
" (646)
? a*
RESEARCH FOUNDATION OF ILLINO/S INSTITUTC OF
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111.0 siumus cuRam4amnrs0 TRANSMOR
1)ael.....oifons
Frequenor 60 cycles per second.
AskdAnat temperature: 65*C.
Madame temperature rises 140.10;
Primary: 125/13005 Tolls.
Secondary: 5,5 volts, 10 amperes, 13.5 ampere short-circuit
current.
Protections Grade 1 (most resistant to adverse environmental
conditions).
2) Chosen Quantities
Cores Scrapless EI laminations.
Steel: AISI N-10 grade, oriented silicon, .014 inch thick.
Constructions Encased, hermetically sealed, with sand-loaded
aephalt filling compound.
Core space factors 0.87
Approximate stack ratio: 1.0.
3) Nomograph Values
Rating based on secondary output:
Wr ? V8 I ? (5.5)(10) ? 55 volt-amperes.
?
Winding dissipations
W AT 1.25
a 41 / k_
8--
.49 watts per sq. In.
.110...dimirvimulogrestiftworoArt.qmoCits.m. .
AL' ? 40 mill4A-mumi tivietnwiciwwimp 41411,W A44
? .
?
IC 71 = constant from Table 11-1.
r1L111:ti.141' space factor:
= 6 F (.6)(.289) = .173,
- c
= .08 log10 + = (.08)(1.7h)
= 0.15 = constant from Fig. 11.2
.ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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i
tr,
III
111
1
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?????????????orp ? ?
Nomograph scale values:
KO /Jr
rir ?
? 0.8?
0.66,
? 0.091,
? constant from Pig. 11-3 or U-4
corresponding to $ ? 1.0,
Gore space factor,
.930 ? resistivity, the valve few Fig. 1.1-6
corresponding to 105?C, increased 2 per cent.
Flux density:
Select so 100 kilolines per square inch,
B
s p
? 119 kilolines per square inch,
P q. s 1111
V. 11.351(.85)(55) mi 11.2 volts,
areprowarimommen
yp It q-
.% 0.0# 26 2
V.11.1
r
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10,00. I 010 ' 'SAN .0 N 0. 000/ '
IP, . 0 00
Sis .276 ? core steel density in lb. per sq. in.
i
Core loss and excitation:
For 13 a 100 kl. per square indh:
core loss so 1,0 watts per lb.
excitation ? 3 volt-esperes per lb.
For Be ? 49 kl. per square inch,
core loss ? .27 setts per lb.,
excitation ? .35 volt-amperes per lb.
" (3.1/2)(1.0 + .27)(1.4) a 2.7 watts (4.9% of rating),
Wex (3.1/2)(3.0 4 035)(4) 21 volt-amperes (38% f rating).
4) Core Dimensions
Core exposed surface area:
Si a K22 (23
1)(1.2)2 ? 33 square inch,
K2* 23.1 constant from Fig 11.3 or 1144 corresponding
to s at 1.0
U
11
Core dissipation per unit area:
fa 2.7/33 = .082 watts per square inch.
? Lamination width:
L m 4 (L/4) 's (1 2)(1 07) 1.28 inches L 1.25 inches,
114 1.07 constant from Fig 11-3 or 114 corresponding
to 8 Is 1.0.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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VP'
?
Con eross-leotional aroma
41- 2?01-
Li, a -iv-- tiler ? 1.76 mum inches.
Ae
Stack heights
A
el. IF ar
St?aek ratio:
are
ItindingS_alculations
Illqattalent minding exposed surfaes area:
1E3 42 ? (13.02)(1.2)2 18.8 square inches,
1.41 ie, apinvezismitaly 1-3/s lashes.
1.23
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE Giv? TECHNOLOGY
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vrimottim.
'??'??? Mr. "Ir...I ??? ??? 1K ? '
Iv
wasurromessmwmatmoomaa
977
?
110) SI 97 volt-amperes.
1
where X is leakage reactance referred to secondary
winding.
?Primary wire else:
cm
(500)(i 17) ? 585.
se No. 22 MO (6211.14 CPO.
Secondary wire miss:
CM a (500) (10) a 5000. Use No. 13 MOO (5178 CM).
Primary turns per volt:
A P1
105
4.144 f
Secondary turns per volts
No 105
r". 1.-.14&tgr P
icr5
O4aild(60)T100) C1351( tivir
105
(11.44)(60)(149)(1.76)/ .18?)
Correction for resistance drop:
if
Turns:
9.2
.1675
C ???
(12S) (
Place tape at b 28 and 27e
uuT1119
916)
280 turns.
Total available winding length equals window length minus
margins and magnetic shunt thickness.
+ (1/3)(1.25189
sz 5 inches.F2)(1/8) 2(5/32)
RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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? or?ovoo.??????
t
1
??,
? V
??? _% I vv.- v
Turns per law
Primary:
(34)(.6)(.895) al 18.2, use 18 turns per
Secondary
? (12)1(.14(.895) ? 101
use 4 turns per layer.
V.
A check of the secondary build elms that it is excessive while
the primly build is low. Both winding 3angthe are then
changed so as to use the window area more effectively.
Revised turns per layers
Primary use 17 turns per layer,
winding length 17/311 .500 inch,
tubs length is 11/16 inch.
Secondary: use 5 turns par leyer,
winding length it 5/12 it .436 int*
tube length is 11/1,6 inch.
Layettes
Primary: 280A7 III 16.5, use 17 layers.
Secondary: 30/5 it 6 layers.
7) Cbedc of Coil Build
Maar
Thickness (inches)
Tube .010
17 Were of lio. 22 ?(17)(.0276) .165
1,4 llnewpa sir normal. nil) a .048
irtrapper .010
.553
mud a .5531.625 es 88.5%
Secondary:
Tuba
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????????????? "11.
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VIP
6 layers of No. 13
5 layers of paper
Wrapper
r 1111"6-14
??? ???.
Build ? J52/.625 ? 88.5%
8) SumrofDeei.e
Core:
Tubes*
(6)(.0753) .452
(0( 010) a .00
.010
.552
Lamination: scrapless IT with center leg width of 1-1/4 inches,
Steel: oriented silicon, AISI 144.0 grade, .014 inch thick
Stack: 1-3/8 inches,
Both are .040 inch thick, 1 -1/L x 1-7/16 x 11/16 inch long.
Primary winding (125/115/105 volts):
Wire size: No. 22 AWG single-layer enamel,copper vire,
Turns per layer: 17,
Layer: 17)
Turns: 280, taps at 258 and 235 turns,
Layer insulation: .003 inch paper.
Wrappers .010 inch paper
4 0.
? 4,
i;
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?.
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?00. .0-00100. '1100.00 ?
9) Check of Windinit Resistanoe
Primary:
Re:datenee equals ohms per Inch tines aean length of
turn tilos Was tines correction to operating
Ulmer:1We.
ip a 111165600 (7.27) (280 ? 3.75 ohms,
Ness length of turn equals length of inside turn
plus pi times build-up of winding.
na 2(1.25 + .080) + 2(1.4375 .+ .080)
eP
Secondary:
s
a go 2(1.25
cs
2.00
0'.
11(.503) ? 7.27 inches.
498 alas,
.080) + 2(1 4375 + .080) 11( .50 ) te 7.27 inches.
10 Check of Voltage Ratio
Primary voltage:
V ? n
3n) ( 97) 2 109 volts
+ .0108 + 3.$ AU? .0928 alas.
(280)2
This indicates that the secondary voltage will be sonsehat
high, but it is isot:gb....ecanaary to chew the twns ratio
since a slight change in the 1.'eakags --taiwtanerp by=6.1reaft
of adjusting the magnetic shunts will give the correct
voltage.
il?oiskl. Calculations suid
Nagratic shunts:
Thickness of each shunt. (along the long window dimension)
is .50 inch (max.),
Width of each &matt IL 1-3/8 inches,
ARMOUR RESEARCH 'FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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???- ma, ^WAR 1111,4111 ." ? '
Length of each shunt (window width minus air gap)
.625 - .016 mg .609 inch
Air gap:
4 52 p q 118 Is
1 B
g SO
(4 2) 1.35 (.8 )
100 x 3.0
(10). .016 ineh
12) Calculation of TEperature Rise
Surface temperature rise:
W0+ W
i (1.1)(10.12 +.2.1)
0 im F * 18 0?C
surf Bull 13case)(110+ hr)/ w(87.4)(.003L2 + .0056)
2 2 ,2,
R +I Rok0) (.0498)+(1.17/ 0,75)111 10.12 watts,
ss pp
W m 2.7 watts,
S 87.4 case area in square inches
case (3.875 x 3.300 x 14.313 inches),
F ? 3..1 e form factor of surface from Table 11-9,
surf
Ii
3.75 x 10"3
?surf .44 a 3.75 x 10 7.77711r
mime -1
.22
-3 20 .00342,
87
?
so (.0062)(.9)
9)(18.0)
NI
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? 1/2 Nan+ Sce+ 1/2 (87.4 f 18.8 33)
? 69.6 STEM inches,
e 28.8 square Indies,
? 33 mem lathes,
k 43n5 thermal wade:MA* from Table n-ao,
eause 80+ si d4612 inches .
asie". ?t ? it
Coil bot spot torporaturees
Primer
V ?
op
rill,. )7 ? ( .32) (5.2)4"
op
11.5?0
1.17) (3 751 ? 5?14 watts,
a as 1/2 (.625) ? .3125 inch,
? 18.6/2 ? 9.1& aitowo inches*
.003 (tar, fo?Aa
_ is7.05 ate"
+ 1
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TEC,HOOLOGY
Ell
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?????????? ?"%po. ??? ? ? or ???????? ?
`M. ?16?1? -????"
cs .?
S 18.8/2 is 9.4 square inches,
R ...Tritr?It) ? 403 (NIPS a .0128,
R ? lirr.07196 ? 6 .15
Average winding temperatures*
Primary:
Tpri %eQ* 474/hp
65 4 18.2 + 12.5 + (47)(11.5)? 104.6'0 (AT 39.66C).
Secondary
T ? T + +
sec arab uarf Qimp hs
? 65 + 18.2 +12.5 + (.77)(10.0) ? 103.4*C. (AT ? 38.4?C).
The factor .77 is the average of .90 and .65 from Table 1142.
. I
1
11
1
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? ??????^???? .91
?
,???? ??????,? *NWT 01/1111
) Specifications
Frequanch voltages, esoundow load and sbort-eirottit currents, tape
of load filters t?mperitnres(iiiiant and mina rice), grade of
mitotic's.
Owen Quantities
Typo of cores vide and Motown of laminations mina core loss
and musitation? oore apace factor, apprembute stack ratio, tape of
ecestruation.
3')
Sacondary RIB voltages
Vs is the sum of average load voltage Vim plus rectifier foreard
voltage drop and circuit resistance voltage drops multiplied by
2.22 if no filter is used, or voyage load voltage multiplied
by a ratio from Table 1303 for a oaPasitionceatiltirld load.
Seocadary NS currents
Is is average load current hic? multipliad by 1?57 if no nate`
is used, at by a ratio from Table 13-1 for a capacitance-filtered
load.
Diuivalent secondary ratings
Ls. a Irslas 'Olt amperes,
em.14 efts, /14:ag4viiiik..401?110
11114111111114.141 vidie ummagemagpobwomme
The factor in (6-17) allows space for the taunt and is taken as
0.6 for a scragess lamination. However a value of OJ is to be
used for units rated less than about 50 vat aspens. For a
non-scrspless lamination, the factor is usually greater than 0.6
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reo?fte. grill 'qr.+ ".".? iv "
and can be estimated by allowing space for a shunt and extra
margins. The total width (in the direction of the long window
dimension) of the epistle allowed should be a little greater
than the outside log width of the core.
Naaograph scale values
ICO Wr 14 We
1r1r. dT-
Flux
g7
densitiTs
Select Bps using a value from Table 11-2 decreased about 10
per cent. This reduction is made to obtain reasonable values
of excitation volt-amperes, which would otherwise tend to be
excessive because of the unbalanced magnetisation.
Via
B? B w-rAt kilolines per mg in. (6-12
s p v fit
q 4
sot, short-circuit current
volts, (8-6)
color
e reactance at short circuit
e e reac ce a ra CLU"Thle7
8 tYpiss1117
Characteristic linear dimensions
Obteinifron noraograrlo Fig. 11-7, Usti, Be
Approximate core weights
11 Skit pounds.
yawl length of Inap4daie an:1dt t
inches.
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?Ar? ? ??^`
?
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110.1111 .? T ?
sh?
Factor for calculating unbalanced nignstising ones:
?is95 loc (549)
14pprozbisto unbdanood ssapatising force in primary portion of core:
s .7 lima was. eastPds (74)
pproximata =h2agood lognstising force in saoondarry portico of owes
s 1.3 Him average oersteds (74)
Care loss sod Imitations
Usa design =me Mg. 134 era* 134),
and half of the cora might 4th each nnx
dosity and usipatising forms to obtain total V4t and Wat.
is) Core dinansiom
Coro aposad surface area:
? rie
Coro dissipation per unit area:
VOL setts per sq. in.
Ar_sa Products
(240
i
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?????? .?????????????? ?
_
4444. ? "4 444 .V0 ". 444 4. NI
"44444441 ?44,4 IC..
Stack ratio:
sL
'8=
5) Sliding Ca3.oulations
Equivalent :finding exposed surfaces
50 a 13 t sq. in.
Approxbiate winding loss
-rm. watts.
arcular sae per soperst
op ON
(IC
t W 5 c
0 0
(2-26)
(2-27)
(2-31)
Primary component of load volt-amperes:
W? s V 1 2 12 volt-amperes
pL DC
Primary currents
1-1
a LI'
P vp
(5-31)
I
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...a.... it' .' .`11110.1111
a ??
1 ) toms
.701
) turns
g wr
Fora capacitance filter, maim .707 bi
us two previous equations. WIC
6) Winding Law%
Total mailable winding length:
Window length aims (four nergins plus nagnetic /bunt tbidtness).
Atoms magnetic shot thickness (dinend.en parallel to coil
ans) to be at least (2/3) L for a simplemiwpe core, and (1/3) L
for a shalletrpe core. Increase shot thickness *en necessary
so that shot flux density does not exceed 330 idlolines per
square inch during short circuit. (Sae Qi. ris paragraph 6)
Turns per Wars
Primary turns per War are approxinateki equal to turns per
inch tines .6 of total available of winding length.
Seccadarr turns per lifer are approxinate3y equal to turns per
inch tines .4 of total available winding length.
1111111113,,
9) Check of landins Resistances
Resistance equals resistance per unit length (corrected to
operating temperature frost Fig. 11-6) times -seam length of
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? ???? ? re--. a
turn, times number of secondary turns.
Mean length of turn equals length of inside turn of the
winding plus pi times the build-up of winding.
10) Check of Voltage Ratio
Calculate primary voltage:
Vp h + 1.1 ID? (Rs + ) + (1.1 Zoe)
where Rp and Rs are obtained from step 9.
Adjust the turns ratio if the calculated primary voltage
differs appreciably from the specified voltage.
11) aria Calculations and Desimpeck?
Magnetic shunt:
Thickness of shunt(s) (along the long window dimension) has
previously been determined in step 6.
Width of shunt(s) is approximately to core -stack height, 4.
Length of shunt(s) is equal window width minus air gap.
An expression for the air gap associated with the shunt,
or with each shunt if there are two is
1 4.52 p q N.
inch. (646)
mg
1 so w
12) Calculation of Temperature_Rise
Follow basic method.
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(
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?? ."71111. .11,1117 Ilra. a ". ?
XVIII. EXAMPLE: CURRENT-LIMIT110 TRANSFORM WITH DIBILLANCEDMAMIZATION
1) specifications
Frequency: 1400 cycles per second.
Ambient temperatvre: 65?C
Maximum temperature rise: 110?C
Primary: 60/65/71 volts.
Secondary: 65 volts EMS, 1.2 amperes EMS, .75 ampere DC,
1.65 amperes ENS shart-circuit current,
half -wave rectifier 4th resistance load
and no filter.
Protection: Ore& 2 (less resistant to adverse environsmento
conditions).
2) Chosen Quantities
Core: Screpless EI laminations.
Steel: AISI-10 grade, oriented silicon steel, .004 inch thick.
Construction: Open core end coils.
Care space lector: .85
Approximate stack ratio: 1.0
3) Nomograph Wyss
Secondary HMS voltage
V = 65 volts EMS.
Secondary BMS current
I -1.2 amperes EMS.
Equivalent secondary rating
W es Vs 'I' (55)(1.2) = 78 volt.amperes.
r s
Minding dissipation:
(AT )1.25
140 1.25
"pr 36 watts per square inch,
ARMOUR RGSGARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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1??
11100???,.
AT ? 40 0 maxims temperature rise in ?C,
K 0 91 0 constant from Table 11-1
Winding space factor:
F a .6 F ? (.6)(.25) a
rc a .08 log10 Wr + F 0 .08 log10 18.5 4. .15 .25,
W 78
Wr a is 18.5 wittte,
f 400 0 frequency in cycles per second,
F 0 .15 a constant from Fig. 11-2
Nomograph scale values:
.058
lel
Ko ? .630 a constant from Fig. 11-3 or 114 corresponding to so 1.0
F .85 0 core space factor.
/9 .930 resistivity, the value from Fig. 11-6 corresponding
to 1056t and then increased 2 per cent.
Flux aitkusity:
Select B 0 50 kilolines per square inch to account
P for unbalanced magnetization
V
wit Bp v;/: m 50 166g 20.5 kilolines per square inch,
V /n
p q V
81(451
.1,70 0
IS I
VP2 q-1 1.37) (.8)
1.65
P a 1.37.
.11.41L
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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?
?
1
1
al*
? ?11,41/ 11P--" P ` ? ". ????? ? -`??
q In.08 (estimated factor to account for change in leakage
reactance).
Characteristic linear dimension:
1.05 inches frau nomography Fig. 33.-7.
Approximate core weight:
NI 0 11 !live a (7.45)(.85)(.276)(1.05)3 2.02 pounds,
?
a 7.115 ? constant from rig. 11-3 or 114 corresponding to s ? 1.0.
? .24/6 ? core steel deasitiy in pounds per square inch.
Neon lame& E sicastio arcuit:
mi a a ? (6.115)(1.05) 6.77 inches,
a " 6.145 ? constant from Fig. 11-3 corresponding to $ ? 1.0.
Approximate secondary turns:
N is 116 vs
alI otosamarararesersairsomm
fi Bar (400)(.85)(20.5)(1.05)
KA la. 19,1480 ? constant from Fig. nft3 or 11-4 corresponding to
s ? 1?00
80
6
"165 turns,
.ftm1mailfte4fter 119.the1meed nignegiving forces:
Jr4UWA &U1S- Weisi.WWwwwas
?405 ID0
Hoc
md.
16
9.05,
Iva a .75 ? average load current in asperse.
Approximate unbalanced magnetising force in primary portion:
Esc p ? LIN ? (.7)(9.05) ? 6.3 average oersteds.
Aipproxisate unbalanced magnetising force in secondary portion:
KV! a '1.3 Rix (103)(9 1000 II 12 average oersteds.
Gore loss and excitations
For Bp ? 50 kl per m4. in. and Nix p "6.3,
core loss = 3.4 matts per lb. from Fig. 13-8,
excitation = 40 volt-anperes per lb. for Fig. 13-7,
gap m .13% frcel Fig. 13-7.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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goto. ?vew. 11114".... "
For Be al 20.5 kl per sq. in. and Hpc 8 14
core loss a 1.5 watts per lb. from Fig. 13-8
excitation a 15 volt-amperes per lb. from Fig. 13-7.
gap a ?28% from Fig. 13-7.
W a (2.02,2)(3A * 1.5) a 5 watts.
'ex (2.02/2) (40 15) ? 55 volt-amperes.
Effective gap a (.0028)(6.77) a .019. Use butt joint with .014
inch of paper in secondary portion.
4) Core Dimensions
Core exposed surface area:
Si K22 ? (2301)(1005)2 44 25.5 square inches,
X2 23.1 As constant from Fig. 11-3 or 114 corresponding to
s w 1.0.
Core dissipation:
W/81i ? 5/25.5 n .196 watts per square inch.
Lamination width:
L e(La) is (1.05)(1.077) 1.13 inches, use L go 1.125 inches.
La a 1.077 from Fig. 11-3 or 114 corresponding to s is 1.0.
Area product:
A A a lit a (1?0)4 a 1.215 inchesh.
i
Window areas
Ac .95 square inch.
Core cross-sectional area:
p4 1.215 it 1.28 square inches.
Stack height:
Ai
as 1.28 . 1.14 inches, approximately 1-3/16 inches.
a
Stack:
1,1 11 "I /11C
41.0?11.C.7
la 1 :01 .4.
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?
?
? 11,111 W.".
5) Winding Calculations
Equivalent winding exposed surface areat
" 151,2 " (13.02)(1.05)2 square inches,.
13 al 13?02
V.
constant fru Fig. 11-3 or 114 corresponding to
s -1.0.
Approximate winding losses:
W (vo/So) So (.36)(1644) al 5.2 watts.
Circular mils per were:
Fc1 n (803)(4110 510,
F
id) %
15 as-803 ? constant from Fig. 11-3 or 11-4 corresponding to
$ 1.0.
Primary component of load volt-Amperes:
OW S1VI 2
. ,
Primary current:
1.1
IP In -ram.
'a
vs
1=2 6511(1.2)2
- (.702 s 61 Irolt-uPeres.
ipcik
65
(1.1)( .75)
&AL ...11 I 01 I
lik1031, 116
is 177 ohms referred to secondary winding,
- Inc2) aL177 [(1.2)2 - (.75)
Primat7 wire size:
CM (510)(3.78) a'1920. Use No. 17 ANG (2048 04).
Secondary wire size:
(X 0 (510)(102) sm 612. Use No, 22(624.4 CK).
2]
0 156 volt-amperes.
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II
Ii
11
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? ??? ? ?,1 .111???? ',MP.... ? ^ ? ?? ????
?
Primary turns per volt:
.1v42- nue 101 vi m TEINROYMENT(783) in 143
105
Secondary turns per volt:
. 105
1
.
2.524 1
. 14.14 05 Bs
Correction for resistance drop:
Wrc 5.2
trug slr
Turns:
? .0668.
? ??
N? .707
N 0
VP -itc- (1 - ) as (71)(1.03)(.976) 11 turns.
Place taps at 65 and 60 turns.
.707W
Ns 0 Vs -it? (1 ) m (65)(2.52)(1.024) ? 168 turns.
wr
6) tli.2413114ts.c.ut
Total available winding length equals window length minus the sum of
shunt width plus margins. Shunt width is approximately 1/3 of lamina-
tion center leg width.
1.6875 - [i.4)(01)ir
.8125 Ah.
/1/1%,1 nej
Turns per layers
Primary: (19)(405)(.8125) ? 9.26, use 9 turns per layer.
Secondary: (30(.0(.8125) ? 11.0144 use 11 turns per lsvere
Dignmrs:
Primary: 71/9 ? 7.9, use 8 layers
Secondary: 168/11 s' 15.3, use 16 layers
7) Check of Coil Build
Primary:
Tube
8 layers of No. 17
7 10wmipc of rumor
g
Wrapper
Thickness - inch
(8)(4469) .375
(7)(.097) "(t00%
410
Build mg .465/.5625 83%
.assc
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? v.. %Ow ? 111,10 W..* ego I,.
Secondary: Thickness - inch
Tube .030
16 layers of No. 22 (16)(.0267) 61 .427
15 layers of paper (15)(.003) is .045
Wrapper .010
MI
8) Summary of Design
Core:
Build is .512/.5625 ? 91%
Lamination: scrapless II, with venter leg width of 1-1/8
inches,
Steel: oriented silicon, ATM 1440 grade1.00h inch thick,
Stack: 1-3/16 inchee.
Construction: Butt joint with .007 inch paper in secondary
portion of care.
Tubes:
Primary: .030 inch thick, 1-1/8 x 1-3/8 x 11/16 inch long,
Secondary. .030 inch thick, 1-1/8 x 1-3/8 x 9/16 inch long.
Primary winding (60/65/71 volts):
Wire size: No. 17 AW0 single-enamel copper wire,
Turns per layer: 9,
Layers: 8,
Turns: 71, taps at 65 and 60 turns,
Layer insulation: .007 inch paper
r?r--
Wrapper: .010 inch paver
Secondary winding (65 volts ENS):
Wire size No. 22 single-enamel copper wire,
Turns per layer: 111
Layers: 16,
Turns: 168,
Layer insulation: .003 inch paper,
Wrapper: .010 inch paper
9) Check of Winding Resistances
Resistance equals ohms per inch, times correction to operating
temperature from Fig. 11-6, times mean length of turn, times
turns. Mean length of turn equals length of inside turn,
plus pi times build-up of winding.
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rge)(65/1(qi
RP a ,
111r.11/ yr- I ???? +????
(6.57)(71) .269 ohms,
? ?
* 2(1.125 * 060) + 2(1.375 + 1,060) + w(.425) n 6.57 inches.
op
Is aL111;100) (64)72)(168) 2.08 ohms.
ace = 2(1.125 * .060) * 2(1.375 + .060) + w (.472) ? 6472 inches.
10) Check of Voltap Ratio
Mawr voltage:
V 0 n + 1.1 l'ac (Re + Riptg2)] 2+ (1.1 lac 1)2
? IA \11165 + (1.1)(.75)(3.59)] + B1.1)(.75)(177)J 2
0 68 volts.
R + R /n2 2.08 + .269
s p In' 3.59 ohms
This indicates that the secondary voltage would be slightly law,
but it may not be necessary to change the turns ratio
since a slight change in the leakage reactance by means
of adjusting the magnetic shunts would give the correct
voltage.
11) Special Calculations an11/2112.91sti
Magnetic shuntst
Thickness of each shunt (along the long window dimension)
e 7/16 inch (stsx.),
Width of each shunt is eggal core stack height: sL is 1-3/16 inches,
Length of each shunt equals window width minus gap
0 .!62!- #0199 gs 506 innh_
Ow:
14.52 p q Ns Is .(1:12)(1t37)(.8)(168)(1.2). .0199 inch.
B 103
g sc
12) Calculation of Temperature Rise
Surface temperature rise:
0 ma F +W
surf surf (Sc*S1,Thc+
50 x 103
$6.84 + 5.0) m nry
1 39 .9 K ? 069911) ? I 00n
Us
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11
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6
? ...It, 1#1.1111 Yr.*
2 R + 2R 11 (1.2)2(2.08) + (3.78)2(.2e) a 6.8h Matti
C 8 p p
? 5.0 watts,
So w 14.4 square inches,
Si 25.5 square Inches,
Faurt a .9 - form factor of surface from Table 11-9,
0,m?f?n ?Isit
ho 345 x 3.0-
(so +i)414"-
? 3?75 10-3 28622
ah.14 25,J4717
w .0048,
bri (.00610(.9) = .00576,
Pawl is assumed to be 28*C.
? surf assumed .9calculated a (.1)(28) + (.9)(27.0)
27.1`C.
Coil hot-spot temperature
(.11 ,
lip UP 0..2)(3.81)'85
oP
110. Rift a (3.78)2 .269 3.814
r
.281 )1'14. 19.9.0
.v..L.Ly f?Z
a a (1/2) (.5625) - .281 inch,
Sop as lit.i4/2 gi 7.2 square inches,
1.. - 10. MI /1(12 6.3 PB .0119
I R + 1
' a`i %.u. R ? ) ?,......... 1.58 s
.01453
Seconds?Ty:
?7 .85
)1.4 3.5 2 c
Ohs " F Weslerc- Is
(1 2)0 0) ( 281
0124 x 7.2
... 2
W n 115 (1.2) 2 (2*08) 311 360 watts,
es s
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S ? 14.14/2 7.2 square inches,
08
R + 1 6.8
k ? ki .003 or
.0253
-760111".- m 5'8'
II 601216
Average winding temperatures:
Primary:
Twill; Taub + Oeurf + .85 Ohp
? 65 + 23.9 + (.85)(19.9) a 105.9C (ST- 110.9.0
Secondary:
Tee? -T amb 4 Osurf +.850 hs
? 65 + 23.9 .0, (.85)(15.2) so 101.8*C (AT el 306.8*C).
The factor .85 is an average of .90 and
.80 from Table 11-12.
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r mower Ir.-. a ? v. v?- ? ? --?.?
v.
11I. TII OCIMURS: VIERATON4UPPLT TRANSFORMS'S
1) 10modlicetions
frequency (usually 115 cpm), supply voltage, load, type of
filter, temperatures (ambient and maxbasm rise), grads
of protection.
) Chosen Quantities
Type of core grade and thickness of lamination, core space
factor, apProximate stack ratio, type of construction.
3) Nomograph Vanes
RMS voltage of half the secondary:
Ts/2 is average load voltage Vms plus estimated rectifier
average forward drop plus other series-resistance voltage
drops multiplied by 1.1 for an inanite inductance-input
filter, or multiplied by 1/nrif no filter is used (T is
the ratio of vibrator contacting time to half a period,
between .70 and .85), or ;In multiplied by the ratio from
Table 1244 for a capacitann-filtered load.
RMS current in secondary:
V J... V
.1. ay awn-ago JAPEAA VIIT-CUll 10 &pc, .thratip-Ja."grums t?gy ? 44"9/111 aa'or
infinite inductance-input filter, multiplied by .707ff
U no filter is used, or multiplied by the ratio from
Table 12-2 for a capacitance-filtered load.
Squivalent secondary rating:
Wr 2(V8/2)18 volt amperes. (8-15)
twii nirrinatinn ?
W 1.25
AT
Winding space factors:
watts per square inch.
F .08 log10 +F
(2-19) or
Fig. 11-1
(20-20)
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. ? ...I. ...we ow, ? .W4 ? IIPWI? 111
NomograPh scale values:
K W're "owe
ir-r- and -ruin.
p, we
Flux density:
Select flux density from Table 19-1 and then decrease this
value by the ratio of most probable operating voltage
to the maximum operating voltage using Table 19-2.
Characteristic linear dimension:
Use nomograph, Fig. 11-7 to obtain 4.
Approximate core weight:
Mi 0 Ki Fi S i 43 pounds.
Care loss and excitation:
Use material curves,
and core weight to
4) Core Dimensions
Area product:
A A 0.414
c
Lamination leg width:
L go 4 7 inches.
Window area:
correction factors (Table 11-))
calculate Wi and Wax.
Calculate Ac from lamination diownsi-ne.
Core cross-sectional area:
4
1--- sq. in.
Ai
Stack height:
A
inches.
sL
Stack ratios
-17-
0 Ili
so
(2-23)
( 2-20
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...at, mons S ????
Core exposed surface area:
2
Si ? K2 sq. in.
Core dissipation per unit area:
watts per sq. in.
5Y sous calculations
Winding exposed surface area:
3o3 $2 sq. in.
Approximate winding loss:
W is We ftwatts.
Eanrwoos"
c
Conductor weight:
M mK F S $3 pounds.
C 4 o uo
Circular mils per ampere:
CMre-7
amp-
tric7ws-HIC5 Fc).
Ot:
Primary input power:
ir r as w wc 1.41L .ex watts.
RMS voltage of half the primary:
V/2 = (Vb - tri me volts,
? ??
(2-25)
(2-26)
(2-27)
(2-.3o)
(2-31)
(8-16)
(8-18)
where V. is the supply voltage, and one volt
is assumed for contact drops.
EMS current in the primary:
W
RES amperes. (8-17)
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.11
If N
Wire sizes:
Calculate from circular mils per ampere using
primary and secondary R1 currents.
Turns per volt:
Primary turns:
turns per volt.
N ? 2(V0) .7-(1 turns.
wr
Secondary turns:
U
c
N 0 20/8/2) -I-(1 + Tr-) turns.
6) Winding Layout
Winding length:
Window length minus two margins.
Turns per layer:
Appropriate turns per inch times winding length.
Layers:
Appropriate turns divided by turns per layer.
7) gttEk.s.L.C...oild
Choose tube, layer insulation, and wrappers, and check build to
make sure that it is between 80 and 90 per cent of window width.
8) Summarr of Deep
List core material, dimensions, weight, tube, winding wire sizes,
total turns, taps, turns per layer, amber of layers, layer
insulation, wrappers, and shield data.
(2-33)
9) Check of Winding Resistances
Resistance equals resistance per unit length (corrected to
? operating temperature from Fig. 11-0 times mean length
of tarn, times number of secondary turns.
Mean length of turn equals length of inside turn, plus pi
times build-up of winding.
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10) Special Calculations and De3ign Checks
These are to be made when a quantity is near its madman
peridssible 1i1t, or to check operation in other ways.
11 Caloulatiore Rise
Follow basic method.
? ??
14?101.
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???????????????
4
0.16.04411061414066466.
"ete 'Vele 16,-14 6 "* ? ? "...I
MLR 19-1
?
SUGGESTED FLUX DENSII7ES FOR SILICON-STEEL CORES
IN VIBRATOR-SUPPLY TRANSFORMS
(Kilolinas per square inch at maximum voltage
Material and core
ImwasialOWN116?06111181?6461INNINMINIONIONNINIIIIIIII?160681.
Frequency - cycles per second
115 250 400
Non-oriented steel,
stacked core
Oriented steel,
stacked core
Oriented steel,
sound care
041161.0.160611111,
60
70
75
55
65
70
50
55
TABLE 19-2
TYPICAL OPERATING VOLTAGE RANGES FOR
NOMINAL VOLTAGE SYSTEMS
416111101?411411?111.11614MeNI?668?00110146.
Operating Range
3-5
5-8
10-16
20-30
27-44
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1
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4.111P11. 'Ir.'? I ???? ???
U.=WM VIBRATOR-WPM TRANSFORMER
1) Specifications
Frequency: 115 cycles per second.
Ambient temperature: WC.
Maximum temperature rise: WC.
Supply: 2h volts DC.
Load: .050 amperes DC from full-wave rectifier with an inductance-
input filter.
Secondary voltage: 572 volts HMS
Protection: Grads 1 (moot resistant to adverse environmental
conditions).
2) Chosen Quantities
Core: scrapless la laminations.
Steel: AISI-M-22 grade, hot-rolled silicon steel, .025 inch thick.
Construction: encased, hermetically sealed with sand-loaded
asphalt filling compound.
Core space factor: .9.
Approximate stack ratio: 1.5.
3) ....12NbEEML11011.1.1
RMS voltage of half the secondary:
Vs/2 sig 572/2 * 286 volts RMS.
RMS current in half the secondary:
Is ? 707 Ipc st (.707)(50) .0354 amperes RMS
where the factor .707 is the suitable ratio of currents
for an
.14infiniteA Al Mb ? la ?
infinite41111AWIttinee-anpuv
Equivalent secondary rating:
Wr ? 2(V8/2) Is ? (2)(286)(.03510 20.3 volt-amperes.
Winding dissipation:
IF
AT 1.25 1,25
(1t-) .45 watts per square inch,
K 75 = constant from Table 11-1,
AT m 40 = movianym kedurutbratiwe ri..J. s".
Alit v.
11
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?
? ? .m0...0 '????
r
Winding
F ?
space factor:
.08 log ler + F = .08 log 12.h +.10 = .19,
20.3
le 4?.amigrWr / a 0 m. a 12.h volt-amperes,
r / / %.o3 / ,%.(c
?01, tiv
F ? .10 from Fig. 11-2 since both primary and secondary are
center-tapped,
f 0 115 0 frequency in cycles per second
Scale values:
K0 Wr (.649
Fir
FW
Fel .092, ar
K ? .649 from Fig. 11-) or 11-14 corresponding to s a 1.5,
F ? .9 0 core space factor,
(203
m 1,1,
ra.G1)
p = .930 0 resistivity, tho value from Fig. 11-6
corresponding to 105?C, increased 2 percent.
Flux density:
2/1
B 60 55.0 148 kilolines per square inch from Tables
19-1 and 19-2.
The supply voltage is nominally 214 volts but may be
assumed to be as high as 30 volts.
Characteristic linear dimensions:
$ = .76 inch from nomograph, Fig. 11-7.
Approximate core weight:
mi Ki F1 13 as (8.23)(.9)(.272)(.76) .89 pound,
Ki m 8.23 from Fig. 11-3 or 11-14 corresponding to s = 1.5,
= .272 pound per made inch.
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4.
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???? WM" .1ro, ? .? ?
Core loss and excitation:
From the curves for the material at B ? 148 kilolines per
square inch,
core loss el 1.15 watts per pound,
excitation m 2.2 volt-amperes per pound.
Applying correction factors from Table 11-3, and mmatigying
by care weight,
ir ? (.89)(1.15)(1.3) ? 1.3 matte,
(.89)(2.2)(2.5) ? 4.9 volt.amperes
? 14) Corellimensions
Core exposed surface area:
Si = K212 m (24)(.76)2 13.8 square bathes,
Xi 24 ? constant from Fig. 11.3 or 11.4 corresponding
to s m 1.5.
Core dissipation per unit area:
V1/8i a 1.3/1.3.8 a .0914 watts per square inch.
Lamination center leg width:
L ? 4(L/4) ? (.76)(.97) sm .737 inch, use L m .75 inch,
L/4 = .97 st constant from Fig. 11-3 or 11-14 corresponding
00 0 ? 464,g?
Area product:
AA' . 44 im (.76)4 6334 inch4.
c
Window area:
Ac = .422 square inch.
tow-a CrOaSeCtiOrmial. ?sag
Aia 71-0-- is 424- .79 square inch.
Stack height:
A
1.055 inches, approximately 1-1/i6 inches.
eL m
77;
11
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Aww, -W.01 '00P.,' 0
. 1.05t ma 1.41
4/5
5) Winding Calculations
Sc ?
54;2 s (10.61)(.76)2 ? 6.12 square inches,
a
10.61 ? constant from Fig. 11-3 or 114 corresponding
3 to a a 1.5.
Approximate winding loss:
We
u ? (45)(6.12) ? 2075 watts.
uo
Conductor weight:
Mc KhSte e3 a (4.49)(.19)(.321)(.76)3 .12 pound,
K4 a 14.49
Se w .321
= constant from Fig.
to s a1.5
= conductor material
inch.
041141,01..01...
wAhavuu4,44- M440 per ampere:
=117p7041F--(K5 Fc)
;571":1
.40?40014100/0
amp
11-3 or
density
114 corresponding
in pounds per cubic
*7 (826)(.19) 450'
x5 m 826 a constant from Fig. 11-3 or 114 corresponding
to s = 1.5
Primary input power:
"rp
..wr w + 1.414 W 1= 20.3 + 2.75 + 1.414 (4.9)
ex
= 30 volt amperes.
RMS voltage of half the primary:
ADMritIP PccrARCY
F
r
LL ;G
-212 -
iwsnrur Or
TECi4NOLOCiY
APO
1.011IIIM0101=0020
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Vp/2
? "4,r ,111.1111 ',11...."^ a " I'
b-lArie? (24-1) Piot 21.2 MIS volts,
s 24 I. MAT VOltage
?
T ? .85 a ratio of Titration contacting time to half
a period.
Primary 1.15 currents
Ii
A. is .708 MS amperes.
?2)
Primary wire sisal
al a 060(.708) ? 318. Use number 25 AW3 wire (320.h CM).
Secondary wire size:
CN = (4.50)(.0354) a 15.9. Use number 38 Alki wire (1.5.72 ON).
TWINS per volt:
105 105
r Li* f IL trlaiTrESITTIMM3
5.73 tams per volt.
Correction for winding resistance drop:
2.7g
mr;4r? a *135
Primary turns:
=
= 222 turns.
Secondary twins:
?
V_. ?
r - (5.73) (2) (M..2) (1-1.3512)
8 is ^iv M1 N
cvlislc, r'4
sit 3500 turns.
6) lanai Layout
Winding length
(5..r.3)(2%) (2)(1
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??? ? ?????11.111/ ?????,.
..11.1. %raw yr-, a a -
inch.
Turns per layer:
Primary: (118)(.875) la turns per layer.
Secondary: (2014(.85) 0 178 turns per layer.
Layers:
Primary: 222;" 5.3 use 6 layers
Secondary: 3500/178 11 19.7 use 20 layers.
Revised turns per layer:
Primary: 37 turns per layer.
Secondary: 175 turns per layer
7) Vaick Qf 92pil Build:
Thickness inches
Tube
20 layers of No. 38 AWO wire (20)(00145) ?
19 layers of paper (19)(.002) s
Wrapper
6 layers of No. 25 AW) wire (6) ( .0191) ?
5 layers of paper (5)(.002) =
Wrapper
.322
Build = -75,r 100 . 86%
.030
.090
.038
.020
.114
.010
.020
.322
irnna
Core:
Lamination: scrapless El with center leg width of 3/4 inch,
Steel: Hot-rolled silicon AISI-M-22 grade .025 inch thick,
Stack: 1-1/16 inches.
Tube: .03 inch thick, 3/4 x 1-3/32 x 1-1/16 inch long.
Secondary winding (next to core):
Wire size: No. 38 Alf3 single-enamel copper wire,
Turns per layer: 175,
Layers: 20,
r
IMAM
MEW?A A% 6.1 es ? r r * g r I Al I% A I 01 LI
P?PirlAJWO% AgGJC/%1%%. rs r ti 1.? 1I a
OF ILLINnIg INSTITUTE OF TECHNOLOGY
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? two ? , V
.www -ft WII/0" "%VW VV.. a .?
Turmas 3500, tap at 1750 turns,
layer Insulation: .002 lush paper,
Wrappers .02 inch raper.
Primly windings
Wire sizes No. 25 AM singlemenanel copper vire,
Turns per layers 37,
Logru.st 6,
Turns: 222, tap at 111 turns,
Iyer insulations .002 in paper,
Wrappers .02 inch paper.
?-
???
9) Check of Winding Resistances
Mean length of turn equals length of inside turn, plus pi
times build-up of minding.
Resistance equals ohms per inch, tines wan length of turn,
times turns, times correlation to operating temperature.
Seoonderys
m s 2(.75 + .060) 2(1.094 + AO) + (.188) w 4.33 inches,
cs
Re ? ((f27-14i :2) 04.33)(3500) 1122 obis.
Primary:
g, 2(.75 + .060) + 2.0.0914 + nfin
up
R (32.37) ( .93) f
p (12060) (.679) 6.184)(222) = 11.186 ohms.
10) Calculation of Temperature Rise
Surface temperature rise:
W
?c?+
F
BUT surf (5 )fh + h_N
case ix
*sin% e LI 4
? ?????1404 - "1.+AhAsagorup
12.3C,
c s Ip (Np)s. (.03514)c(1122) + (.708)'(14.1i6) 3.614
watts,
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W 0 1.3 watts,
S 0 42.6 square inches (3.19 x 2.63 x 3.07 inches),
case
Tsarf ? 1.1 ? form factor of surface from Table 11-9,
hr ? (.0069)(4) .00629
is assumed to be VC.
surf
agu
. su + . Q
med calulated (.1)(30)+(.9)(12.3) 0 e w?1 as9
14.1.0
Temperature difference across impregnantl
.188
.0122 x 6.12
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4,0 ? .4. ???????????????????? 41..?
??? ? ,s? ????
?
mriu a .. ? ??? ? ????.,
st ? 1/2(.35) ? .188 inch,
a hi( +1r....4A0. a .033 4. .0122,
5.6
Average winding temperatures:
Primary: Tree Tale Oar: + gimp + .65 Oh
? 65 114.1 * 104 f (665)(7?4)" 94.6?C(6T ? 29.6.0)
Secondary: Teeo ? Tub+ Owe Oiv +
?6 + 14.1 + 10.7 + (.9)(7.1)m 96.5.C(tef ? 31.5?C).
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? .???????-? 71.111. Ie."' '
XXI. DESIGN PROCEDURE: LOW-CAPACITANCE TRANSFORNERS
MOIMONIMMI16,
-
1) List qpecifications
frequency, voltages, secondary currents, capacitance from
secondary to primary and care, secondary working voltage,
temperatures (ambient and swab= rise), grade of
protection.
2) Chosen Quantities
Type of core, grade and thickness of lamination or strip
steel, core space factor, type of construction.
3) Nomograph Values
Secondary Ratings
W ?V I volt-amperes,
r as
where V = secondary HMS volts,
Is = secondary RMS amperes.
Allowable secondary winding dissipation:
CO faT1.25
?... ? watts per eq. in.,
os
where = secondary losses, watts,
s
(9-114)
A is sonowinwer awratimesA derminfana Avian dm_ 41,y__
4 wwwwwwwui willisawymo wroNovio,
AT,simaximum permissible temperature rise, 'C,
X is parameter from Table 21-1.
?Rinivalont rating (hainad nn AO mreliam nnei hnin
Wi =
63 volt amperes
-7 776 T - A
cie (-7,3.)?
? where f so frequency. cps,
AT = maximum temperature rise,
Rating and capacitance function:
2..21)
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114,114 'Ye-. 4 ???????? ?
k01: 2/7 k le .286
r
ar
where Wr a equivalent rating (60 cps, 1,10.0 rise)
C ? desired secondary capacitance
kc * correction factor for secondary supports
and any dielectric between secondary and core.
Winding space factor:
'0 is found from Pig. 21-1.
Highest of two vamp for Fc is preferable.
Geometric factor:
? .22
Nomograph scale factors:
W F W
Or
Find -1111--w-- and C :9
Fi
where Wr a secondary rating, volt amperes,
F core apace factor (usually given by manufacturer),
f a frequency, cps,
(9-15)
1B resistivity of conductor material, KU:robs-inches
(For copper wire, increase the standard for 100
per cent conductivity by about two per "-Ant),
Flvx density: Choose B in kilolines per sq. in.
Characteristic linear dimension: Find from nomograph.
Area product: Calculate AcA1 a $4, (2.6)
where A a area of core window,
A a gross cross-sectional area of care.
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?
x? ? ',NM. lir.,
14) Core Propertiee
Approximate core cross-sectional area:
A = 1.642 VT sq. in.
where 4 ws characteristic linear dimensions,
F= winding space factor.
Approximate core window area:
Ac Ai
Ac or
Ac
(9-214)
(9-25)
Select a lamination and coredimmusions:
Lamination thickness should be suitable for frequency.
Assembled core should have approximately the calculated
Ac and L. if it is suspected that working voltage is
too high for the core else, a rough check may be made
by considering that assembled primary will occupy about
110 times F. per cent of the window, and that secondary
will occupy about 100 times Fc per cent of the window.
If clearances are inadequate, a smaller Fc
chosen to find a larger 4.
Ivo
0111J u.a.u. uhriw
Core weight:
This can be found using data of manufacturer, including
space factor, or from
Mi mi Fi lbs., (2-22)
where m = mean length of magnetic circuit, in.,
A m care cross-sectional area sq. in.
= core material density, lbs, per au. in.,
r. ? core space factor.
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VP,
1
Excitation (wa) and core loss OW):
Volt amperes and watts respectively are each calculated as
the Epstein values per pound (functions of density, E) times
correction factors (to account for increases over Antall:
due to joints and other factors) times core weight in pounds.
5) Wading Calculations
latimmte of Winding losses:
2 Iles
Vic is 224: -sr-- 'matte.
011
Circular Nils per Ampere:
Find
(MO To Pd.
Primary Current (For resistance load):
1
Ip
where V im primary volts,
s secondary rating, volt amperes,
w estimate of winding losses, watts,
tv, care losses, watts,
(9-26)
ampere 8,
W as excitation, volt-amperes,
12 x e X
leakage-reactance volt-amperes, estimated
as 10% of W far COnegantrin windings.
Wire Sizes:
Calculate circular mils cross section for each winding:
equal circular mils per ampere times amperes. Then select
the standard wire sizes having areas closest to the results.
Turns per Volt:
N 2.05
7-21 hal f gi B
(2-33)
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.1rlep .41p...? I ? ? .? ft* ? .? ? ? ????.,
where f = frequency, ops
F = core space factor
A ? gross core cross-sectional area, sq. in.
B = flux density, kl. per sq. in.
Xinding Turns:
Primary: Np ? 11- x VP turns
tr
Secondary: NB X Vs (1 + 4.4) turns,
"r
'there the term in parenthesis corrects for
resistance drop.
6) Winding Layout:
Primpry: Find winding axial length, equal window length
minus margins. Find permissible turns per layer,
from winding length and permissible turns per
linear inch. Then calculate number of layers.
Choose a tube, layer insulation, and wrapper, and
calculate radial build.
Secondary: Choose number of layers, turns per layer, tube
size and insulation such that secondary is centered
in remaining space, preferably so that it is about
equidistant from core and primary. The secondary
tube may be made round if tube diameter mast be
large compared to primary size. Otherwise a
square shape with rounded corners is necessary
to obtain equidistant spacing.
Check of Secondary Insulation
Secondary test voltage may be a little over half of predicted
breakdown voltage. For a creepage path, breakdown voltage
may be estimated as:
KV -18t'7 kilovolts EMS
where t = length of path, inches.
For breakdown by strike through air, a relation for typical
irregular electrode shapes is:
KV = 28t4 kilovolts RMS.
Permissible working (peak) voltage for a straight creepage
path equal to secondary spacing is found by calculating
breakdown and choosing a test voltage. Working voltage is
then:
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? ???111- Tr?-?? ? ".."1
1KVT-
gi kilovolt: (peak),
(9-2?)
whereT ? test kilovolts, RFC
Obis relation is the same as the camas ENS test volts ?
2 tines rated volts plus 1000.) If permissible working
voltage is not MO enough, a new design using a larger t.
mg, be made, or it miy be possible to raise breakdown ? '
by increasing creepage paths In the same design. In the
latter case the equation for breakdown by strike moor be
applicable.
ej yindinavistances and Losses:
Find mean length of turn of each wiskt,m4., equal to the length of
the inside turn plus pi times the radial build of that winding.
Resistance of each winding is length times resistance per unit
length times a correction for operating temperature.
Losses of each winding are current squared times resistance.
The sum is W
0.
9) Capacitance (For concentric windings, from secondary to primary
and care:
3g: glen
C?
In
'2
crUacwoum,
(9-2)
? wheremem ? an length of secondary turn, inches,
um
k ? correction factor for secondary sw*-ee
and say dielectric between secondary
and core. (Typical values:are 1.2 to 1.5.)
?perimeter of remaining window space with
-1 primary in place, inches,
0 ri'ser4usgoter of indiformulaimy woes section, around
a 2 wire only, inches.
10) leakage Reactance (Concentric Windings):
Er m o
5 f12 0
obms,""-
10 it h
-f
(940
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where f ni frequency, cycles per sec.,
N ? turns of winding to Which X is referred,
0 effective separation from secondary to
primary, equal to actual separation of
closest wires plus one-third sum of
radial builds, inches,
h ? axial length of seconderv. equal turns
per layer times wire diLo;ter, inches.
11 Transformer IrmasLance and Load Resistance:
Turns Ratio:
Load resistance, reamed to primary:
V
R s n2 .T.. ohms,
where V ? load volts,
I In load current, amperes.
X referred to primary and RL may be compared to check the
accuracy of the assumption that I5
:2l(is 10 per cent of lc m
I 2s RI. Equivalent transformer resistance, referred to primary,
is
R R+n2Rohms,
where R ? prim&ry resistance, wum",
Rs secondary resistance, ohms.
Transformer impedance (referred to primary):
ni V 2 X2 ohms.
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12)
immokommmw#
no effect
?necessary
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'1,..11 I ? + +
Z and it should be compered to see that.Z is lees than111:.
Otherwise paver output coed be increased and temperature rise
decreased increasing load resistance. This indicates that
vire sizes should be increased and turns ratio (as defined)
should be increased.
Cho* of volualtutt
Primary voltage (needed to give the specified output):
nVe + Rp +nig Re)- + (
tns
volts (9-6)
where I.. ? primary current, amperes,
1.1
Is si secondary current, amperes
V secondary or load volts,
I "'leakage reactance referred to primary.
If calculated Vp is not sufficiently close to required Vp,
should be Changed. This chalices n, but has practically
on I. The term :ye is unchanged. Therefore, it is not
to recalculate impedances if Change of n is small.
13) ......jacalciALIK414?!AELLIEtet1262:
Approximate Secondary Surface Area:
5 ? 1.5 m P2 eq. in.,
es es
where is mean length of secondary turn, inches,
10 ? perimeter of secondary cross section,
.2
around mire only, inches.
Secondary Dissipation is Ce
Cs
wherees is calculated secondary loss, watts.
?
(9-29)
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? ??? .re W.'. S -
If this is too much higher than the preliminary value, wire
sizes should be,increased and number of secondary turns reduced.
If it is too much lower, wire sizes can be decreased and
secondary turns increased. In the latter case, the gain in
weight may be too small to warrant redesign, particularly if
transformer series impedance is an appreciable fraction of load
resistance.
lb) Design Summary:
List core dimensions, lamination thickness, steel grade, winding
tubes, vire sizes, vire insulation, total turns, location of
taps, layers, turns per layer, layer insulation, and wrappers.
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???????????????
??? ??????? ?
:????
TABLE 21-1 INEIRILTURE-RISIS PARDO= OF WW-CAPACITANI1E TRANSFORM/1
(OPEN-Tin CON8111UCTION)
01111?1111.1111.10.
.4111?11..0
Ambient Torperattusso s?C
011111.11411111?
411110111MMINIIMINIMMIIIPSIMOINIMMOSUMMIN
65
85
115
125
200
130
124
120
117
1114
108
106
90
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???????????????
??? ??????? ?
:????
TABLE 21-1 INEIRILTURE-RISIS PARDO= OF WW-CAPACITANI1E TRANSFORM/1
(OPEN-Tin CON8111UCTION)
01111?1111.1111.10.
.4111?11..0
Ambient Torperattusso s?C
011111.11411111?
411110111MMINIIMINIMMIIIPSIMOINIMMOSUMMIN
65
85
115
125
200
130
124
120
117
1114
108
106
90
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ron.vomve.
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',ono yr". ? ?
V
XIII. ZUNIS: DISIGN OF LOW-CAPACITANCE TRANSFORM
Speeitications:
Ittequencys h00 cps.
Primary: 115 volts.
Secondary:' 10 volts, 5 amperes.
Capacitance from secondary to primsry and ewe:
9 micro-microftrads.
Secondary working voltages 2 kilovolts.
Ambient temperatures erc
Maximum rises 115?C.
Grade of proteotions Grade 2(1ess resistant to
adverse environmental conditions).
,
EhmeitetEtilr
Com Laminations will be selected to yield an
approximately square core cross-section and a
square sidzWksr.
Core steel: lh mil non-oriented silicon steel AISI4-19
grade. (This thickness and grade were chosen only
because of availability.)
Core space factor: .88
Construction: Open core and coils, primary and secondary
to be placed around the sans cord leg.
31 lee-21133.2.?eet
Secondary rating:
Wr 8 ? V I no (10)(5) es volt-ampere 5.
Allowable secondary winding dissipation!
1.25
efiTr ) se
? I,
IIC 1025
( ) 11 01 watts per sq. in.
AT is 115 sig maximum temperatuxe rise in ?C,
K - 1114 es constant from Table 21-1.
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+,
MEM
Equivalent rating (based an 60 cycles and 40.0 rise):
Wr 50
a 6.05 vol
wr. .76 al .63 400 .75,115.63 t-amperes,
(10-)
f 400 0 frequency in cycles per second.
Rating and capacitance functions
I 2/1 2/7
k
c r
......e........
-.28
kc ? 1.5 ? factor 'which accounts for high temperature
material to be used for supports,
= 9 = capacitance in miaro-mierefarade.
Winding space factors
Fe 012, from Fig. 21-1.
Geometric factors
.
.11 *22
22
(Fe). i737277 ? 487.
Nomograph scale factors:
V16?
'0 "r
.112,
Fe Wes .12
.37. = Tar 1.01 ? .1030
75 10
where p is taken as 1.16 from Fig. 11-6 increased 2 percent.
Flax density: Choose B =65 Ii. per
.in.
Characteristic-linear dimension, from nomograph:
= .67 inches.
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lunar mr--? 1.? ""
Area products
Ao w Ah .674 ? .201 init.
h) 12ELEV2511!!'
Cross-sectional area:
Ai 1.642 1.6 x .672 PT
.2148 sq. in.
Window area:
Ao
.81 sq.
c
The nearest else In stock is the Alleghemy-Ludlum I,4 ludnetion,
which has width of 1/2", and yields a *indult of 3/14" x 1-1/2" ?
1.1$ K. in. A square cross section may be.weed to mike the
steak 1/2". Although this gives an area product somewhat larger
than calculated, the windings will be somewhat manor.
Core weights (Using manufacturer Is data)
iti 1ri times weight of solid square stack
.88 (.142) .388 lbs.
Excitation in volt-amperes per pound is approgimately proportional
to toriionano3r. The 60 cycle Epstein valve at a kl? si
is 2.4. Increasing by 2.0 because of Joints and other 'each
mlww1wlaw 2 mnipromt4nn far freamenov. and multiplying
factor;, OM 21,12 sop otiordwo ~we a ,
by weight gives:
W w 2.4 x 2.0 x 76- x 0388 ? 12.14 volt-asperes.
ex
Core loss in watts per lb. is appragimately 13.0 (Epstein) at
1400 u?tcles, and the correction is estimated at 1.2. Total
me loss is then:
/(tCa....
01.9 v _IRR
6.1 watts,
Es.:),mate of winding losses
111
W w 22 r0 so 22 (.67)2 1.01 w 10 watts.
cs
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?
???......? 'rat .1111r*, ? ' ???
Circular mils per ampere ?
io led is
ro.45:107--
Primary current:
V57-(1000 x .787 x .12) ? 241.
15)
Estimate Is2 X as 10% of We
Then
IP
2 + (12.4 + 5.0)2 0 .595 amperes.
Wire Bill032
Primary: .595 x214 ? 2.144 CM. Use No. 28 wire.
Secondary: 5 x 241 is 1205 CM. Use No. 19 wire.
Turns per volts
e
10'
"r1LzihtfrA4
Primary turns:
N x V ? 3.95 (1.15) 455.
P P
Secondary turns:
N_x V8 .Ts (1 +12--.)
= 3.95 x 10 X(1 4- .2) is 47 turns.
6) Winding Layout:
Primary:
Winding length = 14/2" min= 2 x (1/8")
is
0 3,95.
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Vit.^.. ?.. ????
Turns per layer 0 1.2$ x 67
8h, use 76.
Layers ? -hi- ? 5.42, use 6 layers.
Itistry build.:
palm
Tube .02$
Wire: 6 x .0136" .082
Insulation:
5z .0015 .007
Wrapper .010
Total .12$ in.
Secondary: (To be concentric with primary)
The space remaining, after the primary is inserted, is
.625" x 1.$*. To obtain a secondary cross section of
roughly similar proportions, use 3 layers and 16 turns
per layer.
Winding length is 16 x .0374 ? .60".
Use tube length a .731/.
Secondary build:
inches
Tee .0h0
Vire 3 x .03714" .112
Insulation 2 A
4,001" .01h
Wrapper 010
AMIIIMI???????
Total .176
The secondary tube may be made in the shane of a square with
rounded corners. The flat portions should be at least .9
long in the direction of the vire. Inside clearance between
flat sides, so that the secondary is properly centered in
the window, shnuld be
.5" + 2(.12$") + 2(.3$0") = 1.14$"
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7) Check of Secondary Insulation:
Minimum separation from secondary to the primary or core is
about .35 inches. If straight secondary supports are used,
having a creepage path only this long, breakdown voltage
would be approximately
KV 180 a 18 (.35)4
go 8.65 kilovolts,
For a safety factor of almost two, test voltage can be 4.4
kilovolts. Permissible working voltage is therefore about
KV-1 44 - 1
KV_ wimmola . 9/1 2.h kilovolts.
VT VT
Thus the straight supports are
voltage of 2KV.
8) Resistances
Primary: (No. 28, 455 turns)
Mean length:
mop 1(.5) + % (.125) a 2.39"
Resistance at 200eC:
adequate for the required working
= length x (ohms/1000
g temp. aorrection
?p.O x miV64.9 x
Secondary (Ndaft 39, 147 turns)
Mean lengths
mos is 14(.5) + n (1.145 - 5) + (.176) gi 5.54s
Resistances (Add length of two turns for leads)
5.54 x 49 1.16
12,630 x 8.05 gj 311 ohm'
Winding losses:
5952
Wre in .
x 9.83 4. 52 x .311
m 3.139 + 7.77- 11.26 watts.
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9) Capacitances
1?35 ko nee
C
?
?
11,31.W.?2c,,j,a,mk
2(.625 + Lc)
n t(ith + 126)
(.1,26 is build of secondary wire and interlyer insulation)
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!minim vit?, a ??????????????( ??-?-???? ?
C ?313.4 micro-ssicrofarads.
10) Leakage Reactance (referred to primary, for concentric windings):
n 0
5 ? Iff2co
ansmagoorramone oball
10
5 54 ( * .126k .40)
5 boo ( 2
1455)
(.40 is :wpm. separation between primary and secondary)
?? ohne.
13. Transedanoorner e and Load Resistance:
Since the turns ratio is tentatively
"
...Er ? 9.68
9
the nominal load resistance referred to the primary is
V
1,26 al 01.682 It srp 10 1 oboe.
- Is *L""'
This shows that assuming I to be 10 per cent of W
r
wits good because I is about 10 per Gen---1-? of flt.
At this point a check nay also be made to see that transformer
series impedance is less than load resistance. Equivalent
transformer resistance referred to the primary is
RR +?2 R 9.83 + 9.682 (.311)
P 3
38 . 9 0/11115
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Transformer impedance referred to the primary is:
Z ? * 12 ' \68.92 18.42
? 43.1 ohms.
Since Z is less than RI:1, the transfwrar is not operating in
the undesirable region *ere 'watt output could be increased
with a loser temperature rise.
12) Check of Voltage Ratio:
Calculate primary voltage:
a I. X
+ I_p R +nI Re )'
e p s
...................----, .
gi \1 (9
7.68 x 10 + .505 x 9.83 +9.68 x
+ ( 5 x 18.4)2
suITSZEr"
1 0 .2
+ m 3.18 volts
This is the primary voltage needed to yield a secondary
voltage of 10 under the specified conditions. However,
since the temperature rise factor X is intentionally
conservative, the rise Will probably be someilhat less
than imazinum, and resistances An then be lees than those
Amu. This yields a primary voltage closer to the
nominal 1g.
Secondary Dissipation
Exposed secondary surface area is appradmately
S ? 1.5 mceP2
e
1.5 x 5.514 (2 x .726) In 12.0 sq. in.
Therefore
We 7.7Ces
*65 matte per eq. in.
1
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???
This is considerably low than the preliminary value. One
MOM is that wire sins are slightly larger than the
calculated values. Another reason is that the care is
larger than calculated, asking the winding smiler. Since
the calculation of current densitr did not account for this,
secondary losses we', reduced non than surface avec In
some cases it would be desirable to nodify the design to
obtain a higher towantwe rise.
Dottie theosarr:
Notes Use materials suitable for 200?C operation
Core
laainationst Type 104, 1/2" vide
Window: 3/14" x 1-1/2!
Stack: 1/2"
apace factor: .88
Steel: A1814.19 grads, MO thick (29 10P)
Priam (31,5 volt)
Wire sizes No. 28 AVG, single enamel
Turns: US
Lams! 6
Turns/layers 76
Tube: .025? x x .5? 1.50 unit
layer insulations .0030
ilkspper ,009"
fitt: (10 vo3.ts, 5 amperes)
Mount concentric with primary
Wire sise No 19 MICI, single enamel
Turns: ia
Layer!: 3
tr----umslivent
Tube: .040" thick, .73m long; 1.45" arum: (inside
din.) with rounded corners, flat ;nations MP
sides are 1/2".
Layer insulation: .009"
Wrapper: .010"
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CONCLUSIONS
1. The basic design procedure which was developed under Contract No.
DA-36-039 3C-5519 has been extended to special types of transformers, including
transformers with unbalanced magnetisation, current-limiting transformers,
current-limiting transformers with unbalanced magnetisation, vibrator-supply
transformers, low-capacitance transformers, and instrument transformers. It
is possible to design these types of transformers with very little trial pro-
cedure, and the methods given should be understandable to an engineer not
normally associated with the transformer industry. The design method accounts
for operating temperatures to 200.0, ambient temperatures to 20ed, pressures
between 30 inches and 1,32 inches of mercury, power ratings to 5 kilovolt amp.
(ores, RNS voltages to 50 kilovolts, and frequencies between 25 and 2500 cycles
per second.
2. The design of transformers with unbalanced magnetisation requires
suitable data on magnetic materials under unbalanced conditions and suitable
relations among the cLectrical circuit quantities. Uta have been compiled to
give core loss, excitation and nonmagnetic gap as functions of AC flux density
and DC or average magnetisation. It has been found that the desired non-
magnetic gap (if any) should be based upon the conditions which give minimum
excitation current. It is possible to compute secondary voltage and current
from circuit constants and with the aid of published data. Primary current is
computed by approximate equations which include load current, losses, and ex-
citation as terms. The design of transformers with unbalanced magnetisation
may be accomplished using the previously-developed design procedure with a few
modifications.
3? Current-limiting transformers require the calculation of proper turns,
turns ratio, and magnetic shunts Relations have been obtained among
primary and secondary flux densities, voltages and currents such that a design
may be made in a straightforward manner. These relations account for the re-
quired ratio of short-circuit to load current and the change in leakage
reactance between normal load and short-eirouit operatinc, ennAitionet It is
necessary that the turns ratio be corrects otherwise it in not possible to
select a Shunt which will yield proper circuit characteristics. ftunt gaps
are so small and so critical that manufacturers will probably be unable to
eliminate production tests in order to make sure that proper output is
obtained. The design procedure for current-limiting transformers with um-
balanced magnetisation combines principles of the two individual tirpes.
Vibrator-supply transformers are designed in a manner similar to that
for the more common filament or plate transformers, but special considera-
tion must be given to insulation problems, the timing capacitances and to the
effects of the vibrator on transformer operation. A proper timirg capacitance
is necessary in order to give a satisfactory voltage wave shape and to prevent
extremely high induced voltages in the transformer windings. It is necessary
to design these transformers using comparatively law4f1ux densities because
of the large supply-voltage variations which are frequently encountered and
because of excessive currents which would occur if the vibrator causes a
circuit unbalance during starting or normal operation. It is common practice
to place the primary winding over the secondary in order to have the higher
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primary resistance than would be obtained with the primary next to the core.
This aids in keeping starting currents low. BOMOVOT, if primary resistance is
increased V' reduction in vire sin over the values that would normally be used,
the design would tend to become uneconomical because of unequal current densit-
ies in the different windings. Vibrator supplies (*orating from a source over
about 15 volts must be designed with special care because contact arcing say
be maestro. Series resistances are santimes incorporated into the primly
circuit to provide *proved starting characteristics.
5. Lowcapacitance transformers are required when it is necessary to
supply a load which must have a low-cepacitance path to the power supply. These
transfonsers are often used to supply a low voltage difference to a filament
circuit which has a high voltage to ground. lipirical equations have been
derived from measurements on medals and troll theoretical studies to establish
important relations among power ratings 'pace-factor, and desired capacitance.
It is found that for a given rating there is a nininue value of capacitance
which can be obtained for any spacing of the secondary winding. In low-
frequency uldtsaleekage reactance has only a minor effect on the value of volt-
age regulation. It is important that voltage drops due to winding resistances
be accounted for in order to obtain the required voltage ratio. Leakage react-
ance will become more important at frequencies over 60 wan, but in all
cases it should be computed and used in the design equations.
6. Instrument transformers for measurement of voltage or current say be
designed using the basic design procedure. It is necessary that the burden be
used as the power rating. Current transformers nust be designed with a very low
flux density in order that they may provide a reasonable ratio of load to in-
strument currents for load currents above the normal rating of the circuit.
When the design of an instrument transformer is completed it may be checked to
determine whether ratio and phase angle errors are within the limits required
for the particular design.
7. An ammayvis has been sada to deta......zurile how minding current densities;
should be selected, that is, whether different densities should be used for
inner and outer windings. It has been found that minimum losses would be
obtained if current densities were somewhat higher in the inside windings.
However, if total densities were constant, then temperature rise would be min-
imised for higher densities in the outside windings. But the assumptic:. of
constant losses and higher densities in the outside windings would result in.a
lower power rating. Therefore it is recommended that current densities be
uniforms as a compromise for reasonable losses and heating.
w. A etaq of optimum core portions which was carried out during the
previous contract has been extended. The recent work gives optimal proportions
for certain laminations. The proportions of these specific laminations reo-
present restrictions which make it impossible to obtain the over-all optimum
core proportions, but it is possible to obtain certain most favorable proportions
for each lamination. Results are given in the form of optimum core-stack
ratios. These ratios are functions of the relative costs of the core and
minding per unit volume where ',cost" may be taken as weight, volume, losses,
or manufacturing expense.
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9. Test results and calculated results have been compared for develop-
mental models constructed during the course of the contract. Important corn-
parisonsare those between test and calculated operating temperatures. It is
important that the maximum be approached as closely as practicable, but not
exceeded. Actual temperatmres et a given design can be expected to vary some-
what with manufacturing practice. It has been the intention to establish design
parameters such that the maximum temperature rises are used in the calculations,
and such that the resulting designs will have temperature rises ranging from
75 to 100 por cent of the
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4
1321r. RBOONNIBETIONS
It is recommended that the design method be applied by menufacturing
canoe xis and by government agencies to the types and ranges of transformers
mbich have been analysed. When a designer has gained experience in the use
of these methods he should be able to devise short-cuts in the selection of
design parameters and to omit some of the calculations. When a manufacturer
has gained experience by production and evaluation of large quantities of
transformers, it viii probably be found that more accurate parameters can
be specified in some cases. This is partioulaety true where the parameters
depend on manufacturing practice and upon choice of materials, variations
which it has been impossible to account for in a stu4 of this kind.
It is believed that the basic philoscplIf used in the development of
the design procedures could be applied to other electrical apparatus with
advantage. Ixamples might be indhotances? relay coils, and rotating
machinery.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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UT. LOGBOOKS
The data obtained on this project are recorded in the following
Armour Research Foundation logbodkst C-3280, C-3296, C-3598, C-3723,
Cm3858, and 0,4296.
nu. am CONTRIBUTORS
Principal c?trihutors to this research study have been the
followings
R. M. Bergslien
P. E. Bows
00 A. Forster
H. L. Wisteria?
Principal
C. C. Peterson
L. J. Strattom
R. 14 Zenner
participants for the subcontractor, Gramersaalldorson
Transformer Corporation have been:
F. R. Cooper
G. Galls
F. E. Zimmerman
V. H. f anon Manage
Electrical ftgineeri
Research
Respectfully submitted,
ARMOUR RESEARCH FOUNDATION of
ILLINOIS INSTITUTE OF TECHNOLOGY
Associate Electrical Engineer
/
?Y-7,44?4-0
#. L. Oarballinc
Machines, Components and
Measurements
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BIBLIOGRAPHY
1. Rex, H. B. "Bibliography on Transductors, Magnetic Amplifiers",
Instruments, 21 (April 1948), 332.
2. Miles, J. 0. "Bibliography of Magnetio-Amplifier Devices and the
Saturable Reactor Art", Trans. EEL 70 (1951), 2104-2123.
3. Niwa, Y. and Y. Amami. Magnetic Properties of Sheet Steel Under
Superposed Alternating Field and Unsymmetrical Hysteresis Losses",
Researches of the Electrotechnical Laboratoq, No. 124, Tokyo,
Jaw 1923.
is. Niwa, Y., J. Sugiura and J. Nature. "Further Study of the Magnetic
Properties Of Electrical Sheet Steel Under a Superposed Alternat-
ing Field and Unsymmetrical Hysteresis Losses", Researches of
Ia1pjq, Tokyo, No. 144,71;17113--
5. Spooner, T. "Effect of a Superposed Kiternating Field on Apparent
Magnetic Permeability and Hysteresis Lose", Natal Review, 25.
(1925), 527-540.
6. Battelle *serial Institute. Research and Develo nt of Various
Co 0 ations of Core HS
ract pt. o e , .rps
Rnalneering Laboratories. Final Report, 1952.
7. Harris, F. K. Electrical Measurementa. New York; John Wiley, 1952.
8. Charlton, O. E. and J. E. Jackson. "Losses in Iron Under the Action
of Superposed Alternating and Direct Current Excitations",
Trans.._,AIEL 44 (1925), 824-831.
9. Hanna, C. R. *Design of Reactances and. Transformers Which Carry D. C.",
Imp. AIRE, 46 (1927), 155460.
10. Lee, R. Electronic Transformers and Circuits. New York: John Wiley,
1947.
U. E. E. Staff, Massachusetts institute of Technology. Magnetic Circuits
and Transformers. New York: John Wiley and Son's, 1941
12. Legg, V. E. "Optimum Air Gap for Various Magnetic Materials in Cares
of Coils Subject to superposed Direct Current", Trans. AIEE,
614 (1945), 709-712.
13. Carter, R. O. and D. L. Richards. "Incremental Magnetic Properties of
Silicon Steel, with Particular Reference to the Design of Air-
Gapped Smoothing Chokes", Proceedings IEE, 97 (1950), 199-214.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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14. Schade, O. H. "Analysis of Rectifier Operation", Proc. IRE, 31
(1943), 341-361.
15. Seely, Samuel. Electron-Tube Circuits, New York: McGraw-Bill, 1950.
16. Garbarino, H. L. "Some Properties of the Optimum Power Transformer
Design", Trans. AIEE, 73 (1954), paper 54-118.
17. Mallory and Co. Vibratory Power Supply Design. Indianapolis,
Indiana: P. 1. Mallory an o.
18. Connelly, F. C. Transformers. London: Pitman, 1950.
19.
20.
21.
Dietin, L. S. "Modern Vibratory Power Convertors," Post Office
ElectE1222.12r0Journal..........0 Vol. 39, Part 27=7-137 53.
Evans, R. H. Vibrator Power Units. Report No. L. 1482. Royal
Aircraft Establishment, England. Oct. 1952.
Dixey, K. H. and Wilman, C. V. "Methods of Increasing the Power
Rating of Vibratory Convertors," Proceedings I. E. E.,
Vol. 98, Part III (March 1951), p. 105.
22. Mitchell, J. H. "Recent Developments in Vibrator Power Packs,"
Journal of the British Institution of Radio ineers,
o PP
23. Kiltie, O. "New Type of D-C to A-C Vibrator Inverter," Trans. AIEE,
Vol. 59 (1940)) PP. 245-247.
24. Allen, A. L. "Long-Life Contacts for Unidirectional Currents of 1-20
Amperes," ftostt_queLL.E., Vol. 100, Part 1 (July 1953), p. 158.
25. Hunt, L. B. Electrical Contacts. London: Johnson, Matthey and Co., 1946.
26. Evans, R. H. The Use of Grain-Oriented Silicon-Iron ,C-Cores for Vibrator
Transformers on o t
Triiiiat Establishment, AREZWough, England. June 1950.
97. Plankhurn, J. F. Convonanta Handbook. LIeTe RAMA:Linn Laboratory
Series, Vol. 17. tew York: McGraw-Hill, 1949.
28. Terman, F. E. Radio Engineering. Second Edition. New York: McGraw-Hill,
1937.
29. Bell, D. A. "Vibrator Power Packs," Wireless World (August 1948)1 P.
30. Williams, N. R. "Heavy Duty Vibrator Type Power Supplies" Radio News
(June 1946), p. 46.
31. RMA Standard Vibrator Power Transformers. REC-119 (Sept. 1948).
stems.
OC
ote
0.
6.1.?
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32. Rawlings, L J. Radictrom Da Nandbook. Fourth Edition.
Vibrator Power 32. garrison, Now Jersey:
CorporaUon of America, 490.
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APPENDIX A - CONDITIONS FOR MUNN TOTAL WINDIN3 LOSSES
Consider first a two winding transformer; then the results can
be extended to any number of windings. Winding losses are the sum of
current density squared times resistivity times conductor volume for the
windings.
w ? 62 pm A F +
P cp cp cp
212
pes Acs Fco watts, (A-1)
where Am current density of the winding
denoted by subscript, kiloamperes
per square inch,
/010 0 conductor resistivity, microhm-inches,
mc = mean length of winding denoted by
second subscript, inches,
Ac 0 window space occupied by winding denoted
by subscript, including its insulation
and clearances, square innhes,
Fc = space factor of winding denoted by subscript.
For each winding, ampere turns must be constant, and are equal to
N I ? A A F ampere turns,
P P A-4P cP cP
Substituting for
AA, F05 ampere turns.
8
ande from (A-2) into (A-1) gives
(N 1)2
(N 1)2
s
Tic . A P emep + ,pm watts.
CB
CS CS
op -op
But since tie total space avelable for
WAInAlrffm 11 COTIBUffitl.
A +A CI a constant.
cp es
Substituting for Acs in (A-3) according to (A-4), differentiating
with respect to Acp, then removing the constant C gives
ARMOUR
rir c CA Or 1.1
(A-2)
(A-3)
(A-4)
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APPENDIX A - CONDITIONS FOR MINIMA TOTAL WINDING LOSSES
Consider first a two winding transformer; then the results can
be extended to any number of windings. landing losses are the sum of
current density squared times resistivity times conductor volume for the
windings.
Vr ? A2pm AF + 212pm A F watts, (A-1)
C
P cp cp cp 8 08 cs co
here L\- current density of the winding
denoted by subscript, kiloamperes
per square inch,
10 10 conductor resistivity, microhm-inches,
mc m mean length of winding denoted by
second subscript, inches,
At m window space occupied by winding denoted
by subscript, including its insulation
elmaseanAmmi nevirrok innhan;
Fc m space factor of winding denoted by subscript.
For each winding, ampere turns must be constant, and are equal to
NI?A A F ampere turns, (A-2)
pp ""P cP cP
N I on fl A F . ampere turns.
6 S 4,..a up Now
Substituting for A
and As from (A-2) into (A-1) gives
(N I )2 (N )2
wc s 3
mI
P em 1...p. loCS watts. (A-3)
A cp
Op cp cs cs
But since the total space available for windings is constant,.
A +A m CI a constant.
cp cs
Substituting for Acs in (A-3) according to (A-4), differentiating
with respect to A then removing the constant C gives
cp
(A-h)
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APPENDIX ELOPTIMUM CURRENT DENSITY DISTRIBUTION IN A PLANE
The distribution of heat sources is to be found which gives min-
imum total temperature rise from the center of a plane of thickness 2x0 to
the outside ambient. The heat sources are assumed to be currents
(flowing parallel to the surface), of density which varies linearly from
the center to the surface. Irtai a medium of constant resistivity, a linear
distribution of current yields a parabolic distribution of heat sources.
An exception is the case of a constant current density, which yields a
constant distribution of heat sources.
To simulate a transformer coil of fixed load, total current
through the plans must be kept constant, although distribution is changed.
Therefore minimum total losses in the plane are obtained ,When density is
constant, as can be seen from Appendix A, for the case of equal path
lengths. A function of density which satisfies the requirements is
Ko + 1 ( tx ?_),(B-1)
-
where 4
A m _
Aarks44-tr
assumed symmetrical about center of plane,
K 0. a constant, equal to the average value of density,
0
K1 ? a parameter to change distribution of density,
x ? distance from center of plane.
The basic equation of Poisson for one-dimensional heat flow in
a medium containing heat sources is
d2 T
where T ? temperature, iegrees C,
W si loss per unit volume, watts per cubic inch,
k ms thermal conductivity, watts/inch -.C.
Since loss per unit volume is proportional to density squared, Poisson's
equation becomes
d2T
...."1"5"11111.11M
de
CA 2
where C is a constant of proportionality.
(B-2)
Substituting the value of density from (B-1) into (B-2), integrating
twice and using the fact that dT/dx im 0 at the center (x.,0), gives
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II
c le2 2 KO 3% Xg
- 40 u Ko
where T so temperature at the center of the plane,
T = temperature at surface.
0
(B-3)
To obtain results without unreasonable complication requires a
fairly simple relation between total losses and surface rise. The one
chosen is
AT ? rit
where AT ? surface ries, degrees C,
m surface rise parameter,
Yt ? watts per square inch transferred from the surface.
Total loss in a square inch cross section from the center of the plane to
the surface is
t
se IX? W dx ? Ci
zo 2
(ix
0 0
Substituting for dv--44-4,
Memo!
andintemmAtinit gives
r2 2
2 1. '0
(1c, +
.401?10611711111?1111111110
(a-6)
surface rise and coil rise, from (B-3), (B-4) and (B-6), is
Tt m + (T1- To)
2 2 2 2 2
2 K1 X()Cx0 2 K0K130 K1 x0
m X C x00 -26"r`KO
(B-7)
Ki (which
rAfferentisting (-7) with respect to the parameter
varies dmuttriffsta1ltdd.cm), and setting the result equal to
seri, gives the condition for minimum total rise
(M)
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Since Ki is tbe slope of the density function (B-1), a very small value
for K1 indicates almost constant density, while a large value indicates a
low density near the center increasing to a large value at the surface.
Typical values for the thermal parameters are K ? 200 and k .02.
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APPENDIX C - N SCRAPLESS LAMINATION
The size of a transformer is a function of power rating. However,
several different types of construction and maw different proportions can
be used to fulfill a given set of design requirements. For a transformer
or inductor constructed with conductor material and a magnetic core two
extremes in proportions are possible: a relatively large quaatity of
conductor material and a small quantity of core material might be used, or
a large proportion of magnetic to conductor materials might be used. The
compromise between these possibilities depends upon the relative 4---rtance
of weight, volume, losses and cost. The rating of a transformer is
approximately proportional to the product of core window area and core cross-
sectional area. A relatively large window area compared to core section
indicates that the volume of the winding structure, including conductor and
insulation, is generally larger than the volume of core material. The
converse holds when the ratio of window area to core cross section is small.
Conventional SeranleAA Lamination
For reasons of economy, the scrapless EI lamination has been used
for most single-phase, shell-type transformers requiring laminations small
enough to be punched and handled readily. Fig. C-1 shows how two E's and
two I's are cut from a section of the material without arty waste. Fig.
C-2 shows bow one E and one I are laid to form a layer of a transformer core.
The other layers of a core can either be placed the same way to form a butt
joint, or alternate layers can be reversed to form a butt-lapped joint, in
which the abutting edges in one layer are bridged over by another layer.
Since the proportions of the Aeraplens lamination shown in Fig. C-1
and C-2 are fixed, the proportions of a transformer core can be varied only
by changing the height of the stack of laminations. Most common ratios of
stack height to center lag width film 'within the range from 1:1 to 21.
Reasons for this are: (1) a winding is more easily wound on a square form
thaa on a rectanglevcs.u.Atwo verymusek
4h longer aiAsm and (2) A ratio some-
what larger than 1:1 is usually the most economical shape within the
limitations imposed by the use of this lamination.
A survey of currently-available laminations reveals an interesting
situation in that the conventional scrapless lamination has extreme or un-
usual proportions compared to special or non-scrapless laminations. These
special laminations are used to a much lesser extent because of the wasted
material. They are characterized by their greater window area for a given
center-leg she than has the conventional scrapless. This indicates very
significantly that another scrapless landnation having a larger window
would meet a need in the industry.
The New Lamination
A search for new scrapless laminations led to the scheme shown in
Figs. C-3 and C-4. Fig. C-3 shows the cutting pattern which yields two sets
of E's and I's from a rectangular piece of material, and Fig. C-4 shows haw
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one layer is formed for a single-phase, shell-type transformer core. If and
when this lamination is produced, it should be very valuable for many trans-
former designs and applications. However it is intended to supplement, and
not to replace the conventional lamination.
The new lamination offers a saving in weight over the conventional
lamination for almost any design. This reduction is achieved becalm designs
with the new lamination tend to have a higher proportion of winding volume
to the core volume than those made with the conventional lamination. Although
the density of copper is about 15 per cent greater than that of steel, typical
transformer windings are practically always less than 30 per cent copper by
volume, the rest being paper and impregnant. In high voltage designs typical
copper volume is only a few per cent of winding volume. It is estimated that
transformer weights can be reduced at least 25 per cent. This would be of
great importance in military requirements. Direct manufacturing costs wou3d
also be reduced if the expense of the additional copper wire and insulation
were more than compensated for by the reduced magnetic material.
The new lamination should be particularly well suited for high-
voltage designs, which need adequate winding clearances and space for solid
insulation. Required clearances with a core using the new lamination could
be obtained only with a heavier or poorly-proportioned core using the con-
ventional lamination.
Another desirable feature of the new lamination is that the
dissymmetry of the E part can be used to advantage for reducing the no-load
or excitation current of a transformer. In the conventional transformer,
layers of laminations can only be stacked two different ways, whereas they
can be stacked four different ways with the now lamination. This makes it
possible to distribute in twice as many places the abutting lamination edges
at the corner joints. This yields a better core because crowding of flux
in the butt-bridging laminations is somewhat allevtated. However the two
joints at the ends of the center lee are unchanged in cores made with the
new lamination.
In mall transformers the effect of fietro jeieee is to increase
no-load current from about two to fern' times the values which would be
obtainable if there were no core joints, depending on the length of the
flux path. It is estimated that improvement of the corner joints in a
shell-type core will give reductions of from 15 to 30 per cent, in no-load
current over the conventional sarapless lamination. However this feature
need not be utilised since it is possible to stack lamination layers only
two ways as before.
A dipAdvAntage of the new lamination is that it would probat7_
involve an increase in punching expeeeee ovAr the conventional lamination
since the latter is very readily produced with a progressive die. However.,
if material costs greatly outweigh punching costs, as appears to be the case-,
then a more complex punching operation is not a formidable obstacle to the
production of the new lamination.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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??? ?
WOW
APIMMINO
FIG. C- I CONVENTIONAL SCRAPLESS El LAMINATION!
AS CUT FROM SHEET MAGNETIC STEEL
(TWO SETS)
1
FIG. C-2 ASSEMBLY OF CONVENTIONAL SCRAPLESS LAMINATIONS
(ONE LAYER)
ARMOUR OSSEARCH
??? I I 16.? Oil e VIISTrriliTC or TCC4Nell..601V
253 -
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FIG. C-3 NEW SCRAPLESS EL LAMINATIONS AS
CUT FROM SHEET MAGNETIC STEEL
(TWO SETS)
/A
L.
FIG. C-4 ASSEMBLY OF NEW SCRAPLESS LAMINATIONS
(ONE LAYER)
- 751, -
=IN
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MD= D: mD,L1AR SPECEFICATIONS
Photographs of ten experimental transformers which were sutedtted
as models are shown in Fig. D-1 and 1)-2. A circular secoviary winding which
mei be substituted for the square secondary winding of one of tha low-
capacitance transformers is also shown. The purpose of constructing
emperimmental transformers was to obtain empirical data and to verity the
design procedures. Specifications and temparature data for ten experimental
transformers which were selected to be submitted as models are presented on
the following pages. In addition, temperature data on four of the esseples
in the final report of the previous contract (Jo. DA-36-039 SC4519) are
11101Udild ?
ARIVIUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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11.11111111111111111111111Minwirmummr
FIG. D1 PHOTOGRAPH OF CURRENT-LIMITING TRANSFORMERS AND
TRANSFORMERS WITH UNBALANCED MAGNETIZATION
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?
FIG. D-2 PHOTOGRAPH OF V1BRATOR-SUPPLY AND
LOW-CAPACITANCE TRANSFORMERS
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K-12: Plate Transformer with Unbalanced Ma tization
Requirements:
Frequency: h00 cycles per second.
Ambient temperature: 85.0
Maxima temperature rise: 115.0
Primary: 115 volts.
Secondary: 560 volts RMS, 1.0 ampere RMS, 0.50 ampere DC, hall-
ways rectifier with capacitance-input filter.
Protections Grade 2 (less resistant to adverse environmental
conditions).
Dee
Core:
Tube:
:II
Lamination: Scraplesm EI with 1 inch center leg width.
Steel: 1-5/i6 inches.
Construction: Butt joint.
Dimensions: .030 inch thick, 1-1/614 x 1-5/16 x 1-7/16 inches long.
Material: Quinterra.
Primary winding (next to core, 115 volts):
Wire size: No. 17 AWG, teflon-coated wire,
Turns per layer: 23,
Layers: 3,
%mit 69,
Layer insulation: .009 inch Quinterra,
Wrapper: .009 inch Quinterra.
Shield (connect to core):
Material: One layer of .002 inch thick copper sheet,
Wrapper: .009 inch Quinterra.
Secondary winding (560 volts Rh):
Wire size: No. 214 AWG, teflon-coated wire,
Turns per layer: 49,
Layers: 3140,
Layer insulation: .006 inch Quinterra,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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Wrapper:
Primary: o.1975 ohms,
secondary: 5.67 ohms.
IPAM!.:LLICLBeet.
Calculated average winding temperature rise:
Primary:
Secondary: 92.C.
Measured average winding temperature rise:
Primary: 113.C,
Secondary: 96.C.
.012 inch Quinterra.
FOU
N tATI
ON
OF
iLLI
NOIS
INSTITUTE
CVINOLOG
1
1
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nsforPlateTzmeustithIlnbaancedMaetization
_Requirements
Frequency: 60 cycles per second.
Ambient temperature: 65?C.
Maximum temperature rise: 40?C.
Primary (3 to 4, 5, or 6): 105/115/125 volts.
Secoaftry (1 to 2): 180 volts RMS, .11 ampwee RMS, .055 amperes
DC, half-wave rectifier with capacitance-
input filter.
Protection: Oracle I (most resistant to adverse environmental
conditions).
Core:
LaminatiOn: scraplees EI with 11/16 inch center leg width.
Steel: Non-oriented silicon, .014 inch thick, AISI M45 grade.
Stack: 1-3/16 inches
Construction: Lap joint, laminate 2 x 2.
Tube:
Dimensions: .030 inch thick, 11/16 x 1-3/16 x 14/32 inch long,
MatariAl: Paper
Secondary winding (next to core, 180 volts RMS):
Wire size: No. 33 AW0 single enamel copper wire,
Turns per layer: 91i,
Layers: 13,
Turns: 12114,
Layer insulation: .001 inch paper,
Wrapper: .010 inch paper.
Shield (over secondary, connect to core):
Material: One layer of .002 inch thick copper sheet,
Wrapper: .010 inch paper.
Primary winding (outside, 105/115/125 volts):
Wire size: No. 30 AWG plain enamel copper wire,
Turns per layer: 71,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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a
?? ?
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Wars: 12.
Tarns: 778, taps at 716 and 653,
Layer insulation: .0015 inch paper,
Wrapper: .010 inch paper.
Dimensions: 2.5625 x 2.125 x 3 inches.
Filling: Sand-loaded asphalt compound.
Measured Resisten.c.elittM)
Primary: 39.02 ohms (115 volt tap),
Secondary: 106.45 ohms.
Data
Calculated average winding temperature rise:
Primary: WC,
Secondary: 29.C.
Measured average winding temperature rise:
Primary: 35?C,
Secondary: 39eC.
ARMOUR RESEARCH FOUNDATION
Or ILLINOIS INSTITUTE OF TECHNOLOGY
?",i;
. ? :?
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I MI
wiffil
K-22: Cuz_:mt_:qa-Limi Filamenir. Transformer
Requirements
Frequency: 60 cycles per second.
Ambient temperature: 65*C.
Maximum temperature rise: hO'C.
Prilmary (1 to 2; 3; or 0: 105/115/125 rote%
Secondary (5 to 6): 5.5 volts, 10 amperes, 13.5 amperes
short-circuit current.
Eta.. n
Core:
Protection: Grade I (most resistant to adverse environmental
conditions).
Lamination: Scraplass EI with center lag width of 1-1/4 inches.
Steel: Oriented silicon, .0114 inch thick, AISI M-10 grade.
Stack: 1-3/8 inche104 s.
Construction: Lap joint, laminate 2 x 2.
Tubes (primary and secondary):
Dimension: .0h0 inch thick, 1-1/h x 1-7/16 x 11/16 inct long.
Material: Paper.
Primary winding (1054.15/125 volts):
W4)e size :
No. 02 AWG single enamel copper wire.
Turns per layer: 17,
Layers: 17,
Turns: 280, taps at 258 and 235,
Layer insulation: .003 inch paper,
Wrapper: .010 inch paper.
Secondary winding (5.5 volts):
Wire size: No. 13 AWG double enamel copper wire,
Turns per layer: 5,
Layers: 6,
Turns: 30,
Layer insulation: .010 inch paper
Wrapper: .010 inch paper.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
? ? -
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ww ,
Magnetic shunts (two required):
Thickness of each Shunt corresponds to 9 laminations, each
.025 inch thick.
Length of each shunt (length of each lamination) ? 1-3/8 inches.
Width of each shunt (width of each lamination) w .605 inch.
Case:
Dimensions: 3.875 x 3.300 x 4.313 inches,
Filling: Sand-laded asphalt compound.
Measured Resistances (at 65?C)
Primary: 2.91 ohms (115 volt tap),
Secondary: 0.0454 ohms.
.Temperature Data
Calculated average winding temperature rise:
Madlimbammemplom 1." Of.
AAAAMAJ4 1141,1 W,
Secondary: 38?C
Measured average winding temperature rise:
Primary: 39?C,
Secondary: 34?C.
ARmouR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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VP'
K-23: Current-Limiting-Filament Transformer
!!!!921EME!!
Frequency: 400 cycles per second.
Ambient temperature: 65?C.
Kazis= temperature rise: 140?C.
Primary: 115 volts.
Secondary: 6.3 volts, 5 amperes, 10 amperes short-circuit
Le211E
Core:
uta
Protection: Grade 2 (less resistant to adverse environmental
conditions).
Lamination: "L" trot having a width of 1/2 inch, window
dimensions are 0 x 1.1/2 inches.
Steel: Oriented silicon, .006 inch thick.
Stack: 0 4nch.
Construction: Lap joint, laminate 2 x 2.
Tubes (primary and secondary):
Dimensions: .030 inch thick, 1/2 x x 1/2 inch long.
Material: Paper.
Primary winding (115 volts):
Wire size: No. 27 single enamel copper wire,
Turns per layer: 19)
Layers C'k0)
.1,70
lurraii )(Up
Layer insulation: .002 inch paper,
Wrapper: .010 inch paper.
Secondary winding (6.3 volts):
Mire size: No. 17 single enamel copper wire.
Turns per layer: 5,
Layers: 6,
Turns: 28,
Layer insulation: .007 inch paper,
Wrapper: .010 inch paper.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
11111111 111111 --- IIIi
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Magnetic Shunt:
Thickness of shunt corresponds to 14 laminations, each .0185 inch
thick.
Length of Shunt (length of each lamination) m 0 inch.
Width of shunt (width of each lamination) n 0.1190 inch.
Measured ResistanosiEtgael
Primary: 60115 ohms,
secondary: n onci 4 ohms.
Temperature Data
Calculated average winding temperature rise:
Primary: WC,
Secondary: WC.
Measured average winding temperature rim:
Primary: 310C,
Secondary: 30.C.
ARMOUR RESEARCH
IIIMEMMengnannamosins.
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FOUNDATION
OF ILLINOIS
INSTITUTE OF TECHNOLOGY
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K-26: Current-Limiting Transformer with Unbalanced Magnetization
Requirements
Frequency: 1400 cycles per second.
Ambient temperature: 65?C.
Maximum temperature rise: ho%
Primary: 60/65/71 volts.
Secondary: 65 volts RMS, 1.2 amperes RMS, .75 amperes DC, 165
amperes RMS short-circuit current, half-wave
rectifier with resistance load and no filter.
Protection: Grade 2(lees resistant to adverse environmental
conditions).
Design
Core:
Tubes:
Lamination: Strapless EI with center leg width of 1-1/8 inches.
Steel: Oriented silicon, .0014 inch thick.
Stack: 1-3/16 inches.
Construction: Butt joint with .007 inch paper in secondary
portion of core.
Primary: .030 inch thick, 1-1/8 x 1-3/8 x 11/16 inch long,
Secondary: .030 ..1- "i .1 in ft /0 n AL. ?
4414.-4L .1.1./0 A .1.0.j/U A 7/.1.V 14111:41 JVC18,
Material: Paper.
Primary winding (60/65/71 volts):
Wire size: No. 17 AUG single enamel copper wire,
T pe er:urns r?Ay 9,
Layers: 8,
Turns: 71, taps at 65 and 60,
Layer insulation: .007 inch paper,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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?
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w
Wrapper: .010 inch paper.
Secondary winding (65 volts RHO:
Wire size: No. 22 .610 single enamel copper wire,
Tarns per layer: 11,
Layers: 16,
Turns: 168,
Layer insulation: .003 inch paper,
Wrapper: .010 inch paper.
Magnetic shunts (two required):
Thickness of each shunt corresponds to 18 ...alen.ations? each
Ja25 inch thick.
Length of each shunt (length of each lamination) w 1-3/16 inches,
Width of each shunt (width of each lamination) w .5425 inch.
ikasured Resistances ttI.?115:2)
Primary: 0.2205 ohms (65 volt tap),
Secondary: 1.786 ohms.
TANnerature Data
0:=QAMPIMMMIIMMOMM?10.??????1?????11?11
animal:AM average winding temperature rise:
Primary: WC,
Secondary: 40.C,
Measured average winding temperature rise:
DIVA==T9V.
lihaMmaird,*
Secondary: 36.C.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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MEE
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K-27: 171._ brator-Sir roans rmer
Reuiremnts
Frequency: 115 cycles per second.
Ambient temperature: WC.
Maxim= temperature rises 40.C.
Supply: 24 volts DC.
Load: .050 amperes DC from full-wave rectifier with an
inductance-input filter.
Secondary voltage: 572 volts RMS.
Protection: Grade 1 (most resistant to adverse environmental
conditions).
12ttlim
Core:
Lamination: Scrapless EI with center leg width of 3/4 inch.
Steel: Hot-rolled silicon, .025 inch thick, AISI M-22 grade.
Stack: 1-1/16 inches.
Construction: Lap joint, laminate 2 x 2.
Tube:
Dimensions: .030 inch thick, 3/4 x 1-3/32 x 1-1/16 inch long.
Material: Paper.
Secondary winding (1 to 3, 2 center-tap) - next to core:
Wire size: No. 38 AWG single enamel copper wire,
Turns per layer: 175,
moginovemere. In
144711G104.
Turns: 3500, tap at 1750 turns,
Layer insulation: .002 inch paper,
Wrapper: .020 inch paper.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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014.0.4.....4.1.11.1.10111044
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PrbserY winding (i1 to 6, 5 centor-tap):
Wire else: No. 25 IWO single enamel copper wire?
Turns per layer: 37,
Layers: 6,
Turns: 22, tap at 111 twos,
Wer insulation: .002 inch paper,
Wrapper: .020 inch paper.
Measured Resistances at WC)
Primary: 344 ohms,
OVUUUUL644,,
Oel PANS.
JI,11 '1041mmwti,
IAPEEIELPEIE
Calculated average winding temperature rise:
Primary: 30%,
Secondary: 32.C.
Measured average winding temperature rise:
Primary:
ikr y
?
SeCOhda37 4 ? ..7. 11/ ??P
?
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
Niiimmow
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4
-
IC-28: Vibrator - Suelv Transformer
!192AESS12
Frequency: 115 cycles per second.
Ambient temperature: 65.C.
Maximum tewerature rise: VO.C.
Supply: 12 volts DC.
Load: .11 amperes DC from a full-wave rectifier with capacitance
filter.
Secondary: .094 amperes RAS, 51411 volts RMS.
Protection: Grade 1 (most resistant to adverse environmental
conditions).
Core:
Lamination: Scrapless EI with center leg width of 1 inch.
Steel: Non-oriented silicon, .01875 inch thick, AISI M-15 griAio.
Stack: 1-3/32 inches.
Conatructiont Lap joint, laminate 2 x 2.
Tube:
-Dimensions: .040 inch thick, 1 x 1-3/32 x 1-7/16 inches long.
Material: Paper.
Secondary winding (1 to 3, 2 CT)- next to core:
Wire size: No. 34 AWG single enamel copper wire,
Turns per layer: 146,
10
.1.40JCW04 LV
Turns: 2618, tap at 1309 turns,
Layer insulation: .002 inch paper.
Wrapper: .030 inch paper.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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Layer ineulation: .005 inch paper,
Wrapper: 4020 inch paper.
Measured Resistances (at 614.C)
primary! 063 ohms,
Secondary: 343 ono.
jmaLt:i....we Data
Calculated average winding temperatme rise:
Primary: 35?C,
Secondary: 37QC.
Hemmed average winding temperature rise:
Primary: 34?C,
gacondary: 39?C.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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111111111
WW d
K-24: IETtEvacitance Transformer
Requirements
Frequency: 400 cycles per eecond.
Ambiea temperatures 85*C.
Naximum temperature rise: 115*C.
Primary: 115 volts.
Secondary: 10 volts, 5 amperes.
Secondary working voltage: 2 kilovolts.
Capacitance from secondary to primary and core: 9 micro-microfarade.
Protection: Grade 2 (less resistant to adverse environmental
conditior-).
Design
Core:
Lamination: "L" type having a width of 1/2 inch.
Steel: Oriented silicon, .014 inch thick, AISI M-19 grade.
Stack: 1/2 inch.
Window: )14 ld-1/2 incnes.
Tubes:
Primary: .025 inch think; IP x Y 1.1/2 Inch lona,
11
Secondary: .040 inch thick, 1.45 x 1.45 x .73 inch long,
Material: Quinterra.
Primary winding (115 volts):
Wire size: Ab. 28 Ain teflon-coated wire,
Turns per layer: 76?
11 Turns: 1455 6,urns: 455
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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lam. insulation: .003 inch Quintarra,
Ihmpriars .009 inch Quinton**.
Secondary winding (10 volts):
Wire slam. No. 19 AVG telom-coatedieLne,
rii?ruto per lievirs 16,
Layers: 3,
Turns: ler,
Lam insulation:
.009 Inch quintorra
livortviatv. ? _ A 4 visit OM Ira firveva
v.warm. 44 14 4.
Measured Issistanose (,t84?)
Primary: 7.9 ohms,
Secondary: 0.218 ohms.
.!..1112E1.2611
Calculated average winding temperature rises
Secondary: 82*C.
Maasnred average winding temerature rise:
Primary: 62*C
letanewtarlaiov Art"
Measured Cepacitane
Capacitance fromawoondry to primary and core equals ill micro-
microfarads when sQuinterrabord" supports are used and windings
ihrtJtittemorlall41111& artitg ?
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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K-20: Low-Cpacitance Transformer
Req irements
Frequency: 60 cycles per second.
Ambient temperatirm: 65?C.
Maximum temperature rise: 40?C.
Primtry: 115 volts.
Secondary: 6.3 volts, 20 amperes.
Capacitance from secondary to primary and core:
microfarads.
0
Protection: Grimm 2 (lass resistant to adverse
comitions).
Core:
18 micro-
environmental
Lamination: Special type giving two core leg widths of 1-1/4
Inches and the other two 1-5/32 inches.
Window: 4-3/4 x 6-9/16 inches.
Steel Non-oriented silicon, .0185 inch thick, AISI 11-19 grade.
Stack: 1-5/32 inches.
Tubes:
Primary: e065 inch thick, 1-5732 x 1-5/32 x 6-7/16 inch long.
Secondary: 1/8 Inch thick =11, with 5.0 hien outside diameter.
Material: Paper for the primary and phenolic resin for secondary.
Primary winding (115 volts):
Wire size: No. 19 AWG single-enamel copper wire,
Tarns per layer: 112,
Layers: h,
Turns: 448,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
Lgyer insulation: .005 inch paper,
*upper: .010 inch paper.
Secondary winding (6.3 volts):
Wire dee: Mo. 7 AVG double enamel copper wire,
Turns per layer: 6,
'Ayers: 5,
Turns: 28,
layer insulation: .007 inch paper,
likapnars ..01n inch paper.
Measured Resiste.mincs113
Primary: 1.755 ohms,
Secondary: 0.0222 ohms.
Calculated average winding temperature rises
Secondary: 21C. .
Measured average winding temperature rise:
Primaryt 16?C,
Secondary: 23*C.
Measured Cap.vitance
Capacitance from secondary to primary and core equals 17
micromiorofarads when polystyrene supports are used and
windings are concentric.
AIIHOUN NESEAPECH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
1
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1111111111111
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K-4: Low-Capacitance Transformer
Frequency: 60 cycles per second.
Ambient temperature: 65.0
Maximum temperature rise: 40%
Core:
Tubes:
Primary: 115 volts.
Secondary: 8.0 volts, 15 amperes.
Capacitance from secondary to primary and core: 16 micro-
microfarads.
Protection: Orade 2 (less resistant to adverse environmental
conditions).
Lamination: "L" type with leg width of 1.0 inch. ,
Steel: Non-oriented silicon, .0185 inch thick, AISI M-27 grade.
Stack: 1-1/4 inches.
Window: 14 x h inches.
PrimAry! 40 inch thick, 1 x 1-1/4 x 3-15/16 inches long.
Secondary:.195 inch thick i h h "1-3/8 inches long.
Material: Paper.
Primary winding (115 vnitim)!
Wire size: No. 19 AWG single-enamel copper wire,
Turns per layer:
87,
Layers: 5,
Turns: 433,
Layer insulation: .005 inch paper,
ARMOUR RES EARCH FOUN DATION OF I LU NOI S INSTITUTE OF TF.CI4NOLOGY
-276-
ii
T I
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1
1111.1111111 I
?
?
Wrapper: .010 inch paper.
Secondary winding (8.0 volts):
Wire sise: Mb. 9 AWG single-enamel copper wire,
Tarns per layer: 64
Layers: 6,
Turns: 37,
Layer insulation: .010 inch paper,
Wrapper:. .010 inch paper.
ftlElAkete.EVIL(IIIEE)
Primary: 1.66 ohms,
.
"" ra
? ? rig nom:.
011NRIBIIILTJ a ".'4iao
ITEnture Dtta
Calculated average winding temperature rime:
Secondary: 27.C.
Measured average winding temperature rise:
Primary: 33wC,
Secondary: lin.
Capacitance from secondary to primary and core cquaie
16 micro-mircofarade when imports are wood blocks
and windings are concentric.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
- 277 -
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????1**.*????????????:a..........,???...**?????????????/,??".
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11111111111111111111111111111111111
?IIIIIIIIIIIIII
MIL
1335155www"---Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
?
0.4
The design data for the following four examples are given in the
final report on Contract No. DA-36-039 5C-5519.
Maximum Calculated average Measured average
Example rise rise windhg rise
nmarlovi A
.Le00.0.084
Filament
Transformer
140*C
Design B,
Autotrans-
former 140*C
37*C
Design C,
Rectifier
Transformar 40?C 3hen
Design E,
High Temper-
ature Rectifier
and Filament
Supply Trans-
former
ARMOUR
85%
RESEARCH
FOUNDATION
36*C 31*C
43?C
28*C
yol! WC
77*C 71?C
64*C 66*C
OF ILLINOIS INSTITUTE OF TECHNOLOGY
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APPENDIX Es TEST DATA FOR TRANSFORMERS WITH UNBALANCED MAGNETIZATION
Pertinent data on four typical transformer cores tested are:
1) Wound-type core, windings on one leg
Two butt joints
Mean length of magnetic circuit: 7.22 inches
Wet ernes.sectionml area of ears: A?ltd.,el
w square inches
Core weight: 1.5 pounds
Steel: Oriented silicon
Thickness: 12 mils
Test frequency: 60 cycles per second
_nI lomt
2) 611011-mue core,4nefirmi
VWAT Awm
Leg width: 1 inch
lencrfh of magnetic circuit: 6 inches
Core weight:
A A
Coo'l.) putassuo
Steel grade: Audio type equivalent to AISI-W15, non-oriented silicon
Thickness: 14 mils
Test frequency: 60 cycles per second
3) ItsmArAlet_gsm? coils on one leg
Two butt joints
.4u mismuitir nirnnitt 4.93 inches
fl -
ea" Jowals..
Imns-e weieht: A.5 parinAn
Steel: Oriented silicon
?
Test frequency: 400 cycles per second
4) Shell-type core, EI laminations
Leg width: 0.695
Kean length of magnetic circuit: 3.75 inches
Core weight: 0.3907 pomds
Steels Grain-oriented silicon (Armco Tran-Cor
Thickness: 4 nils
Test frequeney: WO cycles per second
The following equations give the approximate per cent gap which results
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
WWWWWWWW111
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in minimum excitation.
T.. A. ft Oa%
LIS galWAM
of the enraa it has been found that the per
cent gap is almost independent of flux density below some value of flux
density. This behavior can be accounted for by using the indicated value
in the equations.
1) % gap ? 0.015 Hic- 0.003 B + 0.24
(Use B = 90 if density is less than 90):
where Hic Im magnetic field strength in oersteds, o.495 times
average ampere-turns per inch,
B is flux density in kilolines per square inch
2) % gap el 0.021 Bic osol6 B * 1.0
(Use B ws 70 if density is lees than 70)
3) % gap se 0.025 Hic - 0.0052 B + 0.29
(Use B 70 if density is less than 70
4) % gap ? 0.019 Hric - 0.008 B + 0.5
(Use B 60 if density is less than 60)
Application of these equations might yield a negative value for the
per cent gap. In this case the core joint with minimum effective gap
should be used, a butt joint for cut, wound cores, and a lapped-butt joint
for stacked cores.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
-280-
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EXCITATION - VOLT AMPERES PER POUND
ARMOUR
120
100
CORE: WOUND, TWO BUTT JOINTS
STEEL: GRAIN - ORIENTED SILICON, 12 MILS
60
40
1
.08
I
6 8 10 12 14 16 I8 20 22
I ? 111
VP IN,
AV rwRsTIEDS
FIG. EXCITATION OF WOUND CORE AT 80 KILOLINES
PER SO. IN. (60 CPS)
IiISS&ANCN FOUNDATION OF ILLINOIS
- 281
INSTITUT&
OF TECNNOLOGY
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120
100
EXCITATION - VOLT AMPERES
60
CORE: WOUND, TWO BUTT JOINTS
STEEL: GRAIN ORIENTED SILICON, 12 MILS
111111111111111111
MIN .61% GAP 11111111
X MOM III
xi
20
.46%
0
Il
Al
.31%
X
1
X
I --I-
0 2 4
6
8 10 19
? AVERAGE
HDC
14 16 iu 10
20 22 24
OERSTEDS
FIG. E-2 EXCITATION OF WOUND CORE AT 100 KILOLINES
PER co IN. (60 CPS)
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Amur
3.0
2.5
IS
1.0
-
.1/ 11?" ?
r.?.......re,......r.........
1
1
CORE:
STEEL:
1
I
BUTT
1
SILICON,
1
JOINTS
1
12
1
MILS
.........................r....
I
I, 1
I
1
WOUND,
GRAIN
1
1
TWO
-ORIENTED
-
0?
89%
-%
olo1/45%)
1
?
Or-
70=.;?- %Ir.
-
? ?s?-?
C,ilatki-1.0--.---
_-?t?CP
%%'.31%1
I
.24/o
I
" III ,....7-t',:--
-
--:"-:.?011
A
i
2
A
14
1g
Mac AVERAGE OERSTEDS
18 20 22 24
FIG. E-3 CORE LOSS OF WOUND CORE AT 80 KILOLINES
PER SC). IN. (60 CPS)
ARMOUR RESSAPICH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
EMORINIONIMMOmmalwasul""g500.0.--__
- 233 -
4
4
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PER POUND
CORE LOSS - WATTS
1Y,
CORE: WOUND, TWO BUTT JOINTS
STEEL: GRA1N-ORIENTED SILICON, 12 MILS
?
0 2 4 6 8 10 12 14 16 18 20 22 24
HDC ? AVERAGE OERSTEDS
IC I 41
1 I %JP ? L -r
CORE LOSS OF WOUND CORE AT i00 itILOLINES
PER SO. IN, (60 CPS)
mminig Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
IllrEmmulmin Declassified
ij
I 11'
1
I 1
111
?
1 11
I
II
?
1
ff. I
1 0
I
I 1
in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
0
0
X
a.
AMPERES
60
0
40
6
CORE: EI LAMINATIONS
STEEL: NON -ORIENTED, AI SI- M 15, 14 MILS
DENSITY, 80 KILOLINES PER SQ. IN.
yririf I
e
EXC iTAirt ON
0 2 4
6 8 10 12
14
Hoc - AVERAGE OERSTEDS
16
18
20
AG. E-5 EXCITATION OF STACKED CORE (60 CPS)
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
? 2Fi5 ?
22
iggsweims Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-9
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?
2,0
I I
1 1
CORE: El LAMINATIONS
I
STEEL: NON- ORIENTED, AISI-Sa-15, 14 MILS
DENSITY: 80 It ILOLINES PER SQ. IN.
.44% GAP
010
, 084 % iBUTT)
4-11
I I I I I I II I Il?
0.5 ?
I I I ill i I
I
22 214 I
6 810 12 14 IS IR 20
Hoc ? AVERAGE OERSTEDS
FIG. E-6 CORE LOSS OF STACKED CORE (60 CPS)
286 -
_
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CORE: WOUND, TWO BUTT JOINTS
STEEL: ORIENTED, 5 MILS
DENSITY: 70 KILOLINE-S PER SQ. IN.
2 4
st
Hoc ? AVERAGE OERSTEDS
FIG. E-7 EXCITATION OF WOUND CORE (400 CPS)
ARMOUR RSSEARCH FOUNDATION or ILLINOIS INSTITUTS OF ISCHNOLOGY
1
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11111.11.
cl
.. ... .... Deassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/09/06: CIA-RDP81-01043R002500190.001-9
111 .. -
4
:TT r
I
I
CORE: WOUND, TWO BUTT JOINTS
STEEL: ORIENTED, 5 MILS
DENSITY: 70 KILOL1NES PER SQ. IN.
o 5
IMOIMPOINI.00100.0.1111.4.00?1
+00-4.
.ozelo
x x GO Burr
?
4Y
I I I
2
4 6 8
Hin - AVERAGE OE R STEDS
10
FIG. E-8 CORE LOSS OF WOUND CORE (400 CPS)
LimannimmimmomimmiNI
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0
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PER POUND'
VOLT AMPERES
EXC IITAT1ON
*AA
ft-lry
220
coRE:
STEEL:
DENSITY:
200
110
160
1
140
120
100
SO
60
40
20 X
co
El LALISNATIONS
ORIENTED, 4 MILS
(TRAN COR TO)
70 KILOLINES PER SO. IN
!
I I
I I
.13% (BUTT) I
2
4
i2
14
16
Hoc ? AVERAGE OERSTEDS
ifs
20
FIG. E- 9 EXCITATION OF STACKED CORE (400 CPS)
ARMOUR 116?Aric::: FOUNDATION OF
ILLINOIS OF TECNNeil.,"fitt,
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110
CORE:
STEEL:
DENSITY:
EI LAMINATIONS
ORIENTED, 4 MILS
(TRAN ?COR T-O)
70 KILOLINES PER SQ. IN.
2
2 4 6 8 10 12 14 16 18 20 22 24
H AVERAGE OERSTEDS
FM; F? 10 CORE LOSS OF P,TAricrn trnRF
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1
.ar-aa 'TO" a
APPENDIX ?OBVIATION OF EQUATION TAKE MID FIGURE NUMBERS
Correlation between the ambers for the equations, tables, and
figures which are used in this final report of Contract No. DA-36.039 SC42656,
and which also were used in the final report of Contract No. DA-36-039 SC5519
Contract No. Contract No. Contract No. Contract No.
DA-36-039 DA-36-039 DA-36-039 DA.36.039
SC-52656 SC4519 80-.52e0 S0-1$19
uallix.91...iumbers auallion Nunber...?(LorA)
2-1 24 2-20 9-13
2-2 2-9 2-21 9-12
2-3 2-10 2-22 10-14
2-4 2-11 2-23 10-15
24 2-12 2-24 10-16
2-6 10-11 2-25 10-17
2-7 10-1 2-26 1018
2-8 10-2 2-27 10-19
2-9 10.3 2-28 2-3
2-10 10-4 2-29 10-20
2-11 104 2-30 10-21
2-12 10-4 2-31 10-22
2-13 10-7 2.32 2-6
2-14 10.8 2-33 10.23
is i le 311-9 2-3b in...21t
2-16
2-17
2-18
2-19 9-3 11-14 19.14
10.10
10-12
10.13
11-1 12-1
11-2 12-2
12-1 1 3 3
a .
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
IIIIIMINEwswinmerAnimm
ommunimmi Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-111111111
iiiiism 6MEN-9 1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
I
I 1111
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
e" 292 ?
? ???-?r yr-- ?
Contract No. Contract No.Contract No. Contract No.
DA--039
U-36-039 pA.36.A39 n4-36-039
SC.52656 SC-5519 SC-52656 SC.-526,
Malpn Numbers (Cont.) IM22.!Eq#11:22c4nt-)
11.5
124
11-11
124
11.6
12-5
11-12
12-5
11-7
12.6
12-1
15-1
11.8
12-7
12-2
15.2
11-9
12-8
12-3
15-3
11-10
12-9
12-4
15-4
12-10
ii-n
11-12 12-11 11AMELHFbera
11-13 12-12 11-1 37
11.14 12-13 11.2 40
11.15 1244 11.3 44
12.1 lb.2 ii...5 45
124 lh-5
12-5 15 11-6 42
-1
Table Numbers
9-1
6-3
L I.
va? 4
10-1
9-2
9-7
9-6
12=1
12-2
12-3
11-7 143
11.8 47
11.9 47A
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Declassed in Part - Sanzed Copy As.roved for Release @ 50-Yr 2013/09/06 : CIA-RDP81-01043R002500190001-9
?
APPENDIX 0: LIST OF PitireapAL sylsoTs
11!.. rating, volt-amperes
Z. frequency, cycles per second
'c copper space factor
F4 core space factor
Er flux densitr, kilolines per square inch
A currmatdonelAor, kiloamperes per square inch
lc window area, ewe incheo
A4 core cross-sectional area, square inches
Va MS potential, volts
fiNS current, amperes
mc swan length of winding, inches
ms mean length of core, inches
e tomperattuse-rise parameter .
temperature-rise, degrees centigrade
4 characteristic linear dimension, inches
(equal AcAi
A conductor resistivity, siert-Alm-inches
W. winding loss, watts
r core loss, iatts
c exposed area of winding, square inches
S4 exposed area of core, square inches
turns of winding
n turns ratio, primary to.secondary
rimtotal primary volt-amperes
excitation, volt-am)eres
ex,
a, e, c, d, t, g: dimensionless ratios
through KA: combinations of a, bl ol
core weiet, pounds "P 'J a
P 0
MA
s; density of care material, pounds per cu. in.
Nfl winding weight, neglecting insulation, pounds
cc density of conductor material, pounds per cu. In.
40c
leakage reactance, obms
It equivalent series resistance, ohms
nc weight, loss, volume or cost per unit volume of winding
n4 weight, loss, volume or cost per unit vol umft of core
V: volume of 'winding, cubic inches
V7 volume of core cubic inches
0 equivalent rating of a given transformer, which indicates
approximate rating of that unit if operated at 60 cycles
and 110.0 rise, volt-amperes.
L lamination leg width, inches.
a ratio of stack height to leg width of a laminated core.
CM circular mils
F tern in space factor equation 2-20 which is found in Figure 11-2
h heat transfer coefficient of free convection.
ht' heat transfer coefficient of radiation.
94 certain temperature differences,
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
.........morammussified in Part - Copy Ap roved for Release Yr 2013/09/06
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?
m a thickness used in temperature calculations, inches.
C a capacitance
11/4 load resistance, ohms.
a component of primary volt-amperes for units with unbalanced
A magnetization, volt-amperes.
Hic nnbalanced magnetizing force, averaged in time and around
the length of a core, oereteda.
ratio of short-circuit current to rated current
q ratio of leakage reactance during short circuit to leakage
rzactance at rated load.
ml effective air gap, inches
Ft space factor of current-limiting transformers.
ke correction for supports in calculation of capacitance of
low-ospacitance units.
P a perimeter, inches.
Z impedance, ohm,.
ARMOUR RESEARCH FOUNDATION OF ILLINOIS INSTITUTE OF TECHNOLOGY
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STAT
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/09/06: CIA-RDP81-01043R002500190001-9
FINAL ROOM'
Period I March 1953 to 30 August 1955
agligag
2120ALLaUlastia.
This contract is supervised by Electronic Parts & MAterials Brandh.
Components Department. =Lb For further technical. information con.
tact CoMponentn napsrtm-nt. Fort Monmouth. Now Jersav
STAT
STAT
?
STAT
STAT
&
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4
Ii
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: CIA-RDP81-01043R002500190001-9
IZAXICTIVii PAWS 8!?
AlatatiONIC Pg106 P4.44 ASLEMILILS MOO
111% Asafr) inajLikttr 1j4 briirSlikta
GOttiaLM
WW, FM
22 October 1956
1.
This report covers the wait* eoutreot ppriod 1 ,Mey 1953 to 30 Augist
1955. The report was due 31 Unusry 19560 was received 16 April 1156 Ma
team asionap*AA /ismom 19,CA.
2.12Allibiakk
taa
I k ? . V -
It was agreed that the deelp Procedures Presented is Previous
quarterly reports would be presented in outli form in the seventh
quarterly report: lieeh 46s4n grunted in thi4 final report would
include component temperature csicalstiokse
The eamaate and the format or a draft of the Mel Report were
vat...41 enitinsmi mindifinationSe and corrections were made*
It VaS decided that the basic design procedure, as veil as the design
methods developtd for the various types of transformers
would be included in this linelNport. Therefore.
this report 011 contain all of the design information neeeseery for the
types of paw transformere developed under the original ccetract and
ololootoo dorop&Asno4oun Af *ha tenvik
uovo ;to osodo. Irv/8~ osom000 'cr.* mo0o. wow
STAT
STAT
ST
STAI
I
STATEN
STAT
STAT
""usaINCeltaillesftli "MW
- --
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? kitigaillit Mk Wigan&
This contrast wee ? twenty-tour (24) south extension of work cooduoiod
on Contract iii36.039 Sasp5$19 which resulted in a simplified design siethod
for tilementiensformeras plots transformers with so unbalsised del
end Mout. trensfamors with no unbalanced dot and eutotramstomprz?
The amigo' method utilised a samograp,h, charts aud curvet* Work as iiit*
contract hes extended the design method to inelude low ealiesitesas
trinsforaexas eurrent limiting transformers with or wittout usbelasoed
dos piste trimisfavampidth utbsimmmiddol and !Master supply trenetormsre,
The ?Whined work on both contracts kw resulted in a simplified design
method tor all of the types of paver iressformars listed above, *row* on
this eec.ind contrect mated in the modifications needed for the design of
the *T& 141 *vPlum Af *Immindt0=1"Irg 1104d. ft20 Of Us motor solinsatitaii
additions to the basic design procedure are ss follows,
Ibmtasaa.
/Ate in the form of curves were c Ailed to give cora loss, excitation,
and nonemagnetic inp as functions of as flux density end de magnetisation,
ftraulas and charts were included for the amputation of accondary voltage
and current tr- ()Inuit somatopts; and for nrkinsry current en regulation.
IJALLMNI
Relations were obtained emng prim-vy en maeondery flux lionaltiese and
voltages, and current. The equation for winding apace factor woo modified4
Ouldsc were given for the selection of the magnetic shunts.
lama
STAT
Ouidea were given for the selection of flux density. As aquatics for
primary voltaLs we* inaiudad to Anceiiiirit 1,00vP elm^ 4.,.,,mvas?t. B4414% inftcsatios
was given for procedures to keep the starting current love
? kit annotitenal Trams limits=
Iftrical equation were derived from measurements and theorstieal studies
to establish relations swag power ratings, space factor and desired eapsol..
tomes Situations for outing capecitanoe and leaks tes3tance were included.
In addition to the above au anaUsia was wade relating to the seleatice
of current densities. A study nt n11+41'1001
00911,16 ftWODIstre4^mai maarsal..
henuits were given in the term of optismm ?CM A stank $i; to ratio&
width
2
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