A STUDY OF TRANSISTOR VIDEO AMPLIFIERS. REPT. NO. EE278-5611F (FINAL); TECHNICAL REPT. NO. RADC-TR-57-73. (CONTRACT AF 30(602)929).

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• Publication Date: August 6, 1958
• Content Type: REPORT

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STAT
TRANSISTOR ? CIRCUIT APPLICATIONS
A STUDY OF TRANSISTOR VIDEO AMPLIFIERS
??
l????? ?
By
HERBERT HELLERMAN
CARL Z IMMER
Sponsored by
ROME AIR DEVELOPMENT CENTER
Contract No AF 3n I 60;1 -929
SYRACUSE UNIVERSITY RESEARCH INSTITUTE
ELECTRICAL ENGINEERING DEPARTMENT
Report No EE278 5611F
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STAT
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? 1
A STUDY OF TRANSISTOR VIDEO AMPLIFIERS
Final Report
Novrmber 1, 196
AF 30(602)-929
by
Herbert Heileman
Carl R. Zimmer
This rowl was pr.dead war a sponsored
contrad. The mantles ood rocimmoodofilos
exposed ars limso Aitbnr(s) and are
pot oscossarly 'mimed by the *AMC ham
dodos ti this report, or NI polio %twat
most boar Monaco to the orMloal Seirti and
Sponsor.
SHRUM UllIVERSITY fifSffiliCH IIISTITUTE
Approved by: Spoosored by:
Glenn M. Glasford
Project Director
Report No.
MM.-5611F
Rome Air Development Center
Griffiss Aire Force Base
Rome, New York
Date:
November 1, 19%
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PftEFACE
This report is concerned with the theoretical and experimental results
of a study begun in the Fall of 19,, on the general-iabject of transistor
4
low pass amplifiers. Since the work is still in progress, interim results
are reported here.
Mbst of the effort has been concentrated on wide band response through
the use of linear networks to extend the bandwidth beyond that obtainable using
the transistors alone. This approach which is usually called equalization re-
quires as a basic starting point the specification of the network to be equal-
ized. In the case at hand a reasonably accurate transistor equivalent circuit
must be found before the design of the compensatinghetworks can proceed on a
systematic basis. For this reason a good deal of effort has been expended on
the small signal equivalent circuit of the junction transistor from both the
theoretical and experimental points of view. The theoretical work on this im-
portant subject has been filrst to review and check the results reported in the
literature and second, to simplify the general equivalent circuit to fit the
impedance conditions met in the video interstage. The representation used has
for the most part been the common emitter h parameters andj experimental checks
have been made on alloy junction, grown junction and -surface barrier transistors.
Two measurement techniques have been employed. One is a high accuracy bridge
which can give precise results for driving point immittances However, since
the bridge is rather cumbersome from the point of view of auxilliary eauipment
needed and numerical work necessary to obtain the final results, a simpler di-
rect reading type of measuring set-up has been developed which can be calibrated
against the bridge initially and thereafter give important parameters to a fair
degree of accuracy with a maximum of convenience.
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TABLE OF CONTENTS
PREFACE
CHAPTER 1. PRINCIPLES OF WIDE BAND TRANSISTOR EQUALIZATION
CHAPTER 2. THEORETICAL EQUIVALENT CIRCUITS
2-1. Alloy- or Fused-Junction Transistors 4
2-2. Effect of the Base Spreading Resistance ri; 8
2-3. Approximation for the Grounded-Base Parameters 12
2-4. Transistor Parameters in the Grounded-EWitter Connection. . 16
2-5. Approximating the Parameters as Functions of Frequency. . . 20
2-6. Summary 14.0
CHAPTER 3. MEASUREMENT OF TRANSISTOR PARAMETERS 41
3-1. Measurement Techniques 41
3-2. Measurement of Transistor Parameters using Bridge techniques 48
3-3. Results for a Fused-Junction Transistor 60
3-4. Results for the Grown-Junction Transistor 74
CHAPTER 4. CCMPENSATION USING RC NETWORKS 80
4-1. Compensation using RC Networks 80
4-2. Wide Band Response Utilizing Local RC Feedback 88
4-3. Effect of Load Capacitance 94
4-4. Experimental Results with RC Local Feedback Equalization. . 96
4-5. Common EMitter-Common Base Circuit 99
CHAFER 5. COMPENSATION USING RL NETWORKS 103
5-1. Compensated Amplifiers using Simple RL Networks 103
5-2. Single Stage Amplifier with R.T. Network in Output Circuit. . l04-
5-3. EXperimental Single Stage Amrlifiers 110
5-4. Experimental Results 113
5-5. Interstage Equalization 117
5-6. Two-Stage Amplifier with Interstage and Output Eqnplization 119
5-7. Summary 122
APPENDIX . SOME CHARACTERISTICS OF TRANSISTORS UNDER HUSHED BIASING
CONDITIONS 123
?
PXE
1
14.
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Principles of Wide Band Transistor Apalization
The purpose of this section is to point out some of the limits on the
solution of the problea imposed by the characteristics of realizable networks.
It is. usually true in low pass amplifier practice that aldpand gain is exchange-
able for bandwidth. The efficiency with which the trade can be accomplished
and the limit to which this efficiency may be extended by the use of suitable
networks are important fundamental problems. In general it has been found in
vacuum tube circuits that the ultimate gain-bandwidth figure of merit of tae
simplest configuration consisting of a tube working into a shunt capacitance
Co, transconductance gm and a load resistance interstage Ro is
gm
Ko x fo =
2xCo
where K = midband voltage gain ratio fo = 3 db bandwiuth
Since the minimum value of Co is the shunt output capacitance of the tube,
the ultimate limitation on the figure of merit is dependent on tube parameters
only, the interstage resistance Ro just determines the division of gain and
bandwidth within the product which has a maximum value that is a constant
for a given tube.
Since Eq. (1-1) holds for the specified amplifier structure it is reason-
able to inquire into the possibility of obtaining a larger bandwidth for a
given gain by employing a more complicated interstage network. The simplest
general class of such networks is a two terminal shunt interstage. Bode has
shown*that if the gain is to be flat over the desired band the best that can
41'Network Analysis and Feedback Amplifier Design' 1). 08 by 11,-Bode
(D. Van Nostrand, 1946)
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be done with any two terminal interstage limited by a specified shunt capacit-
ance is only a factor of two higher in the figure of merit than for the simplest
case of Eq. (1-1). The next step in complexity beyond the simple resistance
interstage is the shunt peaking circuit (series L and R across the output).
If this is adjusted for no rise in response above the midband value the figure
of merit is about 1.8 times the product of Eq. (1-1) or within 20?/O of the
ultimate.
The four terminal interstage can give further improvements although here
the design often imposes a restriction on the division of input and output capa-
citances which is not necessarily the way these capacitances normally appear in
practical circuits. However, even neglecting this difficulty it is found that
the gain-bandwidth figure of merit for a four terminal interstage is not improved
beyond a factor of about 3 over the very simplest case of Eq. (1-1) without con-
siderable complexity in circuit design, construction and adjustment.
Although the above discussion dealt wIth the tube circuit problem, it is
well to summarize the general conclusions which can serve as a guide to What
one can look for in the corresponding transistor case. These are:
1. The constraints on video amplifier design are principally due
to the parameters of the active device.
2. The parameters of importance as well as an order of magnitude
idea of the bandwidth obtainable for a specified midband gain (or visa versa)
can be found by an analysis of the simplest configuration.
3. The use of equalizing networks can give improvements in perform-
ance over the simplest circuits but the point of diminishing returns is reached
very rapidly with regard to circuit complexity unless the amplifier must be
designed to give ultimate performance regardless of cost and other factors.
The above discussion outlined the broad aspects of the problem. The
logical first step in the consideration of the specific case of transistor low
pass amplifiers is the derivation of a suitable transistor equivalent circuit.
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Using the results of the equivalent circuit investigations, the problem
of wide band response has been sLalied using two distinct approaches. One
has utilized interstage networks to obtain the necessary equalization while
the other has been to employ local feedback using R-C networks to obtain the
desired bandwidth. Preliminary results using both techniques are described
in this report.
It is felt that the initial aims of the study have been accomplished.
Transistor video amplifiers having voltage gains of about 26 db and bandwidths
of 4 MC. have been constructed using conventional triode transistors. The most
important parameters of the transistor intended for use in a video amplifier
can now be specified. Future work on extending the response and a study of
output circuit limitations will be carried on in the next period.
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CHAPZER 2
Theoreticel Equivalent Cirtuits
2-1. Allay - or Fused-Junction Transistor:
For the derivation of an equivalent circuit for the alloy - or fused-
junction transietor, we start with th* analytical expressions for the y-
system parameters of an idealized one-dimensional transistor, as obtained by
Earlyi. The geometry of the situation is shown in Figure 2-1 for the ease of
a PNP transistor, where the boundaries of the regions are plane, parallel, and
of infinite extent. The solution is also applicable to an NPN transistor with
the roles of holes and electrons interchanged.
"V\A/VVVVVVV\ 1VVVV
Emitter
Base
Collector
?./VVN/ `, VV\
Fig. 2-1. Idealized Transistor Structure.
The parameters are obtained from a solution of the diffusion equation
for minority carriers in the base region which satisfies the boundary condi-
tions Imposed by the instantaneous collector and emitter potentials, the "one
dimension" which enters into the solution being that normal to the boundaries
of the regions.
The parameters, for the reference directions and circuit configuration
shown in Figure 2-2, are as follows:
1"Design Theory of Junction Transistore, by J. M. Early, BSTJ, Vol. 52,
pp. 1271-1312, Nov. 1953.
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d 1
Sru Ej
B2=0
kT
V
o
u tanh--
P L
(2-1)
Ie
tanh rio u
d -6sr
Y12 =
EI=0
d 2
Y21 =
? _
kT
E2=0
Y 22
d
2
-7
e Fte
)11
Diffusion
Transistor
(a)
E'= 0
1
PC
L sinh
Pc
L
tanh[-- UP
wo
(2-2)
(2-3)
( 2 -4 )
(b)
Fig. 2-2(a). Reference Directions for small-signal currents and voltages,
grounded-base connection. (b). Circuit representation of the
y-system equations. Note that I and I do not include the
currents flowing into CTE and CTc, resrActively.
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The quantities Involved in Eqs. (2-1) thru (2-4) are:
q = electronic charge
k = Boltzmann's constant
T = absolute temperature
= width of base region
w= time average width of base region
L = D T diffusion length of minority carriers in base region
P P
Vc= collector voltage
T = lifetime of minority carrier in base region
I = collector hole bias current
PC
Ie = emitter bias current
and, in addition, the quantity up as a function of complex frequency s is
given by
U 4,1?=...-rr
P p
(2-5)
For steady-state sinusoidal excitation s = jce and u=1-,n-c?Dz
If we define gll, g12, etc. as the low frequency (i. e., s = 0) values
of yll, y12, etc.: then:
qI u tanh
e p ,
gll kT
o
tanh u
L p
= 0
qr.
(2-6)
U g12 = .37 Ipc
nh -t? p
w.0 1 aw
-.37.-
c
L stall--
IDC
WO
L (2-7)
L si
aW U
P
qIe
821 - kT
V?
up tanh r
S =0
clIe
- kT
= 0
1
wo
sinhLu
P s
w
cosh 12
(2-8)
?
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Iwo
-7-
ir
% cosh ?o u
L p
g22 .,. 4T-? Iy.Yc if
c L sinh --2 u
L p
w
cosh
_1-
zvaw PC -Idy
c
s = 0
Here, the minus signs which are associated with 712_and y21 have been re-
tained, as these result from our choice of current and voltage reference direc-
tions and not from a consideration of the low frequency values. We note that,
in the right band sides of Eqs. (2-6) thru (2-9), all quantities are readily
av w
measured with the exception of mv p wc and ra . On the other hand, there
c
are four equations, so that the measurement of the low-frequency values enables
us to cheek the validity of the theoretical results. This point will be dis-
cussed in detail later.
Referring to Figure 2-2(b), we show the gm and Cm, the emitter and
collector junction capacitances, respectively. The effects of these are not
included in the paramet2rs above, so that the next step in the analysis is to
take them into account. The impedance level on the emitter side is generally
low enough so that CTE may be neglected, even at relatively high frequencies;
on the other hand, Cm is important, due to the much higher impedance level in
the collector circuit. Thus we have
d
Yil = r = Yll + sCIE = Yll
1
E6;
= r = Y22d BCTE
2
(2-10)
(2-n)
TO summarize, the y-system equations incl?ding the effects of Cm and
CSE are:
/1 Yll
d (2-12)
= EZ Y12 4.2
d 721
12 E' + (y sCTc)
= 1 22
(2-13)
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2.2 Effect of the Base Spreading Resistance ril)
One of the assumptions in the one-dimensional analysis previously des-
cribed is that the base is everywhere at the same potential, i.e. that there
is no current flow in the base region parallel to the junctions In the act-
ual transistor, however, the emitter and collector currents are different, and
the current flow in the base region produces a transverse voltage drop.
For a transistor structure similar to that of Figure 2-1 but having finite
boundaries, the most important effect of this on the equivalent circuit, espe-
cially at high frequencies, appears to be the addition of a base spreading re-
sistance r' between the base terminal of the diffusion transistor and that of
the actual transistor.3 More complicated physical structures4 require further
additions to the basic equivalent circuit which make it vite difficult to ana-
lyze. For this reason our attention will be focused upon the effects of adding
r' to the equivalent circuit for the diffusion transistor.
In order to find the y-system parameters of the actual transistor, which
we denote by yll Y12, etc., it is most convenient to consider the problem as
one of two networks connected in series, one of them being the diffusion trans-
sistor and the other being the simple network represented by r itself. The
z-system parameters of the overall network, i.e., the actual transistor, are
then the sum of the corresponding parameters for the two networks. The manipu-
lations involved may be handled through the use of matrices', as transformations
from the y-system to the z-system, and vice versa, are necessary.
The y-matrix for the diffusion transistor, denoted by aid, is
3,4. See, for example, the paper by Early previously cited.
5. Matrix methods applicable to this type of problem are described in
Chapter 15 of "Principles of Transistor Circuits", John Wiley and Sons
(1953).
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fid =
-9-
Y11 yi2
Y21 Y22 8grc
(2-14)
The z-matrix for the diffusion transistor, Izld, is expressed in terns
of the y's for the diffusion transistor as
where
kid =
elinm?
A d
11
z21d
Yil
Y21
12
z22d
Y
12
Y22
1
122
-Y21
= y11
A d
`4Y
mom.
sC
+ TC
/MOM&
-1
+ sCpc - Y12d (2-15)
YD.
(2-16)
(1
02d
+ esr ) - 112d 1d21
Referring to Figure 3, the z-matrix for the network consisting of r.l'a is
simply
=
r' r'
r' r'
b
and IZI, the z.-matrix for the actual transistor, is
[z] =[z]+[z]ri, =
Y22 8CTC rb -Y12 + r 60,
Ad
-Y21 + r'
Ay
(2-17)
(2-18)
oi
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The final step is to convert from the z-system for the actual transistor
to the y-system, as the latter are more accurately measured in the laboratory.
The y-matrix for the actual transistor is
We next evaluatei as
As
11?????? UMEIP
11 12
z21 z22
Zn. z22 z12 z21
(2-19)
2
1 , d dt, d , d
d
. ky22 + sC + r' A )ky + ' A d) - ky + r' A d)(d + r! A d)
TC b y 11 b y 12 b y e by
A
Y
2
1d
y Cy + sC ) - v
d
11 22 TC -12 121 - Ad rb (1d 22 + sCTC + y11 - 1d12 -Yd21 )
A
1 n d
+ rib ky22 + sC +y -y - v
TC 11 12 -21 )
The result for y11 of the actual transistor becomes
Y =
11 ,6
1
d d
Ad 1 + r' ky
a b 11 Y22 4. z''TC -
1
z22d y11 + r' A
by
(2-20)
?
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y + r' A
11 b y
d
1 + r' ty + y22d + sC - y -
b 11 TC 12 '21
(2-21)
We note that, for the case where r11) is zero, this expression reduces to Ylld'
as it should. The other y parameters are
-z12
where D = 1 + r'
b
112 r' 6
b y
(2-22)
(2-23)
(2-24)
Y12 =
-z21
y21d - r' 6
b y
Y =
21 Az
z11
y 22
+ sC + ri A
TC b y
Y22 = A
y Y22d
11
8CTC
d
Y12 121d
(2-25)
I
Of these, the ones with which we will mainly be concerned are y, Y21
and y22 - the first two because they determine m, the short-circuit current
gain in the grounded-base connection for the actual transistor, and y the
latter because it is the same as
emitter connection.
y22 for the actual transistor in the grounded-
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2-3. Approximations for the grounded-base parameters
.Due to our assumption of unity collector and emitter efficiencies, the
y-parameters for the diffusion transistor (with consideration of CTE and Cm
neglected) are not ail independent. Referring to Eget. (2-1) thru (2-4), we
farm the ratio
wo
-qIe u tahn ?
P
kT
sinh ? u
L p 1
Y2.3.
111 kT
wo
Ito
qI u tahn? cos u
ia
e L p
Similarly) forming
wo
tahnr up
ow. T
Tcrc -pc L Binh --2 u
L p
1
W.c,
6W T U
Fir ?-pp P cosh ? u
L p
w o
L tahn ? u
L p
(2-26)
(2-27)
Thus we have the useful relationship yold
/Ylld = Ylld/Y22d which
simplifies the preceeding derivations considerably. For example, the quantity
6y becomes
?d d d d d
,?
"u. = Yll Y22 - Y12 Y21 ' 13.-TC Yll
la Yll Y12
d Y22 J2l1_,.
d
f d ,
Yl2d Ylld -
sClr
Yud
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= y v
11 "12 d
d 1 Y21
Y21
11 11
+ sCTC y
y
d df 1 ylli2
"al
The quantity aa = -
since
d
Y12 Y21
Y22d Ylld
(2-28)
1 - ad2
d d
+ SCTC y11 yn 12 + sC ad TC 111
y21d
which was introduced in Eq. (2-28) is of con-
y,,
siderable importance. ThiS-is the short circuit current gain (for the diffu-
sion transistor) in the grounded-base connection, the frequency dependence of
which is given by Eq. (2-26). The minus sign in (2-26) is due to our choice
of current reference directions, and indicates that current flow is out of the
collector terminal when current flows into the emitter terminal. Also, mince
wo/L is typically in the range 0.14-0.30, the low-frequency value of ad is
very close to, but slightly less than, unit.
This means that.4,brd as given by Eq. (2-28) is approximately equal to
2(1 - aa) glld g12d.
Since 1312 is on the order of 10-3 times gil, and (1 - aa) is on the order
of 0.05 at the most for representative transistors, the quantity ri; 6srd can
us1=11y be neglected in the expressions for yil and y21. This gives us
11
Yu =
21
Y =
21 D
(2-29)
together with the very important result that, since a. for the actual transistor
- --11'
is given by Y21/ Y it is, to a good approximation, the same as aa.
conoidered in detail in Section 2-4.
This is
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Before discussing the frequency dependence of a., we will express the
d
quantity D = 1 + r' IBC + y11d +v1 + + d v ylinasimpler form which
b TC -2 -21 d -22
involves a.. This is done by rewriting it as
d
Y21
D = 1 + (1 +
b TC 11 d) 4- Y22
Yll Y22d
= 1 + sr' C + r" (y d d) (1 m)
b TC b 11 22
since ad -
= 1 + d yilCi - ad)
(2-31)
The last result above is obtained by recognizing that y11 and y22 have
the same frequency variation, and that g22 R3, so that it may be neglected. Also, the source
resistance Rs effectively adds to r11,, so that the effective input impedance
seen by the generator may be expressed in the form
where
Rid 1 + 57'Tb
h +R =R + r' + OE RI
Lie s s bl+ sTb i 1 + sTb
R' = r + Rs + Rid 7' =
i b RI
The ratio haethlle is then
bo
h21e 1 + sTio bo 1
hlle - 1 + s7'Tb . RI 1 + s7"Tb
li*
i 1 + sTb
(34)
(5-5)
(5-6)
which shows that the input circuit will contribute a real-axis pole to
wb
Klr at -7 , and demons tates the importance of a low value of Rs. However,
7
the improvement as Rs is reduced diminishes as Rs approaches rb', so that a
compromise is necessary in this respect.
Eq. (5-6) may be substituted into the expression for Kif to give
-bo 1
(5-7)
v RI (1 4. 8717b) (5722e Y3)
The admittance
+ Y3 is shown in Figure 5-5, where the shunt capacitances
v
-22e
? I
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CL and C1 are represented by a single capacitance C. We see that, for the uncomp-
ensated case where L 0, the load admittance is Y3 at low frequencies, becoming
+ Y2 at higher frequencies Where wC2R2 >> 1. While the exact frequency
range in Which this occurs will depend upon C2, R3, and R2, this effect can-
not be disregarded in the design of an amplifier Where the best possible per-
formance is desired. That is, if the bandwidth is specified, R3 should be as
large as possible, to give the greatest midband gain consistent with other re-
quirements on the response Characteristic. The latter may, for example, require
a eesponse which has maximum flatness, i.e., which never exceeds its low
frequency value for any frequency. Thus, although considerable complication
results from its inclusion Y22e must be taken into account in order to de-
sign for optimum results.
Y22e Y3
0-
0
R2
TC2
Fig. 5-5. The total output circuit admittance y22e + Y3.
The general expression for the voltage gain Kit in terms of the circuit
parameters is
Kv
(l+sT2)(1+sT3)
Kvo (14.87'Tb' Lir2 1(1+s r +R3' (C2 +01 +s2 [C,3(C2+C)+T2CR3] +s3CL3T2}
"0:17
(5-8)
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/09/03: CIA-RDP81-01043R002500170003-9
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/09/03: CIA-RDP81-01043R002500170003-9
-108-
where T2 = R2C2, T3 = L3/R3, and the low-frequency voltage gain K0 is given
by
b R,
K _
vo R1
(5.-9)
As R3 and L3 are the only adjUstable parameters in Eq. 5-8, our con-
trol over the form of the response is necessarily limited. Uwe set
R =R
3 2 4 C
then the general expression simplifies to,
KV 1
K (1+87"Tb)(1+sT 1;TT = R2C
vo L'
(5-1o)
The term (l+sTL) in Eq. 5-11 is of the same form as that obtained for the
vacuum tube amplifier with a parallel RC load. Thus we have a gain-bandwidth
trade as far as the effect of the output circuit is concerned, but the added
term in Eq. 5-11 imposes a fundamental limitation on the response.
This term commonly corresponds to a frequency in the range of 1 to 3
megacycles, while that corresponding to TL is generally much higher. Thus
the simple form of Eq. 5-11 is of very limited value, and the removal of the
term (1+57?Tb) is highly desirable even if a relatively complicated design
procedure is involved.
An examination of Eq. 5-8 shows that either the term (l+sT2) or (l+sT3)
could be used to cancel that containing 71Tb in the denominator._ The former,
however, represents a characteristic of the transistor itself and isnot
subject to control for a given transistor. The alternate choice is to set
y'Tb = T3. This determines the ratio L3/R3, so that R3 may be considered as
the only remaining adjustable parameter.
For this case, Eq. 5-8 may be re-written in the form
?
-
Declassified
in Part - Sanitized Copy Approved for Release
?
Kv
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l+sT2
KVo = l+s IT2+R3(C2+C)] +s2R51:71Tb(C+C2)+T2C.] +s3R3C7111T
(5-12)
where we have a first power term in s in the numerator and a term in s3 in
the denominator. In general, for arbitrary values of R3, Eq. 5-12 will not
be a desirable form ef response, i.e., peaks may exist in the response which
result in ringing When a transient input signal is applied. The value of R3
for maximum flatness may be calculated as
7Th -T2
R3 . 2 C+C2
(5-13)
In general, values of R3 less than this will provide an increased band-
width, but the response characteristic itself may or may not be flat, de-
pending on the values of the other circuit parameters. Thus, the use of a
simple shunt RL circuit in the output offers the possibility of increasing
the bandwidth, but offers no means by Which specified frequency characteristics
may be met. The latter requirement may be met by a more complex network with
added degrees of freedom, but here, as in the present case) the transistor
itself will impose limitations on the performance available with a given unit.
Referring back to Eq. (5-15) the time constant .NoTb is in general larger
than T2' so that the value of R3 required is positive. In fact, the value of
R as obtained from Eq. (5-13) if frequently large enough so that the voltage
gain Kv is quite high. It should be kept in mind that the condition under
Which we may neglect the internal feedback in the transistor requires
lh12eKvI