FINAL REPORT ON THE FERRITE ANTENNAS FOR VERY LOW FREQUENCIES, FINAL REPORT

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78-03424A000500010007-0
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 61
• Document Creation Date: December 22, 2016
• Document Release Date: April 10, 2012
• Sequence Number: 7
• Publication Date: February 15, 1957
• Content Type: REPORT

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FINAL REPORT
on the
FERRITE ANTENNAS FOR VERY LOW FREQIM IES
February 15, 1957
ORIGINAL CL BY .3574q? 7
^ DECL X REVW ON 1/ G ~/
EXT BYND 6 YRS BY FIEASON .3 d C ._-.-
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000 / REV DATE L +900 BY d~irz__.r b
ORIO COMP As- UPI TYPE -710 ORIO CLASS - PAGES (L REV CLASS a--
JUST 2 NEXT REV P G/ 0 AUTHh HR TS4
QFI DENTIAL
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ham! ."~ ~^yy ~A
Page
Scope and Objectives. . . . . . . . . . . . i
I. DISCUSSION OF RESULTS . . . . . . . . . . . . . . . . . . . . . . . . 1
Air Core Criterion and Ferrite Coil Length 1
Induced Voltage (or Effective Height) 2
Signal-to-Thermal-Noise Ratio 3
Conclusions . . . . . . . . 4
IT. DISCUSSION OF NOISE AT 25 kc/s . . . . . . . . . . . . . . . . . . . 4
General. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
External Noise Sources at 25 kc/s-. . 5
Internal Noise Sources at 25 kc/s . . . . . . . . . . . . . . . 7
III. ANTENNA EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 7
? Assumptions* ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? . ? ? ? ? ? ? 7
Air Core Loop. 8
Ferrite Core Loop. 9
IV. COMPARISON OF ATMOSPHERIC NOISE AND THERMAL NOISE IN LOOP ANTENNAS
AT VERY LOW FREQUENCIES . . . . . . . . . . . . . . . . . . . . . . 13
Introduction 13
Assumptions Made in the Calculation of eAN/e TN' 14
Resonant Air Loop. . . . . . . . . . . . . . . . . . . . 14
Non Resonant Air Core Loop 17
Resonant Ferrite Core Loop 18
Non-Resonant Ferrite Core Loop 19
V. COMPARISON OF INDUCED VOLTAGES AND SIGNAL-TO-THERMAL-NOISE RATIOS IN
FERRITE AND AIR CORE ANTENNAS . . . . . . . . . . . . . . . . . . . . 23
? VI. COMPARISON OF TUNED AND UNTUNED ANTENNAS ON A SENSITIVITY BASIS AND
ON A SIGNAL-TO-THERMAL-NOISE BASIS FOR (a) Broadband Antenna;
(b) Narrow-band antenna . . . . . . . . . . . . . . . . . . . . . . 34
VII. E-FIELD PICKUP . . . . . . . . . . . . . . . . . . . . . . . . . . 40
VIII. EXPERIMENTAL METHODS AND RESULTS . . . . . . . . . . . . . . ? . . 42
Introduction . . . . . . . . . . . . . . . . . . 42
Test Equipment and Methods . . . . . . . . . . . . . . . 42
Experimental and Analytical Results . . . . . . . . . . . . . ? 47
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
REFERENCES . . . . ? ? . . . . . . . . . . . . . . . . . . . . . . . . . 57
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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SCOPE AND OBJECTIVES
?
0
The investigation described in this report seeks to
appraise the relative merits of the ferrite cored loop as a
very low frequency receiving antenna. The restrictions imposed
upon the antenna., briefly, are that it operate at 25000 cps and
have a 3 db passband of 2000 cps. The basis used for judging
the relative merits of a ferrite antenna is a comparison of in-
duced voltages and signal-to-noise ratios with an air core loop
antenna of comparable size. Comparisons made are primarily
analytical with experimental dhecks whenever feasible.
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Atmospherics vs Thermal Noise
The relative importance of atmospheric noise and internally generated
thermal noise at 25 kc/s is examined with respect to magnetic loop receiving an-
;,enras. It is found that the ratio of atmospheric-to-thermal-noise volts at the
antenna terminals increases as the 3/2 power of the maxims dimension (Table I).
For median atmospheric noise field strengths found in the U.S.A., the thermal
noise in a tuned-circuit (singly tuned) loop antenna is found to be appreciable
for loop diameters as large as 50 to 100 cros, depending upon the specific loop
rtenra. Noise in larger tuned coops is found to be predominately due to atmos-
pheric noise sources. The amount of thermal noise generated in a singly tuned an-
4
circuit is inordinately high because sufficient noise producing resistance
mast be present to keep the passband 2000 cps wide. At a 25 kc/s center frequency,
this means a circuit Q no greater than 12.5. The advantages of a non resonant an-
tenea circuit (cr an overcoupled double-tuned antenna circuit) with high Q coils is
therefore of interest and is discussed in Section VI. Using untuned loop antennas
with Q's of about 250 (quite feasible with ferrite core loops at 25 kc/s), thermal
rise is reduced so that it becomes negligible with respect to atmospheric noise
for 1.uop diameters of 30 to 60 cms and greater. The resulting improvement in
?
signal-ts--noise ratio is roughly Q untuned 2 Q tuned (Eq. 6-18). However, even with an
ur,i_,~ned :tircuit, enough thermal noise is produced so that, in general, it must be
taken into account - even at 25 kc/s.
A:'-r Core Criterion and Ferrite Coil Length
In order to establish a criterion for evaluating the performance of fer-
r5Je ^ored loop ante*mas, it was decided to use a simple air core loop antenna as
a reference. In Seution III, antenna equations are presented which describe induced
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C/osr y
. Paced Z i fl5
REFERENCE AIR CORE LOOP ANTENNA GEOMETRY
voltage and internal impedance for air core loops and ferrite cored loop antennas.
Experimental data presented in this section together with calculations set forth
in the Appendix indicate that, both from an induced voltage point of view and a
signal-to-thermal-noise point of view, the coils wound on ferrite rod antennas
should extend over the entire length of the rod.
Induced Voltage (or Effective Height.)
Using the reference air core loop and ferrite rod antennas with full
length windings as a basis for calculation, equations and graphs are obtained in
Section V which show the relative merits of ferrite and air core loop antennas
with respect to induced voltage and signal-to-noise ratios. These comparisons
are made for a number of different ferrite rod characteristics; viz., rod length-
to-diameter ratios of 10 to 100 and ferrite toroidal permeabilities of 50 to 3000.
Included in these graphs (Figures 5-3 to 5-8) as a parameter is an F-factor which
relates ferrite rod length to air core loop diameter; i.e., (ferrite rod length) =
(F) (air core loop diameter). Figure 5-8 shows that, when F = 1, ?toroidai. = 3000
and f/d = 20, the best that can be expected from a ferrite rod antenna is that it
produce 53% of the induced voltage produced in the air core loop; i.e., U L = 0.53.
(It seems reasonable to say that ?toroidai = 3000 is good upper limit for stable
ferrite materials foreseeable at present.) This curve further shows that F must to
?
a
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,~ppr-.ximai,ely 1.5 in order to obtain VL = 1; i.e., equal induced voltage from fer-
rite and air core antennas. The relatively poor showing of even the highest per-
meability ferrite antenna is due to the difficulty of improving the effective per-
meabiiity of an open rod. Figure 5-9 clearly shows that the VL increases at a
progressively lower rate as toroidal increases.
Signal. ?t.oThermal Noise Ratio
These same curves for O L also represent the relative values of the signal-
to-thermal--noise ratios of ferrite-to-air core antenna for the case of equal inductance,
qua: Q antennas (see Eq. (5-16)). Hence, the same comments made above concerning
? t;'.e relative induced voltages apply to signal-to-thermal-noise ratios for singly-
.:aied antennas wound with the maximum allowable inductance. Equation (5-15), on the
.'then hand, shows that the curves for ,1 L are all multiplied by the factor
Q fe:r?ri ' r when the Q"s of the ferrite and air core antennas are not equal. Prac-
Q r re
speaking, unequal QTs require that the singly-tuned circuit be abandoned and
-,.n unluned or a doubly-tuned coupling circuit be used in its stead. Using the untuned
as an example, the performance of the ferrite antenna relative to the air core
a enna will, be improved if it, is possible to reach appreciably higher Q loops with
ferrite core than with an air core. For the full length ferrite coil and the
ref- core used in this report, a comparison of Q :educes to a comparison of
`".e c:cre oose..; introduced by the ferrite core and the proximity effects caused by
ale .:Lose` - spaced turns of the air core antenna. Although the matter of maximum
t ~:~.ir:3t>l.e Q has nc:t been examined in detail in this report, indications are that, in
general.,
max. ferrite Q
max. air core Q
Thus the picture presented by the curves of U L are modified at most by a factor
less than 2.
* It is noted that, for specific cases, this number can vary widely.
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Conclusions
As a result of the preceding discussion, some conclusions are reached re-
garding the relative merits of the ferrite cored VLF receiving antenna; viz. in
general., the ferrite cored antenna is comparable to an air core antenna only if its
maximum dimension is permitted to be somewhat larger (1.2 - 1.8 times) than an air
: cre antenna diameter. The practical value of replacing an air core antenna with
a ferrite antenna depends upon the value that can be placed upon the difference in
the geometry of the twc antennas in a specific receiver.
Aside from the physical packaging of an antenna. the line geometry of fer-
rite antenna permits the reduction of stray capacity to the chassis and. hencel a
reduction in E-field pickup, Furt?he:rmor?e, E--field shielding of a line geometry is
somewhat simpler than shielding an air core loop.
The problem of winding high impedance antennas (determined by maximum per-
missible inductance-) and yet maintaining the highest possible Q and the lowest dis-
tributed capacity is simpler for the coi? geometry of the ferrite antenna than fo---
the coil geometry of the air core antenna.
It is noted that the ferrite material introduces problems not found in air
c:)re antennas; e.t;.. ferrite is hard and brittle; extremes of temperature affect its
characteristics; hum pickup is possible due to nor-linear B.-H curve; vibration
stabilization can be destroyed by exposure to high level AC or DC flux fields. ALL
these properties., however, are controlled sufficiently well in available ferrites to
permit satisfactory operation in portable broadcast band receivers.
IT. DISCUSSION OF NOISE at 25 k,-,/s
The minimum signal that can produce a useful output from a radio receiver
is determined by the output signai-to--noise ratio. For any given signal amplitude,
this ratio is set by the external noise entering the receiver via the antenna and by
is
0
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the internal noise generated in the antenna and low level circuits of the receiver.
The antenna and associated circuitry., therefore., is a determining factor in setting
the level of minimum signal reception. In this report., the relative merits of fer-
rite loop receiving antennas are investigated with respect to operation at a center
frequency of 25 kcs and a 2 kc passband. It is of some importance, therefore., to
briefly review sources of ncise generation and single out those sources which are
most objectionable at this operating frequency*
TABLE I
?
NOISE SOURCES
EXTERNALLY GENERATED INTERNALLY GENERATED
1. Atmospheric (electrical storms) 1. Antenna ohmic resistance (thermal)
2. Cosmic (extra-terrestrial radiation) 2. Coupling circuit resistance
(Thermal)
3. Man-made static
3. First amplifier cr mixer
w. Precipitation static (shot noise)
5. Radiation resistance (thermal)
?
Lxcter.rL.+l Noise Sources at 25 kc
Considering first external generators, it is noted that cosmic noise plays
i
no import-3.nt role at. 25 kc/s ( . Also., the radiation resistance of antennas to be
;~rnsidered in this report will be insignificantly small by comparison with other re-
sistive components as a direct consequence of restricting the investigation to an-
tE~nnas which are very much smaller than a wavelength. Precipitation stati ~ is caused
by the discharge of charged particles in. the immediate vicinity of the antenna. Ac-
,.umulaticn of the charged particles can be caused by raindrops, hailstones., snow or
dust clouds. This type of noise is of particular importance in aircraft receiving
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an:.ennas . For the purposes of this report, man-made static and precipitation status
will be grouped together and called electrostatic disturbances. Thus, at 25 kc/s
the main external noise sources are
1. Atmospheric (electrical storms)
2. Electrostatic disturbances
These two sources generate noise signals which are basically different. The former
gives rise to a true radiation field in which the electric and magnetic field in-
tensities are related by the characteristic impedance of frees pace which is a
constant (w 120n ohms). The latter on the other hand is a near-field phenomenon
fcr which the E-field and H-field intensities are related by a factor which is a
function of frequency and which is far greater than 120n ohms for frequencies bei'::w ?
L.S megacycles. In effect, therefore, electrostatic disturbances in the region 25kc/s
are primarily electric field noise signals.
Summing up these points, it is noted that atmospheric noise and desired
transmitted signals both propagate via radiation fields and, in its passband, an
omnidirectional antenna cannot distinguish one from the other. In this respect, then
t antenna is superior to another only if its directivity is higher. An ideal loop
antenna (insensitive to E...field) has a figure-of-eight pattern in the horizontal
plane compared to the uniform pattern of a vertical open antenna.
Electrostatic disturbances can be effectively discriminated against by ?
antennas that respond only to magnetic fields. This attribute is one of the chief
advantages of the magnetic loop type of low frequency receiving antenna.
Thus, in evaluating a ferrite cored loop antenna., directivity and insensi-?
tivity to electric field pickup are important factors to be considered. In this re-
p;rt, only simple loop antennas are considered; hence, directivity is considered only
to the extent that E?field pickup changes the ideal figure-of-eight pattern.
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Internal Noise Sources at 25 kc/s
It is generally accepted that vacuum tube noise generation (shot effect) at
low frequencies (less than 10 me/s) can be made negligibly small by comparison with
other unavoidable noise generators by proper design; e.g., by making the grid circuit
impedance level sufficiently high so that the vacuum tube equivalent noise resistor
is small by comparison.
The coupling circuit and its resistance is associated with impedance level
changing, and the extent to which it affects signal-to-noise ratio will be determined
by such considerations as tuned vs. untuned antenna circuits and the need (or lack of
? it) to interpose a transmission line between the antenna and the first amplifier (or
mixer) grid.
The antenna circuit itself is another and probably the most important source
of internal noise. The ohmic resistance of the antenna is due in part to unavoidable
losses such as copper losses (d.c. resistance, skin effect, and proximity effects)
and for non-air core antennas core losses (hysteresis and eddy current). These losses
can be minimized by the selection of materials and proper design. However, if the
usual practice of tuning the antenna circuit is followed, it is found that a sizeable
amount of additional resistance is required in order to obtain the desired bandwidth.
? It is possible, of course, to circumvent a simple single-tuned antenna circuit at a
cost of additional components and, therefore, other loss elements.
III. ANTENNA EQUATIONS
Assumptions
1. Maximum antenna dimension 5, and > 2
D w
(,-,,,-2)
?
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Ferrite Core Loop
FIGURE 3-2
of = ?f?owAfnfH
rod
11 - 8/27 (a/ff) 2] *
and H = magnetic field intensity (parallel to rod)
Special cases:
Lf
rf
[coil ?o Af of 2
(3-b)
(3-4a)
(3-5)
wL
=
f
(3-6)
Qf
?
f ~r2
?coil ti ?rod
?f x ?rod -\
(3-7)
(3-8)
94 P.R110 rye
?cmril 1, I J
* Bee Appendix and empirical curve of Figure 3-5
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In describing a single ferrite antenna, two different effective relative
permeabilities are encountered; viz, ?f associated with the induced voltage and
?coil associated with the coil self-inductance. Perhaps the use of the term per-
meability is somewhat misleading since that term is often used to describe intrinsic
(or toroidal) permeability which is an inherent property of the material and the
magnetizing force employed. In the case of a ferrite rod antenna, these factors are
used to describe how effectively a magnetic field is deformed and caused to increase
the flux linking the turns of the antenna coil. Thus, effective relative permeability
is a function of coil design and magnetic field configuration as well as core material-
and magnetizing force.
For example, consider ?f. This factor describes the increase in flux ?
linkages in the antenna coil due to external field deformation caused by the presence
of the ferrite core over the flux linkages in the antenna coil when the ferrite is
absent and the external field is uniform.
FIGURE 3-3
ILLUSTRATION OF
On the other hand, ?coil describes the increase in flux linkages in the
antenna coil due to the deformation of the non-uniform magnetic field created by
current flowing in the antenna coil.
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FIGURE 3-4
ILLUSTRATION OF Eimil
Both of these factors describe increases of flux linkages in the same coil
due to the same core, but they differ because two different magnetic field configur-
ations are involved. That is to say, the resulting deformed fields differ from
each other because the undeformed fields differed.
Figure 3-5 shows .if and ?coil as obtained from four equal inductance an-
tennas having identical cores but different winding lengths. Of particular interest
in this figure is the induced voltage curve which shows that the full length coil
antenna has an induced voltage which is 60% greater than that induced in a concen-
trated coil antenna.
The increase in induced voltage with coil length is attributable to the
? fact that more turns are required on the longer coils than the shorter coils in
order to obtain the same value of self-inductance. In practice, maximum antenna
self-inductance is limited by permissible (or unavoidable) shunt capacity. The
highest induced voltage is, therefore, obtained when the antenna coil is wound so
that it maximizes the ratio of turns-to-inductance.
It is also noted that, if coil Q can be assumed constant as a function of
a3 ratio, then equal inductance antennas generate equal thermal noise voltages.
Consequently, induced voltage-to-thermal-noise ratio has the same functional de-
pendence on a/f as does the induced voltage alone. It is concluded, therefore, that
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r it 1~ + at ?~n a kr~4~licc~ vo'.~
_ .. i 4L~-rail
ndd ? a n four 'y~Ua L, u
f ;~k X33. o--
U~~ 1/ - pi 1:0 cm.
` ': 9,7? C:n1,
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f'?1 .c.ng .h windings are more advantageous from the standpoint of induced volts-to-
thermal-noise ratio, of/en, provided coil Q can be kept constant while increasing
:'t/f( ratio.
Since full length coils produce larger induced voltages, and since it is
reasonable to expect that in many cases this also corresponds to larger induced
ir;:,ltage-to--thermal-noise voltage ratios, the ferrite antennas considered hereafter
will have full length coils (unless otherwise specified). In passing, it is worth-
while to note that a distributed winding (full length coil) is, in general, simpler
,. wind with low distributed capacity than a concentrated coil; this, in turn,
simplifies the problem of obtaining high impedance levels. As noted in Equation (3-7)
? fcr full length coils
? N Prod
C
?coil " ?rod
Thee approximations are borne out fairly well by the empirical curves shown in
Figure 31-5.
IV. COMPARISON OF ATMOSPHERIC NOISE AND THERMAL NOISE IN LOOP ANTENNAS AT VERY LOW
f-TtCQ
Intrcduetion
The degree of importance attached to thermal noise generation in the an-
is 'cen'..a. circuit depends upon the relative level of thermal noise volts compared to the
Molise in the system. At 25 kcs (and VLF in general) total receiver noise is
TargeLy thermal-noise plus external noise sources such as atmospherics and electro-
static. disturbances. The last noise source is predominately an electric field
p e :.om,~na arising d:ua to sparking in nearby electrical equipment, etc. (see external
noise source discussion). The ideal loop antenna responds only to a magnetic field.
Tyr-j:_i, if the loop antennas considered are idealized to the extent that E-field pick-
s umed to be zero, then internal thermal noise and external atmospheric noise
as,
roman as the major sources of noise in a loop antenna receiver system.
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14
A comparison of the relative magnitudes of noise voltages introduced by
these two noise sources into a loop antenna will help determine whether it is
necessary to consider thermal noise generation in the design, or evaluation, of a
receiving loop antenna. Such a comparison is provided in the following work by
estimating the ratio of voltage induced in a loop due to atmospheric-noise to thermal.-
noise generated in the loop due to the resistive component of the antenna impedance;
i.e., eAN/e TN
Assumptions Made in the Calculation of eAN/ e TN
Zero E-field pickup in loop antenna.
2. First amplifier noise is negligible compared to thermal noise generated
in antenna circuit.
3. Atmospheric noise field strength. given by median day and night values
for the latitudes of the U.S.A. (1)
4. Antenna circuit must pass a band of frequencies 2000 cps wide centered at
25 kc/s with a maximum of 3 db variation of the band.
5.
6.
Loop antennas considered are-
a) air `;:ore circular loop with closely spaced turns.
b) ferrite core loops with full length coils.
Antenna circuit : a) resonated, b) not resonated.
7. In the case of the non-resonant antenna circuit, it is assumed that
a 2000 cps passband is established by tuned circuits located in the
receiver after the first amplifier stage.
Resonant Air Core Loo
C
eTN
voltage induced in loop
due to external fields
(rms)
thermal noise voltage due
to resistance R
FIGURE 4-1
EQUIVALENT CIRCUIT OF RESONANT AIR CORE LOOP
?
?
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The induced voltage from Equation (3-1) is
ea = ?o w Aa na ff
(4-1)
where subscript "a" refers to air core loop and H = magnetic field intensity (rms).
The electric and magnetic field intensities are related by
Equation (4-1) can be rewritten as
Co
2n Aa a E
ea =
Is
where = wavelength =
(4-2)
(4-3)
f ?o Eo
~1 = 12,000 meters for f = 25 kc
The induced voltage at f = 25 ke is given by
_ na Aa
= (410) 10-6 D 2 $
ea = C 1910 $ a a
?
(4-4)
where Da = loop diameter.
For a passband of 2000 cps at 25 ke center frequency, the loaded Q of the
antenna circuit must be
(4-5)
where R is composed of the internal resistance of the antenna plus additional re-
sistance, if necessary, such that equation (4-5) is satisfied. In the absence of
a signal, the induced voltage is entirely due to atmospheric noise pickup and is
W La
= = 12.5
Ra
given by Equation (4-4) when an equivalent (rms) electric rield intensity, SAN, due
to atmospheric noise is substituted for $.
The effective thermal-noise voltage associated with R is given by
eTN = 4K T d f R (1tkT Q f w) L
(4-6)
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4 (1 37) 10-23
deg.(Absol.)
T = absolute temperature of R y 293? Abs.
z:S f = passband -- 2000 cps
co = 2nf0 = 2n(25000) rad/sec.
Equation (4-6) reduces to
e TN - 2.24 L/Z 0.635 microvolts
The inductance of an air core loop composed of n closely spaced turns is given by
Equations (3-2) and (3-2a) wh.i.ch are repeated here-
1 ti, k ?o n2 D/2
where k -? f'n (8D/d) - 2
A reasonable range of values for D/d is
6 G D/d :1000
The corresponding range cl values of K is
2 < K < 7
For K - 2, inductance9 call. it Ll,, becomes
01",U:)
0
:..1.2) to-3 n\ (4-9)
For K 7, inductance, call it L2, becomes
T V-,?.5 ? a n.~ U (2.1) la-'3 n CD () .:'i0)
Hence, letting the subscripts 1 and 2 denote K - 2 and 7, respectively, the noise
voltages become
01 TN. (0.7l) 10"3 n V D microvolts
.1
eTN, (:1.30) 10"'s n FD microvolts
Comparing atmospheric noise pickup with thermal noise generation, we obtain
eAN
{:? . r 8 D3 / EAN
?
(Lt 7.a)
()i-.1.1b )
(It-12,1)
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-17-
eAN
eTN2
= 0.30 D3P EAN
For daytime atmospheric noise (for a f = 2000, fo = 25 kc):
(4-12b)
LFAN N 50 microvolts(rms)/meter (Median value USA) (1) (t-13a)
For nighttime atmospheric noise
'KAN 100 microvolts(rms)/meter(1)
From Equations (1+-12) and (4-13), we obtain
Daytime
?
29 D3/2
eTN,
eAN
eTN2
Non-resonant, Air Core Loop
?
15D3/2
FIGURE 4-2
EQUIVALENT CIRCUIT OF NON-MONANT AIR CORE LOOP
Nighttime
58 D3/2
30 D3/2
(4-13b)
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-- 18 -
Atmospheric--noise volts to thermal-noise volts ratio for the non-resonant
air core loop is the same as for the resonant air core loop with the exception that
the circuit Q is no longer restricted to the low value of 12.5 in order to pass the
required band of frequencies. The antenna coil Q is made as large as physically
realizable (call it Qa). The results of the resonant antenna are then directly ap-
plicable when multiplied by the factor. Qa/2 (see Section VI). Hence,
Daytime Nighttime
c)AN
eTN1
eAN
eTN2
5.8 \i Q,' D3/2
3.0 V Qa' D3/2
Twice Daytime Values
Twice Daytime Values
Resonant Ferrite Core Lyoo
The induced voltage for the ferrite core antenna is given by Equation (3"4)
f
where df = ferrite rod core diameter.
The thermal noise is given by Equation (4-7) as
eTN 0.635 V L f microvolts
Cuing Equation (3-5) for Lf and the full coil length approximations
?'ccil v prod' we obtain. the ratio e.,
to be
eTN
~A.tv
Tip
oaf ?c, uw Af rf H
n.46, }'rod (df/rf) ff3/2 E
AN
where EAN is given in (rms) microvolts/meter,
nd 2
rf f E
Itf ti
(4T7 Li a )
(i i5 )
Prod and
f2---'
(4-16)
?
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- 19 -
For purposes of comparison with air core loops, let
ff = f = FD
eAN = 0.46 F ILrod (Fd/f) D3/2 _AN
eTN
where F - constant
and D = air core loop diameter
Substituting into Equation (4-16), we obtain
where EAN (rms) microvolts/meter
Daytime
0
eTN
23 N, .od ( f 3/2
f
or in terms of equivalent a
eAN
eTN
Nighttime
Twice daytime values
~r core loops
23 F ?rod(Fa) D3/2
f
Twice daytime values
(4-17)
Non-resonant Ferrite Core Loop
Multiply a /eTN values of resonant case by f Qf/2-a where Qf = maximum
? obtainable value of Q for a ferrite core loop.
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SUMMARY OF ATMOSPHERIC NOISE VOLTS-TO-THERMAL-NOISE
VOLTS RATIOS LOOP ANTENNAS
I. AIR CORE
Resonant (Q - = 12.5)
K 2
K-7
Non-Resonant (Q = Max. air core Q)
K = 2
II-a FERRITE CORE
Resonant (Q = 12.5)
NonResonant (Q = Max. ferrite core
.Q II- Qmax )
e RATIO
eTN
Daytime (Median Value of Atmos. Noise
E-Field - 50 rms ? volts/meter
29 D3/2
15 D3 /2
5.8 D3/2
3.0 / D3/2
23, ?rod (d/f) x,3/2
(1t.6,/ Q') ?rod (d/f) X3/2
NOTE: As a means of comparing Air Core and Ferrite Core loops, write
in terms of D, as follows:
Let X = FD, where F = constant
II-u FERRITE CORE
Resonant (Q 12.5)
Non Resonant (Q = Q,)
,ku
V ' {. o (Fd/f) D3/2
23f'
(t.6[) V L (Fd/f) D3/2
0
?
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?
0
1 2
5
7
8
9
2
4
S
6
7
-
T.
-
1
8
7
4
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6 7
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100
Antenna Dimension (D or f in cm.)
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 DI
mP.t e
H
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r I i * j. r _
:r 1
19
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8 9 11 1 3 4 5 6- 7\ 8 9 110 11
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9 1
0
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S tAD
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23
Referring to Equations (3-1) through (3-7), we obtain
Induced voltages:
Air Core Loop ea = po co Aa na H
Ferrite Core Loop of
Prod Po co A f n f H
Air Core Loop La ^N' K Po na2 Da/2: 2 < K < 7
S
V. COMPARISON OF INDUCED VOLTAGES AND SIGNAL-TO-THERMAL-NOISE RATIOS IN FERRITE
AND AIR CORE ANTENNAS
V
110
x I 2La
Prod Po Af
Ferrite Core Loop Lf =
of
If
nf2
Lf If
Prod Po Af
The ratio of induced voltage for the two loops is given by
e f _ Prod of (d/D)2
ea YT' na
or equivalently in terms of self-inductances
(5-1)
(5-2)
(5-3)
(5-4)
(5-5)
(5-6)
(5-7a)
? of _ K Fi~a ea n Prod D3
t2 (5-7b)
Once again for purposes of comparing air core and ferrite core loops, let
Then for the case of equal inductance antennas
of
ea
V - KF (F )
L- n Prod
Lf n La
(5-8)
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whereas equal turns antennas yield
uL
of = na
L
NOTE: 1/2
n ) ~]
Ra Qf La
(5.9)
Now the ratio of thermal noise generated in the two loops is given by the ratio of
their resistances, i.e.,
e
TNa
Rf - Qa Lf
Signal-to-thermal ratios are given by
of
`
(S/
1N) f
(S/TN)a
0n
TNf
ea
eTNa
ea
TNf
Thus.
(S/TN)f
(S/TN ) a
ef eTNa
ea E'Tid
f
Substituting (5?7b) and. (5-10) into (5-13), we obtain
(S/TN) f
(S/rN)a
or upon letting f(= FD
(S/fir?
(S/TN )a.
K , d
n
_ N'rod 2
1`
d Qf
D3 /2 Qa
KF ?rod ' Fd I\I Qf
TI Q - TI a
(S--:L:1)
(5e..i2)
(5~114b)
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-25-
The factor within the braces in Equation (5-IJb) is identically U L, the ratio of
induced voltage for equal inductance
(S/TN)f -
(S/TN)a
antennas, hence,
FQa for Lf La
L
and Lf # La
Equation (5-15) shows that, when the circuit Q is specified (e.g., for
a V
purposes of necessary bandwidth in a resonant antenna circuit, Qf = Qa = Q and the
ratio of signal-to-thermal-noise ratios is equivalent to the ratio of induced volt-
0
ages when antenna inductances are equal, i.e.,
(s/rN)f I ef
(S/TN)a ea
Qf = Qa
Thus Equation (5-8) which specifies
UL-1
(5-15)
(5-16)
Qf Qa
Lf = La
the ratio of induced voltages for equal
inductance antennas, provides a useful means of comparing air core and ferrite core
loops. V L is plotted in the following figures. In these plots, an optimistic
8D
estimate of air core induced voltage is made by assuming K = fn ( D a) - 2 = 2
w
which corresponds to Da/Dw = 7.
is
FIGURE 5-1
AIR CORE LOOP GEOMETRY
However, for values of K different from 2, as will probably be the case for large
loops, V L can readily be corrected to correspond to an arbitrary value
K = 2
of K by multiplying by K/2 since v L varies as the square root of K.
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
t
I
la~
_
-
r -
i`
.tip
100
k/d, length-to-diameter ratio of cylindrical core
i
0
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
- --
:M- T _TEL
-- I
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
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- 26 -
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
is
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
-30-
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-31-
H- T
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
_
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j
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td-
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 0.6
0.6
0.5
0.4
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0
?
11I-T"
i rt
~fl4
1 -
-'j
~ rr-II
`~ i-t
11
2 LT-t
1000
Toroidal permeability
10,000
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
-3l4-
An important observation can be made from the equations of this section.
Reference to Equations (5-1) and (5-2) shows that the induced signal voltages for
both ferrite and air core loops are proportional to number of turns. The thermal
noise developed in each is proportional to the square root of its resistance. The
resistance in turn is proportional to the inductance (R = coL/ Z ) for a tuned an-
tenna. Equations (5-3) and (5-5) show that the inductances are proportional to
number of turns squared. Thus, it follows that for both ferrite and air core tuned
antennas, the signal-to-thermal-noise ratio is independent of number of turns and,
hence, independent of impedance level. Therefore, signal sensitivity can be maxi-
mized by maximizing the number of turns without sacrificing signal-to-thermal-noise
ratio.
'VI, COMPARISON OF TUNED AND UNTUNED ANTENNAS ON A SENSITIVITY BASIS AND ON A
SIGNAL-TO-THERMAL-NOISE BASIS FOR (a) Broadband Antenna; (b) Narrow-Band
Antenna
In a loop antenna which has a maximum dimension very much smaller than the
wavelength being received, an equivalent circuit representation is simply an RL
impedance in series with an induced emf. The resistive part of the internal im-
pcdance, of course, is a source of thermal noise. Consider now two basic antenna
circuits by referring to the circuits (a) and (b) in Figure 6-1.
e
L (~
[2< Z (6) T4&,/, ~u bz -
Q ? r
FIGURE 6-1
E ~UTVALENT CIRCUITS FOR TUNED AND ?DNTUNED LOOP ANTENNA CIRCUITS
is
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- 35 -
For the untuned antenna of Figure 6-la, the signal voltage at the grid is given by
ega = ea
and the signal-to-noise ratio at the grid is
(S/N)a = ea
4 KT d f (r+Rn )
0
For the tuned antenna of Figure 6-lb
egb = 17 eb
17 eb
(S/N)b =
Thus. by way of comparison, we have
e
ga
It HT A f(Q R + Rn)
-1- (ea)
egb Q eb
0
(SIN)b eb (r + Rn)
(6-1)
(6-2)
(6-3)
(6-4)
(6-5)
(6-6)
In practice, the maximum value of inductance for either the tuned or un-
tuned antenna is determined by minimum capacity restrictions. For example, the mini-
mum capacity of the tuned antenna must be appreciably greater than the stray capacity
introduced when a body is brought near the antenna. Clearly, if such a minimum capacity
is not provided, the proximity of external objects will have undesired detuning effects
on the antenna (see Figure 6-2b). Similarly, for the case of the urrtuned antenna
(see Figure 6-2a), the maximum inductance is limited to a value such that the capacity
which causes it to resonate is appreciably greater than the total capacity appearing
across the inductance (including stray capacity of nearby objects). Figure 6-2a
shows that the untuned antenna operates as a high Q circuit with a minimum capacitance
Cl across its terminals. Although not desired, resonance will occur if the shunting
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-IF (S/N)a ea V R + Rn
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- )0 -
QwZ = (~p z r'
L
3
~o = ~z 7T)(25
wL = Q r
C, Cz
(a) L~ h ~uac a~ 4r, dear L
Ia1
C
Z-= L- _ I
wZC3
Gvo =(2z/zs~%)
C,
~ I
C3
.16 C -4~
(b) Un ~r~ cd~ 4n ~2r~iaa.
FIGURE 6-2
IMPEDANCE OF TUNED AND UNTTJNED
ANTENNAS
is
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- 37 -
capacity is permitted to increase to the value C2. Thus, the maximum inductance per-
mitted in the untuned antenna is such that a capacitance C2 or greater is required
for resonance. To prevent de-tuning effects
C2>> C1+Cx (6-7)
?
where Cx = external stray capacity.
On the other hand, Figure 6-2b shows that the simple resonant (tuned) an-
tenna operates as a low Q circuit in order to pass the desired band of frequencies
with the resonance capacity C3 across its terminals. If L1C/2 is the change in C3
required to reduce the impedance magnitude to 0.707 of its resonant value, then
2 C3
OC =
l+ Z
De-tuning effects are prevented by making
AS C/2 >> Cx
c3 >> (1 + 7) Cx
For 7 = 12.5 and typical values of C1 ti 60 ??f and Cx - 10 ??f, the
minimum values of C2 and C3 are comparable although C2 can usually be made somewhat
smaller than C3.
? As a result of the preceding capacitance considerations, it may be said
that slightly higher values of inductance may be used in the untuned antenna. Assum-
ing, however, that
C2 C3 v CT (6-11)
= L - 1/aA CT
(6-8)
(6-9)
(6-10)
(6-12)
will simplify the following work without introducing appreciable error. Hence, com-
paring similar antennas (equal inductances), the induced voltages are equal, i.e.,
ea = eb = e
(6-13)
Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/10: CIA-RDP78-03424A000500010007-0
- 38 -
The passband of the tuned antenna must be at least as great as the passband of the
receiver. Therefore, let
@ fo
where f 0 = center frequency
o f = passband of receiver
b. Signal-to-noise ratios (Eq. 6-6)
= R (6-1)4b)
For the untuned antenna.' there is no restriction on the Q of the coil; hence, it will
be made as large as possible. Thus, for a broadband system