FINAL REPORT ON THE VHF FERRITE ANTENNA DEVELOPMENT PROGRAM

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• Collection: General CIA Records
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• Document Page Count: 62
• Document Creation Date: December 22, 2016
• Document Release Date: April 10, 2012
• Sequence Number: 3
• Publication Date: April 30, 1957
• Content Type: REPORT

4
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CONFIDENTIAL
FINAL REPORT
on the
VHF FERRITE ANTENNA DEVELOPMENT PROGRAM
?
April 30, 1957
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CONFIDENTIAL
Final Report on the
YIN' FERRITE ANTENNA DEVELOPMENT PROGRAM
I. INTRODUCTION
The objective of the VHF ferrite antenna development program was to study
the possible advantages offered by the use of ferrite materials in antennas from 3
to 30-iic/s. It was felt that ferrite materials had the potential of improving an-
tenna performance by virtue of their high permeability, low losses, and dispersive
effects. The high permeability and low losses were to produce increased gain by pro-
viding greater coupling to the radiating fields. The dispersion of permeability was
to result in increased bandwidth. This report summarizes the results of the study
with particular emphasis placed on the work done in the period from January 1 to
May 31, 1957.
II. RESULTS AND CONCLUSIONS
The present study of ferrite antennas was confined to small antennas having
maximum dimensions much less than a wavelength. The following conclusions were formed
during the study and apply to such small antennas.
The diameter of a loop antenna can be reduced without a loss in gain or sen-
sitivity by adding a ferrite core, but the required length of ferrite rod will be
greater than the diameter of the original loop. If the maximum dimensions of the two
antennas are to be made equal, the gain of the air-core loop will be greater than the
gain of a ferrite core loop.
Expressions were derived comparing the sensitivity of a ferrite antenna with
an air-core loop in the presence of antenna thermal noise. Similar conclusions were
111*6
reached(2); the diameter of the loop could be reduced by adding a ferrite core without
46 a loss in sensitivity, provided the length of the core was greater than the diameter
of the original loop. The results were not verified expermentally., for the receiver
CON ID.N__p.IAL
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noise not antenna noise was found to limit sensitivity. When receiver noise dominates,
it is simply antenna gain which governs sensitivity.
The ferrite antenna will be more convenient to package than the air loop in
certain applications. The ferrite antenna has its maximum dimension in only one di-
rection. The resulting line geometry will at times be an advantage over the plane
geometry of an air loop.
A monopole antenna, like the ferrite antenna, also has a line geometry.
Nevertheless, the ferrite antenna will at times have packaging advantages even over the
monopole. The monopole must be situated perpendicular to a ground plane; e.g., the
? chassis. The ferrite rod can be placed parallel to the chassis. Therefore, the fer-
rite antenna inherently allows a more compact package. However, the use of monopoles
has been extended by simple designs that allow convenient stowing; e.g., telescoping
rods or wire wound on a reel.
A small loop antenna with a ferrite core was found to produce a greater
terminal voltage in the 3 - 30 me/s range than a monopole antenna of the same size.
However, the induced voltage, in contrast to the terminal voltage,was greater for the
monopole. The performance of the monopole was degraded by the coupling network which
? was of conventional design for a capacitively tuned antenna. If the property of con-
venient stowing allowed a monopole to be used greater in length than the ferrite rod,
the performance of the monopole could be made comparable to or better than the per-
formance of the loop.
The voltage per turn induced in a loop decreases 20 db/decade with the fre-
quency. However, when the antenna is designed for a lower operating frequency, the
number of turns on the loop can be increased. For a fixed range of tuning capacitance,
the allowed number of turns is inversely proportional to the center frequency, ex-
actly compensating for the reduced voltage per turn. Therefore, the net induced volt-
age is in effect nearly constant at different center frequencies for a loop antenna
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similar to the monopole antenna. The additional windings will also add stray capaci-
tance, preventing exact compensation at low frequencies.
No advantages were found using the dispersive effects of ferrites in small
antennas. The dispersion was too weak and the losses too great in the dispersive
region. Theory indicates that the behavior required of the complex permeability for
wide-band operation is not physically realizable over a broadband of frequencies. No
attempt to develop improved dispersive material should be initiated without first
giving due consideration to this theory.
The most fruitful improvement in ferrite materials appears to be an extension
? of their useful range into higher frequencies. Materials are not available which have
high permeability and quality factors above 30 me/s. On the other hand, it does not
appear fruitful to develop extremely high permeability materials for small antennas.
The intrinsic permeability becomes ineffective for producing improved performance in
small antennas with ferrite cores of reasonable length-to-diameter ratios.
No evidence was found to indicate that the loop antenna would be lesssuscep-
tible to interference or proximity effects than a monopole antenna. Rather, when both
antennas are considered coupled to the electric field, no fundamental difference be-
9 tween the two antennas is apparent. Details do differ, however, and design parameters
should be chosen to favor the particular type antenna chosen.
Dielectric materials are not expected to yield greater advantages than do the
magnetic materials in small antennas. The theoretical treatment of the dielectric an-
tenna would be very similar to the treatment of the ferrite antenna. For exanple,
there is a de-polarization factor for a dielectric rod which corresponds precisely to
the demagnetization factor for the magnetic rod. Also, the theoretical treatment of
complex permeabilities is directly applicable to complex permittivities.
There is a severe fundamental limitation on the gain-bandwidth product of
small antennas which is described in a theory by Chu(l). The gain of an antenna much
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smaller than a wavelength which is designed for a maximum gain bandwidth product nearly
equals the gain of a half-wave dipole; but the bandwidth becomes vanishingly small as
the size of the antenna is reduced.
III. RECOMMENDATIONS
Ferrite core loop antenna should be used in applications where a compact
package is required. More convenient packaging is the principal advantage provided by
the ferrite antennas.
Improved magnetic materials should be developed for application to small an-
tennas above 30 me/s. High permeability, low loss materials are needed. Studies
should be made of the advantages using ferrites in antennas comparable in size to a
wavelength. There will be a better utilization of the magnetic properties of the
materials in these large antennas than in small antennas. Furthermore, it is likely
that small dispersive effects can be accumulated and used to an advantage in large
antennas. If small dispersive effects can be used, the accompanying losses need not
be prohibitively large. Small dispersive effects accumulated over many wavelengths
are already being used in microwave and optical applications; e.g., microwave ferrite
? phase shifters and achromatic lenses.
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? IV. PROGRESS
A. COMPLEX PERMEABILITY
1. Intrinsic Permeability
a. Concepts
The VHF ferrite antenna consists of a conducting coil wound on a
ferrite core. The ferromagnetic properties of the core material are described
by its permeability, "g". The permeability is the ratio of the magnetic flux
density to the magnetic field intensity
B = giH
?
(1)
The resistivity of ferrite materials can be made very large resulting in negli-
gible conduction losses. In such cases, the core losses are principally hyster-
esis losses.
The hysteresis loss is proportional to the area enclosed by the
hysteresis loop. See Figure 1
FIGURE 1
LARGE SIGNAL HYSTERESIS LOOP
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?
It is shown in Appendix A that, for complex permeabilities,
tLi = W1 - j ?i (2)
the hysteresis loop is approximated by an ellipse. See Figure 2. The approxi-
B
FIGURE 2
SMALL SIGNAL HYSTERESIS LOOP
mation is valid for small field intensities. The imaginary part of the complex
permeability is responsible for the hysteresis losses. When t4 = 0, the hyster-
esis loop degenerates into a straight line. The area enclosed by the loop van-
ishes, and no losses occur.
The complex permeability is a function of frequency. For example,
the real permeability decreases markedly at high frequencies. The magnetic do-
mains simply do not have sufficient time to align themselves with the field be-
fore the field reverses itself. The decrease in permeability at high frequencies
is called the dispersion of permeability. At the same frequencies, where the
material becomes dispersive, the hysteresis losses become large.
b. Measurements
The complex permeabilities of several ferrites were measured from
3 to 30 Mc/s. The permeabilities were derived from impedance measurements. Both
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a ferrite-loaded coaxial waveguide and a ferrite-cored toroidal coil were used.
The analyses required to derive the permeability from the impedance measurements
are included in Appendices B and C. The results for Moldite "M", Ferramic G, and
Ferramic H are presented graphically in Figures 3, 1, and 5. Note that the greater
the d.c. permeability, the lower the frequency where dispersion occurs. Note
also that the greatest losses occur in the region of dispersion.
2. Effective Permeability
The permeability defined in the previous sections is an intrinsic prop-
erty of the material. For emphasis, it is termed the intrinsic permeability. It is
the intrinsic permeability which appears in Maxwell's equations and in their solutions.
After a solution is found to Maxwell's equations, it is sometimes con-
venient to define an "effective permeability" which is a function of both the intrinsic
properties and the geometry of the material. For example, consider a small prolate
spheroid of ferrite material placed in a uniform magnetic field with its axis parallel
to the direction of the field. The quasi-static solution of the field equations re-
veals that the magnetic field inside the ferrite is also uniform(l)
?
FIGURE 6
OBLATE SPHEROID IN A UNIFORM MAGNETIC FIELD
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An effective permeability can be defined such that the flux density
within the material is proportional to the strength of the original field and the ef-
fective permeability of the spheroid
IT = ?e Ito (3)
The effective permeability is a function of the intrinsic permeability and the geometry
Pe = P.O 1+D(?ir-1)
?
?
?o = permeability of free space,
gir - relative intrinsic permeability of the ferrite material.
D = demagnetization factor along the axis of the spheroid.
The demagnetization factor is a function of geometry alone and, for the prolate
spheroid, becomes
e2 1 1+ i-;2
D = 1-e~ 2 1-e In 1 - 17
The eccentricity is
e - b/a
(h)
(5)
By considering the analogous expression for oblate spheroids, it can be seen that
for needles D --WO
for discs D ---p 1
Since the intrinsic permeability is complex and a function of frequency, the effective
permeability is also complex and frequency dependent
?e = Pe' - J ?e (6)
For the prolate spheroid, the effective relative permeabilities are
?ir 1 +D(?u' -1)J +D (?)2 (7)
? e r r D ] + rD 2
and
?!. (1-D)
?er = [l(4r_12+ LD ?~ 2
(8)
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V. REFERENCES AND BIBLIOGRAPHY
1. "Demagnetization Factors of the General Ellipsoid", J. A. Osborn, Phi. Rev.
Number 67, June 1945.
2.
3. Reference Data for Radio En En ineers, 4th Edition, International Telephone and
Telegraph Corporation, 1956.
4. Principles of Electricity and Electromagnetism, G. P. Horxwell, McGraw-Hill.
5. "Inductive Aerials in Modern Broadcast Receivers", H. Blok and J. Rietveld,-
Philips Technical Review, Vol. 16, No. 7, Jan. 1955.
? 6. "Realizability of a Prescribed Frequency Variation of Dielectric Constant",
R. J. Harrison, Proc. IRE, Vol. 45, No. 3, March 1957.
7. "Dispersion Relations for Tensor Media and their Application to Ferrites",
B. S. Gourary, J.A.P. Vol. 28, No. 3, March 1957.
8. "Causality and the Dispersion Relation: Logical Foundation", J. S. Toll,
Phys. Rev., Vol. loo, No. 6, Dec. 15, 1956.
9. Network Analysis and Feedback Amplifier Design, H. W. Bode, D. Van Nostrand
Co., Innc ., N.Y., Rte. 1945
10. Servomechanism and Re tin System Design, Chestnut and Mayer, John Wiley
and Sons, Inc., N.Y. U-51.
U. "Physical Limitations of Omnidirectional Antennas", Journal of Applied Physics .9
? Vol. 19, No. 12, Dec. 1948.
1. "Improving Ferrite Cored Antennas", C. A. Grimmett, Tele Tech and Electronic
Industries, Vol. 14, No. 2, Feb. 1955.
2. Input Impedance of a Spherical Ferrite Antenna with a Latitudinal Current,
W. L. Weeks, Tech. Report No. 6, Antenna Laboratory, University of Illinois,
Aug. 1955.
3. Impedance of Ferrite Loop Antennas, V. H. Ramsey and W. L. Weeks, Tech. Report
No, 13, nEnna a oratory, University of Illinois, Oct. 1956.
4. "Inductive Aerials in Modern Broadcast Receivers", H. Blok and J. J. Rietveld,
Philips Technical Review, Vol. 16, No. 7, Jan. 1955.
5. "A Magnetic Radio Compass Antenna Having Zero Drag", A. A. Hemphill, IRE
Transactions - Aeronautical and Navigational Electronics, ANE-Z, No. Dec. 1955.
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6. "The Magnetic Antenna", L. Page, Phys. Rev.Vol. 69, No. 11, 12, June 19h6.
7. Ferromagnetic Loop Aerials for Kilometric Waves, J. S. Beirose, Wireless
Engineer, Feb. 1955.
8.
0
49
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VI. NOMENCLATURE
?i - intrinsic permeability
?e - effective permeability
?r. - relative permeability
?o - permeability of free space
?t - real part of complex permeability
?" - imaginary part of complex permeability
- modulus of complex permeability
- magnetic flux density
- magnetic field intensity
- Electric field intensity
- demagnetization factor
- induced voltage
- output voltage
?
e - eccentricity of prolate spheroid
V - volume of prolate spheroid
Q - quality factor
R - resistance
L - inductance
C - capacitance
m - circular frequency
f - frequency
f - 3 db bandwidth
11 G - relative gain
T - absolute temperature
- Boltzmannts constant
~s-
signal-to-noise ratio
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A - i
APPENDIX A
The equation which defines permeability is
B = ?i B
Consider sinusoidal time variations and a complex permeability
R = Eo ejo)t
?i = ?i - j ?i
? Then
TIO (?i cos cot + ~Lj sin cot)
+jNo (?i sin cot - ?i cos cot)
The physical observables are
Re[!!] _ (1o) cos cot
Re [ B ] = (110 ?i2 + ?i2 ) sin (cot +Y)
?
??
i
(A-1)
(A-2 )
(A-3)
(A-4)
It can be seen that these expressions define an elliptical hysteresis loop by con-
sidering the equation for an ellipse expressed in terms of Its eccentric anomaly n(n.
y'
x' = a cos ?
yr =bsin0
(A-5)
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?
x = x' cos e - y' sin 9
y = x' sing+y' cos 6
The equations for the ellipse in the new coordinate system become
X = (a cos A) cos 0 - (b sin 9) sin 0
a b2 + (a2 - b2) cos 9 cos (0 + a)
and
y = (a sin 9 cos 0 + (b cos 9) sin 0
a2 _ (a2 - b2) cos2 6 sin (0 + p)
where
tans - (b/a)tan9
? and
tangy = (a,tb) tans
Ho - b2 + (a2 - b2) cos2 9
Ho VILi + ?i2 = ja2 - (a2 - b2) cos2 8
cwt - (O + a)
Y = (n - a)
Then the equations for the ellipse become
Ho cos cot
Ho ?i2 + ?12 sin (cot +
Y)
(A-6)
(A-7)
(A-8)
(A-9)
(A-10)
(A-1-1)
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.A-3
which are identical with the equations describing the physical observables Re [$1
and Re CH] . Therefore, the hysteresis loop is an ellipse.
Ra [~1]
?
FIGURE A-3
?
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B-1
APPENDIX B
Consider the 'input impedance a coaxial waveguide whose electrical length
is much less than one wavelength. Let the guide be terminated in a short circuit with
a concentric cylinder of ferrite partially filling the guide next to the termination.
I
/a _
W
tercr~G2
Approximate the magnetic field intensity by the quasi-static solution
I 2nr eiuot ti
(B-1)
The voltage induced across the wave guide at the reference is
V - dO/dt (B-2)
W.44^ X#-Ca
g f~ae~ir~a,~
L an
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0 = fp, ?H . dA (B-3)
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R x
V = JCO ?o 2nr dr + W ?o 2nr dr
--
AO I y I
+ W r ?o M7 dr + W fX ?i ya: dr
?
where
Now let
Then
I (f-W) fn R/r + W (fn x/r + fn R/y + Iij fn y/x)
(B-a)
?i = 6) ?ir? (B-5)
gir = girt - J ?ir (B-6)
v = J ?I f( In R/r + W fin x/r R/y r/$ + (? , - J t41,) In y/x (B-.7)
The input impedance is
Z = v/I
'o (W f (n y/x) I
C?jr R
+ J C41 . - 1) 2no (W fn y/x) + Zc
. where
Zc d characteristic impedance of empty coaxial waveguide
fn R/r
1/2n CT.-
4 velocity of light in a vacuum
C
?o Eo
Therefore, the series impedance
Z = Rs + j Xs
Rs = 41. Ef ?o (W fn y/x d
(B-8)
(B-9)
(B-10)
as = (?ir. - 1) r f ?o (Wf(n/x+ Zc (B-11)
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B-3
Solving for the complex permeabilities
R
?" - s (B-12)
f go (W (n y/x )
?;t
?
?
Zo = ?o/so
as - Zc 2n + 1
Rs Z0 W (n y/x
(B-13 )
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C-1
APPENDIX C
Consider the input impedance of a toroidal coil wound on a ferrite core of
?
rectangular cross-section. Let all dimensions be small compared to a wavelength.
., #.j, Xs
/e
I*
Appraximate the magnetic field intensity by the quasi-static solution
The induced voltage is
H . 2, , eJcot
2
jw 2n I W In y//
(C-3)
V= N dO/dt s j co ?iN f H ?. di
N2 I y '4
V = jc ?i 2n 1/r Wdr
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The input impedance is
Z = v/I
= Rs + j Xs
?
Let ?i = ?o (? j, - j ?4. )
Rs = N2 f ?o ?,. C W fn Y/xl
7Cs = N2 f ?o ?ir [W (n y/x]
Solving for the complex permeability
?ir
?
Rs
f ?o N2
(C-4)
(C-5)
(C-6)
(C-7)
(C-8)
(C-9)
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APPENDIX D
THE IMPEDANCE OF A COIL WOUND ON A FERROMAGNETIC PROLATE SPHEROID
0
Consider a prolate spheroid of ferrite material wound with "n" closely
spaced conducting turns uniformly spaced along its axis. Analysis shows(4) that,
t Z7
?
Io
(D-1)
flows through the windings, a uniform magnetic field is established inside the core,
directed along the axis, and having a magnitude
Ho - (1 - D) ao (D-2)
The total field consists of the linear superposition of the applied field and the de-
magnetization field.
H = To - DI (D-3)
The magnetization is defined as
II = (? - 1) H (D!..)
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D-2
"D" is the demagnetization factor for the prolate spheroid(-). Thus, % H = (1 - D) _? - D (?ir - 1) H
?
nI
H - (1 - D) 2a
1 + D (?f1)
ei
nIo
(D-5)
(6 )
V (D-7)
Io
too (2a4)2 (1-D) JA
iJAe
?e
?ir
1 + D (?.- 1)
(1 - D)
nIo
2a
(1 - D) 2'o n
a (2a )
( 2 a )2 V (1 - D1 (4 - J ?e )
wo (2a)2 V (1 - D ?e
The induced voltage
The impedance is
is (2)
ei = -J 46o
c'?[2a)2V (--D]?e
R+3 ci L
R = 00? (a )2 V (1- D)
L= ( -)2V (1-D)
(D-8)
(D-9)
(D-l0)
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APPENDIX S
THE EQUIVALENCE OF MAGNETIC AND ELECTRIC FIELD
COUPLING BY LOOP ANTENNAS
Loop antennas are sometimes described as coupled to the magnetic field
component in contrast to the electric field component(s Accordingly, the induced
voltage is said to equal the time rate of change of magnetic
ej
dt
B ? dA
is
For the antenna shown in Figure E-i,
ei s -j to ?o Ho A
FIGURE E-1
,Q
flux linking the loop.
(E-l)
(E-2 )
However, the antenna can just as correctly be described as coupled to the electric
field component. Then the induced voltage becomes
ei = ? E . dd
(E?3 )
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For the antenna shown in Figure E-2,
ei = Eo I a-iP- Bo, I ejf
2jE.f(sin Ow
I*
I L
FIGURE E-2
The phase velocity is
? For small antennas
sine,
ei
7
For a plane wave in free space
'A f - C
(E-4)
(E-5)
(E-6)
1 (E-7)
The expression for the induced voltage becomes
and reo ED H0
ei = -j copoHo A
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Equations (E-2) and (E-9) are identical, illustrating that the loop
antenna can be considered to couple either to the electric or to the magnetic field
component with equal validity. The reader familiar with electromagnetic field theory
will recognize the foregoing discussion as simple application of Maxwellts equation.
X E = at
?
?
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"11-a VI-1 e I ll .6.
F-1
APPENDIX F
THE DLPEDANCE BANDWIDTH OF A PARALLEL
RESONANT LRC CIRCUIT
A. CONSTANT INDUCTANCE
Consider the parallel resonant circuit in Figure F-1. The input impedance
?
1/R+j(wc-1/wL)
? Resonance occurs at
wo C M 1/w0L
The impedance at resonance is
Zo = R
The impedance is 3 db down from its value at resonance for
(wcC - 1/a0L) 1/it
The upper and lower 3 db cut-off frequencies are
wcu - 1/29C + J(1/2RC )2 + l/ -W
r '
wcy - 1/2RC + (1/2RC)2 + 1/U
I AL
(F-1)
(F-2)
(FF3 )
(F4.)
(F-5)
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CONFIDENTIAL
F-2
The 3 db bandwidth is
B . L - LoAw
The input impedance becomes
Z
i,4 + J(% + l/Lo)
The impedance still has its maximum value at resonance
?CU-0'CL
2n
1/2 nRC
(F-6)
F-7)
? Zo = R
?
(F-8)
MoC = l/Lo
The impedance is 3 db down from its maximum value at
(ccC-l/L0) _ ?i/k
The upper and lower cuto-ff frequencies are
bocu i/LoC + i/RC
p1cL = l/LoC - l/RC
The 3 db bandwidth is
-96 f = 1/2n (ccu - c L)
= 1/n8C
(F-9)
(F-10)
(F-11)
Da TIAI,
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