Note: Descriptions are shown in the official language in which they were submitted.
ANTENNA
BACKGROUND OF THE INVENTION
_ . .
My invention relates to antemlas used for either
transmitting or receiving or both.
The main purpose of an antenna is to transmit
electromagnetic energy into (or receive electromagnetic ener
gy from) the surrounding space effectively. A transmitting
an~enna launches electromagnetic waves into space and a
receiving antenna captures radiation, con~erting the electro-
magnetic field energy into an appropriate form (e.g. - a
voltage to be fed to the input of a receiver).
A transmitting antenna con~erts the radio fre-
quency (RF) energy fed by a generator connected to its input
into electromagnetic radiation. This radiation carries the
generator's energy away into space. The generator is giving
up energy to a load impedance. As far as the generator is
concerned, this load impedance may be replaced by a lumped
element which merely dissipates the energy which the pre-
vious antenna radiated away.
The equivalent resistor, which-would dissipate the
same power as the antenna radiated away, is called the
"antenna radiation resistance". In the real world, an
antenna structure has losses (power dissipating merhanisms)
due to the structure's finite conductivity, imperfect
2S insula~ion, moisture and physical environment. To the
generator, these loss mechanisms absorb some of the power
fed into the antenna structure, so that all of the input
1 ~8 6
--2--
power is not radiated away. The ratio o~ the radiated
power to antenna structure input power is called the antenna
efficiency. If the same current flows in the antenna radia-
tion resistance, RA, and in the antenna loss resistance ~,
then the efficiency in percent (E%) can be described by the
simple equation
E = RA x 100%
RA + ~
Clearly, it is desirable to make the ratio RA/RL as great as
possible ~i.e., the antenna would be 100% efficient if RL
could be reduced to zero).
The particular application for which an antenna is
to be used, along with certain physical laws and practical
considerations primarily determines the type of antenna
structure employed. Frequen~y f, wavelength ~, and
velocity of propagation for electromagnetic waves vp are
related by the simple formula A = vp/f. At low and medium
frequencies it may be economically unfeasible to construct
an antenna radiating system whose physical dimensions are
an appreciable portion of a free space wavelength. Typical
2~ vertical antennas must be on the ord~r of one-eighth to one-
quarter of a free space wavelength high in order to have
RA large enough to be considered as efficient antennas --
unless extensive measures are taken to make RL negligible.
At very low frequencies (e.g., f = 15 KHz) even a structure
~5 1,000 eet high must be accompanied by a substantial
engineering effort to make RL small, in order to be con-
sidered as a "practical" transmitting antenna. One might
ask, "Why not construct long horizontal antennas at these
low frequencies, in order to raise the antenna radiation
resistance?" Vertical antennas produce vertically polar-
ized waves (i.e., waves for which an electric field
intensity is perpendicular to the ground), whereas a
horizontal wire produces a wave for which the electric
--3--
field intensity is parallel to the ground (horizontal
polarization). A physical result following from the
properties of wave propagation is that horizontally polarized
waves propagating along the surface of the earth attenuate
more rapidly than vertically polarized waves. Thus, for
situations where ground wave propagation is to be employed,
or for low frequency radiation, a vertically polarized
antenna struc'ture is oten the most desirable or only accept-
able solution (in spite of the physical and economical
disadvantages). The single vertical radiator has another
feature which is often desirable. It is omnidirectional in
the horizontal plane - that is, equal amounts of vertically
polarized radiation are sent out in all direetlons on the
horiæontal plane.
Sometimes a particular geographical region is to
be served by a transmitting station. In this case, an
array of towers or antenna elements spaced an appreciable
portion of a wavelength may be used to direct the radiation.
The resultant physical distribution of the electric field
intensity in space is called the antenna pattern. As a
consequence of an antenna system concentr~ting its pattern
in a given direction, the received field str~ngth is greater
in that direction than when the antenna radiates into all
directions. One may define a figure of merit for antennas
which characterizes this property; antenna gain is defined
as the ratio of the maximum field intensity produced by a
given antenna to the maximum field intensity produced by a
reference anten~a with the same power input.
An additional antenna property is antenna reso-
nance. When a given antenna structure is excited by a
generator at a given frequency, the voltage and current at
the antenna terminals are complex quantities; that is, they
have real and imaginary mathematical components. The ratio
of the complex voltage to the complex current at the ter-
minals is called the antenna input impedance. As thegenerator frequency is varied (or alternatively, if the
4~
--4--
generator frequency is fixed and the antenna dimensions are
varied) there will be a particular frequency (or antenna
dimension) for which the voltage and current are in phase.
At this frequency the impedance will be purely resistive
and the antenna is said to be resonant. A resonant antenna
structure is one which will support a standing wave current
distribution which has an integral number of nodes.
An'antenna will radiate at any frequency for which
it will accept power. However, the advantage of having a
resonant antenna structure is that it is easi~r to match to
the generator for efficient power transfer. This means that
the system losses can be decreased and, hence, the overall
system efficiency is increased at resonance. However, a
vertical tower, for example, is not self-resonant unless
it is electrically onP quarter wavelength tall. At a
frequency of 550 KHz (the low end of the AM broadcast band)
a self-resonant tower must be about 447 feet tall. At
15 KHz it would have to be 16,405 feet tall'
The major problem associated with the types of
antennas discuss~d so far is that the physical size (and
cost) required for a given antenna efficiency becomes
prohibitive as frequency is decreased (wavelength is
increased). Furthermore, even in the ultra high frequency
range (ultra short wavelengths) it is difficu~t to construct
an electrically small antenna which is an efficient radia-
tor. It would often be desirable, at any frequency in the
electromagnetic spectrum, to be able to construct a small
antenna whose physical dimensions are much less than a
wavelength, whose radiation efficiency is high, and one
which is capable of producing a specified polarization or
polarization mixture. For example, it would be desirable
to produce vertical polarization at low frequencies, or
circular polarization for VHF FM broadcasting, etc.
In addition to the antennas discussed so far,
there are other antenna configurations and circuit elements
which should not be confused with my invention. My
~8~(~4~
-5-
im7ention is not a toroidal inductor. A perfect toroidal
inductor has zero radiation e:Ef iciency, and so is not an
antenna at all. My invention is not what is c~m~only termed
"the small loop an~enna", ~hich produces the well-known
azimuthally dirPcted (horizontal) elec~ric field with a
sin ~ pattern, where ~ is the angle of from the spherical
coordinate polar axis, where the loop lies in the azimuthal
plane. My invention is not wha~ is commonly called a
"normal rnode helix"; which is a solenoidally wound structure,
having a distinct beginning and ending to the heli~. My
invention is not what is commonly called the "multiturn
loop antenna", which has multiple windings which either
lie in the azimuthal plane or are coiled along the loop ' s
axis of symmetry.
It is helpful to understanding my antenna to first
present some approximate analytical considerations for
certain prior art antennas.
~h~
A solenoidally.wound coil or helix is shown in
Figure l(a). By assuming the antenna eurrent to be uniform
in magnitude and constant in phase over the entire length
of the heli~ Krau~ has shown that a normal mode helix
~one whose dimensions are much less than a free space
wavelength and that radiates normal to the solenoid axis)
may be dec~mposed into a single s~all loop as in Figure l(b)
plus a single short dipole as in Figure l(c). See ~ohn D.
Kraus, Antennas (McGraw Hill Book Co~ 1950), espe~ially
the portions beginning at pages 157, 160, and 179. Kraus's
analysis assumes that the current is uniform over the entire
helix and is of the form IOeJ t The fields of a loo~ and
short dipole for such excitation are well known and are
given in polar coordinates(r, ~, ~),using s~andard vector
terminology, by
~ 1 ~ 6
--6--
Loop:
(1) E = E~ = ~ sin~e
Short dipole:
(2) E -' E3~ = sin~ei~t ~
where b = the radius of each turn of the helix
s = the turn-to-turn spacing of the helix
By the principle of linear superposition, the ields for
the normal mode helix immediately follow as:
(3) E = E9~ + E~
Equation (1~ may be directly obtained by assuming a uniform
time varying flow of electric charges (an electric current)
along the circumference of the loop.
There is an alternatîve way to derive Equation (1)
which proceeds from the introduction of a fictitious con-
1~ ceptual aid. This very useful tool is a great assistanceto performing field computations for helices and solenoids.
Kraus has shown that a loop of electric current, i.e., --
electric charges flowing around the circ~ference of a loop,
produces the same radiation fields as those o a flow of
fictitious magnetic charges moving up and down the axis of
the loop. The fields external to a helically wound sole-
noid can be found by assuming a flow o electric charges
around the helix, or by assuming a flow of fictitious
magnetic charges moving along the axis of th~ solenoid.
The latter computation i5 much simpler to perorm
analytically than the former.
One quickly notices from Equations (1) and (2)
that the ~ and ~ components are in phase quadrature ~-
~(note: j=eJ /~, that is, they are 90 out of phase.
36~
--7--
This causes the radiation zone E field at a point to rotate
in time and in the resultant polarization is said to be
elliptically polarized with an axîal ratio given by:
(4) AR - IEa I
¦E,, I
S Figure 2 show,s the different types of polarization obtainable
from a normal mode helix. Figure 2(a) is the general case
of elliptical polarization. Figure 2(b) shows the case of
vertical polarization, such as produced when b=0, that is,
when the helix is reduced to a dipole. Figure 2(c) shows
horizontal polarization, such as produced when s=0, that is,
when the helix is reduced to a loop. Figure 2(d) shows the
circular polarization, such as when Ea = E~ .
Propagation Effects on a Helix
The velocity of propagation of electromagnetic
disturbances in free space is the speed of light. Electro-
magnetic waves propagate along a wire with a speed some-
what less than, but very close to the speed of light in
free space. However, an electromagnetic wave propagating
along a solenoid or helix~ such as Figure 3, will travel
with a velocity of propagation (vp) considerably less
than the speed of light (c). One can write this as
~S) vp = Vfc
where Vf is called the velocity factor. In free space
Vf = 1. On a copper wire ~ ~ .999. On a helical delay
lin Vf may be on the order of 1/10 or 1/2. (In~uition
indicates that the wave traveling along the spiral hel-i~
has to travel further than a wave that could ~ravel in
free space parallel to the solenoidls axis and therefore
V~ should be less than unity - but this is only part of
36
--8--
the story. ) What this leads to is that a helix may have a
physical length less than a free space wavelength (~0,
where ~0 = c/f), while it is still elec~rically one wave-
length. Calling the electrical wavelength on the helix
5 the guide wavelength ~g one sees that:
v
(6) ~g ~ P - Vf~o
This means that one can make a helix beha~e electrically
quivalent to a free space wavelength long while it is
physically Vf times smaller. Kandoian and Sichak have
10 defermined an expression for Vf on a helix as in Figure 3
in th e f orm:
(7) V = ~
f ~lt.20(2bQ) (2b/~o)
where b = radius of each turn of the helix
~0 = c/f (measured in th~ same units as the
radius b)
Q = length of the helix
N - numbex of turns
See Reference Data for Radio _~ineers (Ho~ard ~1. Sams &
Co., Inc., 1972) pages 25-11 to 25-13. Equation (7) assumes
that 4nb2/~O<1/5, where n = N/Q.
S.~ T~ L~ C~
An importan~ feature of th~ an~ennas in my
i~vention is that even though they can have a much smaller
physical size than prior antennas, they can transmit or
receive electromagnetic waves with a very high antenna
efficiency. Thus, the antennas of the invention possess
greater radiation resistance and radiation efficiency than
loop antennas of similar size. ~Additionally, antennas
according to the invention radiate controllable mixtures
36~
of vertically, horizontally and elliptically polarized
electromagnetic waves and possess radiation power patterns
different from those produced by small 1QP antennas.
Antennas according to preferred ~mbodiments of
the inventioll are configured to behave as slow wave devices.
The antennas are configured to establish a closed, standing
wave path. The conductor configuration and the path esta-
blished thereby inhibit the velocity of propogation of
electromagnetic waves, and the path supports the standing
wave at a pre-selected frequency. The preferred embodiments
of the invention described herein include various arrange-
ments of conductors arranged in loop configurations; but
the conductor or conductors are configured so that they are
no~ arranged in simple circles, and rather are wound about
real or imaginary support forms to increase the length of
the physical path of the conductor while maintaining a
relatively compact antenna. The path in each case is con-
figured to inhibit the velocity of the electromagnetic
wave and to support a standing wave at a pre-selected
frequency.
An antenna according to one such embodiment
comprises an electrical conductor configured with multiple,
progressive windings in a closed or substantially closed
geometrical shapP. This shape can be established by a
physical support form or it can be a geome~rical location
as where the antenna has self-supporting conductors. Such
a shape can be topologically termed a "multiply connected
geo~etry"; or example, a conductor can be in the form of
more than one winding in a geometrically closed configura-
tion or multiply connected geometry. The cross-section
of this ~onfiguration can be circular (as where the
configuration is a toroidal helix), or it can have the
general form of an ellipse, a polygon, or other shapes not
generally circular in cross-section; the configuration can
be symmetrical or assymmetrical, polygonal, and it can be
essentially two dimensional or configured in three dimensions.
36~
-10-
BRIEF DESCRIPTION OF THE DRAWINGS
Figs. l(a~-l(c) are vector decompositions of
several basic types of antennas (prior art).
Figs. 2(a)-2(d) are ~ector representations of
polarizations produced by a helical antenna.
Fig. 3 is a schematic of a spirally wound antenna
(prior ar~).'
Fig. 4 is a schematic of a helically wound
toroidal antenna according to the invention.
Figs. 5(a)-5(c) are isometric, top and side views
of an antenna of the type in Fig. 4.
Fig. 6 is an isometric representation of a con-
tinuously wound, toroidal helical antenna according to the
invention.
Fig. 7 is a vector representation showing the
geometry for a circular loop antenna of nonuniform currentO
Figs. 3 and 9 show azimuthal plan radiation
field patterns for a resonant toroidal loop antenna
according to the invention with current flow in opposite
directions, and Fig. 10 shows ~he effect of superimposing
the patterns of Figs. 8 and 9.
Fig. 11 shows an azimuthal plane radiation
pattern or an antenna of the type which produced the field
illustrated in Fig. 8 but which has in effect been flipped
over~ and Fig. 12 shows the effect of superimposing the
patterns of Figs. 8 and 11.
Fig. 13 is a bottom view of a multiply-wound
heLical antenna.
Fig. 14 illustrates in schematic form the RMS
field pattern of an omnidirectional vertically polarized
antenna element according to the invention.
In Fig. 15, a quadri~iliarly wound toroidal
helical antenna according to the i~vention is shown in
perspective.
Fig. 16 shows the RMS iled pattern produced by
86~
-11-
a toroidal loop antenna of the type producing the pattern of
Fig . 8, but with its f eed point rotated 90 from the antenna
to which Fig. 8 relates.
Fig. L7 is an isometric view of ano ther embodiment
S of the in~ention including parasitie array construction.
Fig. 18 is a perspective view of a parasitic array
anterma according to the invention, composed of toroidal
loops .
Fig. L9 is a graphi al representati.on of the
10 resistance and reactance characteristics vs. frequency for
an antenna of the type shown in Fig. 5.
Figs. 20 and 21 are VSWR curves for an ~ toroidal
loop antenna according to the invention for two separate
resonance values.
Fig. 22 is a graph of cur~es o~ input ~mpe~ance
V5, frequency for two variations of a toroidal loop anterma
of the typ~ shown in Fig. 13.
Fig. 23 is another emhodiment o the invention
comprising an HF rectangular toroidal loop antenna.
Fig. 24 is a graph of resistance and reactance vs.
frequency curve~ for tne antenna of Fig. 23.
Figs. 25(a) and (b3 show prior art forms of
contrawound helix CiY'CUitS.
Figs . 26 (a) ar.d (b) illustrate the current paths
on the circuits of Figs . 25 (a) and (b) .
Fig. 27 shows an antenna according to my invention
co~prising a contrawound helical torus for producing
vertical polarization.
Fig. 23 shows an antenna according to my inven-
tion including a means for adjusting the resonant frequency
of the antenna.
Figs. 29-33 are isometric views of other antenna
constructions according to the invention.
Fig. 34 depicts an antenna configuration not
within the scope of the invention.
-12-
DESCRIPTION OF THE PREFERRED EMBODIMENTS
_
Fîgure 4 shows an antenna 41 which is an embodî-
ment of my invention. An electrical conductor 42 which can
be, for example, an elongated conductor such as a length o~
conducting tape, wire or tubing is helically wound about a
non-conducting toroidally shaped support 43~ The turn-to-
turn spacing "s" between each winding is uniform. The
dimension "b" is the radius of each winding and 2b may be
termed the "minor diameter" of the antenna. The dimension
I'a'' is the radius of the circle which comprises the center-
line axis 44 of the toroid. Another useful parameter is
"N" which is the number of turns. If the toroidal helix of
Figure 4 is considered to be the helix o~ Figure 3 bent
around into a toroid, one notes that ~ = 2~a and N = 2sa
Equation ~7) becomes,
(7a) [1+20(2b)2-5 (2b/~o)l/2~1/2
Figures 5(a) 9 5(b), 5(c) show an antenna 51 similar
to antenna 41, but adapted to balanced feed. The helically
wound conductor 52 is not continuous, but rather has two ends
52a, 52b which are used as the feed point taps for the
antenna. Preferably, these ends 52a, 52b are as close to
each other as possible without electrically interfering
with each other. These ends 52a, 52b should be near each
oth~r, that is, the ends should be neQr enough that the
electromagnetic waves on the antenna follow a closed path.
Figure 6 shows another toroidal helix antenna 61,
which is adapted for unbalanced feed from an unbalanced
transmission line 62. The conductor 63 is contin~ous. In
addition, there is a shorter conductor 64 helically wound
around the toroidal support between some of the turns of the
continuous conductor 63. ~ sliding tap 65 connects the two
conductors 63, 64. One side of the transmission line is
connected to one end of the shorter conductor 64 and the
~336~4~
-13-
other side is attached to the continuous conductor 63. The
sliding tap 65 is moved to a point for proper impedance
matching. This poin~ is found empirically by actually
testing the antenna at the chosen frequency and moving the
sliding tap 65 to the optimum position.
Before describing more complicated toroidal loop
embodiments, it is useful to present an approximate mathe-
matical analysis of the toroidal loop antenna embodiments
of my invention.
As has already been discussed, helical structures
possess the property that electro~agnetic waves propagating
on them travel with velocities much less than waves pro-
pagating in free space or on wires. By properly choosing
the helix diameter and pitch, one can control the velocity
of propagation in a manner well known in the sci~nce o
transmission line engineering. Since the veloci~y o
propagation for these traveling waves on helical structures
is much less than that Pf waves traveling in free space,
the wavelength ~G of a wave on the helix will be much less
than the wavelength ~0 for a wave traveling in free space
at the same frequency. By bending the helix into the form
of a torus, one is able to excite a standing wave ~or which
the circumference C is one wavelength. The physical di-
mension of the circumference can be calculated from the
equations for velocity of propagation on slow wave structures.
It is useful to note that electric charges
traveling along the helix produce the same fields that
"magnetic charges" (if they existed) would produce if they
were traveling along the axis of the helix. Consequently,
our toroidal helix has the same fields that a loop oscil-
- lating magnetic charges would produce. This is very
helpful in the mathematical analysis of our toroidal loop
antenna and is based upon the principle of duality.
The slow wave feature of helices which is employed
in the t~--oidaL loop antennas of my invention permits the
construction of a resonant structure WllOS e circumference
is rnuch less than a free space wavelength, but whose
~ ~ ~6
-14
electrical circumference is nevertheless electrically a
full wavelength. Such a structure is resonant. At this
point,it is appropriate to mention categories or types of
antennas:
S 1. Electric dipoles. These are straight wires
upon which electrical charges flow. AM
broadcasting towers are a typical example o~
this type of antenna. A vertical electric
dipole will produce a vertically polarized
radiation field.
2. Magnetic dipoles. These are linear structures
upon which "magnetic charges" flow. They have
radiation fields which are the duals to those
of the electric dipoles. (That is, their
magnetic field patterns are the same as the
electric dipoles' electric field patterns.)
A typical example of this antenna is the
Norma~ Mode Helix antenna, already mentioned
above in the Background of the In~ention.
3. Electric Loops. These are closed loop
structures (perhaps having several turns)
in which electric currents flow. They have
the same patterns as magnetic dipoles and
may be regarded as a magnetic dipole whose
axis coincides with that of the loop.
Typical examples are the loop antennas used
for radio direction finding and for AM
broadcast receivers. A flat loop will pro-
duce a horizontally polarized radiation
field.
4. Magnetic loop antennas. These would be
closed loops of flowing magnet-Lc current.
They would have the same field patterns as
electric dipoles. Indeed a horizontal mag-
netic loop would have the same radiation
pattern as a vertical tower or whip antenna.
~36~L9
-15-
Prior to the invention of my toroidal loop
antenna, the typical way magnetic loop
antennas could be made was to excite a circu-
lar slot in a large ground plane. The gro~nd
plane had to be many wavelengths in extent
and the annular slot, in order to resonate,
had to have a mean circumference equal to
a free space wavelength.
Because of the helical winding, the toroidal loop
embodimellts of my invention behave as the superposition of
a loop of magnetic current and a loop of electric current.
The electric loop component generates a horizontally
polarized radiation field, and the magnetic loop component
generates a vertically polarized radiation field. By
varying the helix distribution~ one can control the polari-
zation state of the radiation field.
It was explained in the Background of the Invention
that ther~ has been a methematical analysis of the helical
antenna by Kraus, and Kandoian and Sichak. The helically
wound toroidal antenna em~odiment of my invention can be
analyzed by taking the linear helix discussed above and
bending it around into a torus and exciting it with a high
frequency signal generator. Since the guide wavelength
is much smaller than ~0, one can make a torus with even a
small circumference behave electrically as a complete wave~-
length (that is, C = 2~a = ~g<< ~0), or m~ltiples of a
wavelength. One now has a resonant antenna whose properties
(input impedance, polarization, radiation pattern, etc.),
are distinctly different from the linear normal mode helix
discussed above. For example, one could not analyze this
new structure by assuming that the current is uniformly
distributed in ampli~ude and phase along the circumference.
(Unless of course, the torus were very, very small).
However, there are certain features of ~he normal mode
helix analysis that one can use as an aid to understanding
the toroidal loop antenna.
~ 133G~4911
-16-
Assume that the current distribution is non-
uniformly distributed along the azimuthal angle ~. Also
assume that the helix can be decomposed in~o a continuous
loop of (simusoidally distributed) electric curren~ plus a
continuous loop of (sinusoidally distributed) magnetic
current. The radiation properties can then be ascertained
by employing the principle of superposition. The following
discussion proceeds ~hrough thes~ separate computations and
combines them to determine the toroidal loop's radiation
properties.
Radiation Fields Produced by a Large Loop of Electric Current
We consider an electric current of the form
~ ') = Iocos n~'ei~t excited upon a circular wire loop
of radius a. It should be noted that this uses a standing
wave with n nodes; that is, the analysis is of the nth
harmonic where n = 0, 1, 2 . . .. In other words, the
circumference of the loop is n guide wavelengths: C = n~g.
Figure 7 shows the geometry for a circular loop of non-
uniform current used in the following analysis of ~he electro-
magnetic fields E and H in the radiation zone far from theantenna. The source density may be written as
(8) J (r ) = Iocos n ~ ei ~cos~ a a) ~ .
In the far field (radiation zone) r>>a, and the position
vectors r' of all the elements of the ring dQ may be re-
garded as parallel. This yields:
(9) r = R~a cos ~ .
It has been shown that
(10) R-r' = cos ~ = sinasins' cos ~ cos3cos9'.
~36~
-17-
See E.A., Wolff, Antenna Analysis (John Wiley Book Co. 1966)at page 111. Since ~ /2 one has:
(11) r = R-a sin9cos(~'-~).
An element of the ring of current has an elec~ric dipole
moment
(12) dp = pdQ
where P is the electric dipole moment per unit length of
the wire. The electric and magnetic fields are related to
the potentials as
(13) H = ~ V x A
where ~ is the permeability of space, and A is a vector
potential 9
(14) E = -j~A - VV
where V is a scalar potential,
and in the radiation zone,
(15) E = ZoH x R
where ZO is the characteristic ~mpedance or free space.
Now
J(-)-j~r
(1~) dA = 4~r
where ~ is ~he phase constant 2~ and ~O is the permeability
of free space.
so that
-18-
- ~o ~j~r
4~r
Equation (13) now leads to
(18) dH = ~ e i~rdp x R
4~r
Collecting together Equations (8), (12~ and (18) one has the
incremental magnetic field intensity vector
(19) dH ~ - ei~t-~R + ~a sin~cos(~
cos n~'~cos(~-~')8 + cos~sin(~ ]d~ .
In the denominator of this last equation there are neglected
quantities of the order of a in comparison with R. This
cannot be done in the exponential terms since ~a is not small
with respect to the other exponential terms and has an
important effect in the phase. The magnetic field intensity
can now be found by direct integration:
j~aIO j(~t-~R) ~ os(~ )cos n~ ei
One can obtain an expression for H~ from that of H~ simply
by replacing cos(~ by sin(~ ) in the integrand. Let
p = ~ . Then
(21) cosn~' = cos n~ cosp - sin n~ sin np
This gives
22) H~ -- ei(~t ~R) ~-sin n~ ~ co ~ sin n~ ei~asi
~ + cos n~J co~ cos ~ ei~a sinaco~ ~
1~98GV49
The firs~ integral will vanish because the integrand is odd.
The second integral has an even integrand so that the limits
may be transformed to 0, ~ and the integral itself expressed
in terms of the derivative of a Bessel Function:
~ Jn(X) ~ ~ cos(pcos n,~ei ~COS~d~
where x = ~asin~.
Thus one is led to a 9 component of the magnetic field
intensity of the form
(24) H~(R) = ~ = ~ cos n~ Jn (~asin~)ei(~t ~R ~ )
where the circumference of the loop is n~g. The expression
for H~ may be found, as stated above, by simply replacing
cos (~ ) by sin ~ ) in the integrand. Then
(25) ~ coS~ei(~t-~R) Jsin(~
ei~asin~cos(~ ) d~
Again let p = ~ and use the trigonome~ric identity,
Equation 21, to obtain
(26) H~ --cOs9ei(~t ~R) ~cos n~JcosnPsinPei~aSin~CSPdP
-sin n~ Jsin npsinp ei~a sin3cospd ~
--7r
Now
36~34~
(27a) cos np sinp = 2~sin(n+1)p - sin(n-l)p]
(27b) sin np sinp = ~[cos(n-l)p - cos(n+l)p]
so that
(28) J cos np sinp ei~a sin~cospd O
and
(29) J sin np sinp ei~a sin9Cospdp = jn_
_jn~l~Jn+l(X)
where one lets x = ~asin~, and using the relation
(30) ~ eixcos~cos n~d~ = jnlrJ (x).
Thus, Equation (26) becomes
(31) H~ -- cos~ei(~t ~R)jn [Jn+l(x) + Jn-l(x)](-sin n~).
Now, thP recursive relation :Eor the Bessel Functions can
be wTitten as
(32) Jn_l(x) + Jn~l(x) x Jn~x)
so that one can finally collect Equation (24) into the
expr es s ion
-E -~aI n -J (~asina)
(33) H~ = z ~ -2- ~ ~a tan~
ej(~t_~
Equations (24) and (33) must now be substituted back into
~86~ 9
-21-
Equation (3). One then has the total electric field intensity
vector for a single loop of electric current:
(3) E = E~ ~ ~ E~
and
(34) H -' H~ ~ + H~ ~
At this point one still does not have the radiation fields
of the toroidal loop antenna. Before these can be found,
one must also rompute the fields produced by a large loop
of magnetic current.
Radiation Fields Produced by a Large Loop of Magnetic Current
Consider a circular loop of sinusoidally distri-
buted magnetic current. Suppose a standing wave of magne~ic
current of th~ form
I~m (~ Im sin(n~' + ~) ei~
Pxcited on a circular magnetically conducting loop. (This
is really the toroidal flow of electric charge.) For con-
venience, we lPt ~ = O and choose the electric and magnetic
currents to be in phase quadrature. The sourcP density is
again of the form
(35) Jm(r') = Imsin n~' ei~t S(cos3') S(ra a) ~ .
An element of the ring of magnetic current has a magnetic
dipole moment
(36) dPm = PmdQ
where Pm is the magnetic dipole moment per unit length of the
4~
-22-
source. From Magwell's equations we have
(37) E = - V x F
where E is the permeability of the medium.
(38) H ~ F
where F is the electric vector potential. This time
J -j~r
(39) dF m
which can be written as
(40) dF = ~-~ e i (~j~dPm)
whence
(41) dE- = ~ dP x R
One writes this out explicitly as
(42) dE = ~ ei~t-~R+~asin~cos(~ )]
sin n~' [cos~ +cosasin(~ d~'
This is readily integrated, as before~ to give
(43) E9 = ZOH~ sin n~Jn (~asin~ei(~t 3R ~ )
and
(4h) E = -Z H = ~ - cos n~ n( ) ej(~t-~R ~ )
Now, call the magnetically produced electric fields ~m and
-23-
the electrically produced electric fields Ee. Then,
employing the full symmetry of Maxwell's Equations one
writes
(45) E = Ee + ~m
(46) H He + ~m
where
(47) Ee - Ee~ ~ Ee~
and
(48) ~ = E~ + E~
By the way, the equivalent (fictitious) magnetic current
associated with the electric current Io flowing in a solenoid,
such as in Figure 3, has a magn~tude given by
(49) Im = ~ ~b Ie
where b = radius of the solenoid
s = turn to turn spacing of the solenoid.
See Kraus, An ennas, supra at page 158 (in ~his discussion
Q is replaced.by s, and A by ~a , and there is chosen
Im = 1~
This expreæsion may be used in Equations (43) and (44). We
are now in a position to determine the total radiation field
and radiation resistance of the isolated toroidal loop
antenna of my invention for the case where ~ = 0.
Analysis o the Fields Produced by a Toroidal Loop Antenna
The analysis so far has prepared the way so that
one can consider the toroidal helix to be composed of a
6~ ~ 9
-24-
single resonant magnetic loop (due to an actual solenoidal
flow o~ elec~ric charge around the rim of the torus) plus a
single resonant electric loop (due to the electric charge
flowing along the turn-to-turn spacing of the helix). This
is the basic assumption for the present analysis of the
toroidal loop antenna. A more rigorous analysis could be
made by assuming a spiral electric current around ~he heli-
cally wound torus. Such an analysis would require a great
deal more efort but would probably be desirable for near
field effects. However, the radiation zone effects should
be consistent with this approximate analysis.
The radiation fields of the helically wound toroidal
loop antenna are given by the linear superposition indicated
in Equation (45) where the component fields are taken from
Equations (24), (33), (43) and (44). These results are
collected here for later reference.
(50a) E~e = ~ cos n~Jn(~a sin~)ei(~t ~R ~ ~
( ) ~ 2R ~ ~a tan~ - e ~~
(50c~ E~ sin n~Jn(~a sin~) ei(~t ~R ~ )
~50d) E~m = ~ cos n~ ~n ei(~t-~R
where
(51) I = ~b2 I
Note that if n = O, the electric current is uniform around
the loop and the magnetic current, Equation (35), vanishes.
The radiation fields then reduce to the classical loop field
of Equation (1).
(Jo(x) = -Jl(x) and Jl(x)~
L9
-25-
Of most interest is the resonant toroidal loop
antenna. For this antenna n = 1, 2, . . .. One is
particularly interested in the case fo~ which n = 1 and in
this case the fields of Equation (50) in the azimuthal
plane reduce to
-~aZ I
(52a) F - Ji (~a) cos~
-~aI
~52b) Ea = ~R Ji (~a) sin~
These are sketched in Figure 8 for the case where ¦Im¦ = ZoIo,
I~ = cos~, and Im~ = sin~ . If ~ were other than zero, the
analysis could be repeated for that case. For example, if
a = ~2, Im and Ie would be in phase and both E~ and E~ would
would vary as cos~.
The Radiation Resistance Expression.
From Equation (50) one can compute the total average
power radiated from the antenna from the Poynting integral
( ) Payg ~ R e {~ (E x H ) RdA~ -
That is, for the case where n = 1, one may use Equation (50)
and rewrite Equation (53) as
(54) Pavg = ~ ~ ~z ~ R2 sin~ d~d~
The average power delivered to a resistive load by a
sinusoidal source is
~55) PaVg = 1/2 Io2 R
Equating Equations (54) and (55) gives an expression for the
radiation resistance as
6~ ~ 9
-26-
2~ ~ E2+E2
(56) Rr = ~ J ~ R2 sin~ d9d~
This integral cannot be carried out in closed form and depends
upon each loop geometry.
ThQ following embodiments demonstrate how toroidal
loop elements according to my invention, with the fields of
equation 50, can be superposed to obtain various desired
antenna patterns.
Bidirectional Horizontal Polarization
Recall that the antenna pattern of Figure 8 arose
from ~he situation producing the fields of Equation 52. If
we flip over this toroidal loop (on the x-y plane) and re-
verse the loop current, the antenna will have the radiation
pattern shown in Figure 9. If we now superpose these two
patterns, our new antenna will have the "figure eight" hori-
zontally polarized pattern of Figure 10. The verticallypolarized components have cancelled one another. What has
happened is that the magnetic currents, Im, have cancelled
one another leaving only the fields produced by the electric
currents, Ie.
Bidirectional Vertical Polarization
Flipping over an antenna having the pattern of
Figure 8 generates the radiation pattern of Figure 11. If
we now superpose the antennas giving the patterns of Figure
8 and Figure 11, the resultant pattern will be the vertically
polarized antenna pattern of Figure 12. In this example,
the electric currents have been phased out, and only the
magnetic currents are left to produce the ver~ically
polarized field in the azimuthal plane. One embodiment of
this approach (and one for obtaining horizontal polarization)
is indicated in Figure 13, which is a bottom Vi2W of a
multiply-wound helix. The bars BC and B'C' are for feeding
-27-
the toroidal loop and act as phasing lines. When fed at
AA', the structure produces a vertically polarized field
pattPrn in the plane of the torus. If B and B' or C and C'
are interchanged, the azimuthal plane field pattern is
horizontally polarized.
Omnidirectional Vertical Polarization
Quite often, an omnidirectional vertically polarized
radiating element is desired. The previous embodiment
demonstrates how an antenna constructed of two toroidal loops
could produce a figure eight vertically polarized radiation
field. If one now takes a second pair, that are also arranged
to produce vertical polarization, and excited them and the
previous pair with currents of equal magnitude but in phase
quadrature (i.e., a 90 degree phase shift), the resultant
field would be given by the expression
(65) E~ = sin~sin~t + cos~sin~t
which reduces to
(66) E~ = sin(~ + ~t).
~t any position, ~, the maximum amplitude of E~ is unity at
some instant during each cycle. The RMS field pattern is
azimuthally symmetric aæ shown by the circle in Figure 14.
' The pattern rotates as a function of time, completing one
revolution per RF cycle. So-called 7'turnstile antennas",
that is, the use of multiple antennas with varying currents
but with constant phase differences to obtain an antenna with
omnidirectional coverage, are not new. See Kraus, Antennas,
su~ra, at page 424 and G. H. Brown, "The Turnstile Antenna",
.
Electronics, April, 1936. The embodiments of my in~ention
.. . .
now under discussion differ from the foregoing prior art by
using toroidal loops ins~ead of other elements.
6~49
- 2 8 -
Figure 15 shows an embodiment for implementing this
method for obtaining omnidirectional vertical polarization.
Figure 15(a) shows a quadrifilarly wound toroidal helix phased
for producing omnidirectional vertical polarization (that is,
perpendicular to the plane of the torus). This configuration
is obtained by superimposing ~wo bifilar helices, each of the
type shown in Figure 13, and feeding them in phase quadrature.
Figure 15(b) 'shows schematically the feed distribution for
the antenna of Figure 15(a).
Omnidirectional horizontal polarization may be
produced by feeding bidirectional horizontal polarization
elements in an analagous manner.
Circular Polarization
Toroidal loops may be arranged so as to produce a
circularly polarized radiation field. Consider the antenna
pattern of Figure 8 produced by the basic toroidal loop.
Suppose a second loop is constructed but with its current
distribution (that is, the ~eed points) rotated by 90 degrees.
The second toroidal loop produces the pattern shown in
Figure I6. The superposition of these two patterns will
produce circular polarization in the azimuthal plane if the
two loops are excited in phase quadrature. Omnidirectional
circular polarization can be produced by rotating the
antennas producing the pattern of Figure 10 by 90 degrees
and feeding them in phase quadrature with the antennas pro-
ducing the pattern of Figure 12.
Operation at a Higher Order Mode
There is no reason why one should operate the
toroidal loop only at a frequency where n - 1. One can also
operate at a frequency where n = 2 and the "magnetic" current
distribution varies as
-2g-
(67) I~ ) = Imsin 2~
In this case, the fields are still given by Equation 50 and
the radiation pattern will be more complex than the n = 1
mode. The disadvantage for using a higher order mode is that
the antenna now will be physically larger. This is a dis-
advantage at low frequencies. However, at UHF this permits
simpler const~uction and broader bandwidth.
Array Operation
In order to increase the gain or directivity for an
antenna syst~m one often employs multiple elements with some
physical spacing. For example many AM broadcast stations
~mploy an array of several vertical towers spaced some portion
of the w~velength and directly excited with various amplitudes
and phase shifted currents. Such antennas are called driven
arrays.
Alternatively one may space tuned elements an
appropriate portion of a wavelength from a single driv~n
element and cause the tuned elements to be e~cited by the
fields produced by the driven element. The fields from the
driven element induce currents on these other elements, which
have no direct electrical transmission line connection to a
generator. Such elements are called parasitic elements,
and the antenna system is called a parasitic array.
The toroidal loop may be employed in both the
driven array and parasitic array configurations. The entire
array, or only portions of it, may be constructed of
toroidal loops. For example, in Figure 17 the driven element
is a resonant linear element 1701 and the parasitic element
is a tuned parasitically excited toroidal loop 1702. One
could construct a driven array of several toroidal loops
with various physical spacings and different amplitude and
phased currents. These spacings may be concentric or
linear depending upon the design criteria. Parasitic arrays
-30-
have been constructed entirely of toroidal loops as in
Figure 18~ which shows configuration for a typical two element
toroidal loop parasitic array. The center toroidal loop
1801 is resonant at the frequency of interest and the parasitic
element 1802 tuned as a director (resonated about 10% higher
in frequency) and with a mean diameter about one-tenth of a
wavelength greater than the mean diameter of the driven
element for t'he given frequency of interest. These concentric
configurations of Figures 17 and 18 measured gains typically
on the order of 3 to 5 db over the center elements alone.
DESIGN EXAMPLES
A variety of toroidal loop configurations according
to my invention can be constructed and typical resonant
resistances can be varied (typically between a hundred ohms
to several thousand ohms)> depending upon the values a, b,
and s and the order of the mode n excited on the loop as ~hese
terms were used in the equations herein. The variation of
these parameters has also permitted a variety of polarization
types and radiation patterns.
In the following constructions, it is assumed that
one is using a driven toroidal loop radiating in its lowest
order mode (n=l) with the radiation patterns of Figure 8.
We could of course excited a higher order mode with a
different n. The fields would still be given by Equation 50.
Example A - a conceptual elementary toroidal loop antenna for
use with a home FM receiver.
A resonant frequency of 100 MHz (~O = 3 meters) and a torus'
minor radius of b = 1.27 cm are arbitrarily chosen. If
one winds the helix with turns spaced equal to b, then from
Equation 7a we find Vf = .296. For lowest order resonance,
the circumference c = ~g = Vf~o. Thus we choose the major
radius to be
8 ~ ~ ~ 9
~ -31-
V ~
(68) a = ~ = .141 meters (5.55 inches)
In this example
(69) I~ = ~Y~- Io = 10-03 JO
The fields c~n be determined from Equations 50 and they will
be elliptically polarized with different axial ratios in
different directions.
Example B - a conceptual toroidal loop for use at LF.
Suppose the desired operating frequency is 150 KHz.
(lo = 2,000 meters or 6,562 feet). One arbitrarily chooses
the torus' minor radius as b = 10 feet (3.05 meters), and
the turn-to-turn spacing as 2 feet (0.61 meters). From
Equation 7a we find Vf = .053. Thus, for lowest order mode
operation, the major radius is
Vf~o
~7Q) a = 2~ = 17.02 m. = 55.83 ft.
In this example Im = 56.7Io and the fields follow from
Equations 50. Notice that this antenna has a radius less
than 1/10 wavelength and will be wound with 175 turns.
The following examples present expPri~ental pro-
perties from several toroidal loop antennas according to my
inven~ion which have actually been constru~ed.
Example 1 = VHF Toroidal Loop
This antenna was wound with 70 turns o #16 gauge
copper wire on a plastic torus of major radius a - 6.25
inches and minor radius b = lt2 inch. Ihe antenna was con-
structed as in Figure 5. The turn-to-turn spacing was
s = .56 inch. This antenna was operated in the n = 1 mode
(a~ 100 MHz). The predicted velocity factor was
-32-
Vf(100 MHz) = .336. The measured velocity factor was
Vf(100 MHz) = .332. The measured feed point impedance
Swhich gives the characteristic r~sonance curv4s for n = 1)
is given in Figure 19.
Example 2 - VHF Vertically Polarized Toroidal Loop
The vertical polarization scheme of Figure 13 has
been built and measured. The physical construction parameters
were as follows: a = 12.5 inches, b = .5 inch, s = .26 inch.
The bifilarly wound loop was fed at AA'. The antenna had a
predicted V~ = .153 and a measured Vf = .156 a~ 46.0 MHz.
The ratio of vertical to horizontal polarizatîon field
strength (or axial ratio) was 46. That îs, the polariza-
tion produced was predominantly vertically polarized. ThesP
measurements were made with a field strength meter and the
pattern indicated was that of Figure 12.
Example 3 - Omnidirectional VHF Array
The omnidirectîonal vertically polarized quadri-
filarly wound toroidal helix of Figure 15 was constructed on
a plastic torus. It had 64 quadrifilarly wound turns. The
physical parameters were a = 4.0 inches, b = .3 inch, s
.4 inch. The structure resonated at 93.4 MHz and field
strength measurements indicated that it produced omni-
directional vertical polarization with an axial ratio of
76.4.
Example 4 - HF Toroidal Loop
An HF toroidal loop was constructed with 1,000
turns of #18 gauge wire wound with these physical parameters:
a = 2.74 ft., b = .925 inches, s = .2 inch. The antenna's
VSWR was measured through a 4 to 1 balun transformer and
50 ohm coaxial cable. The VSWR curves are shown in
~ ~ 8 ~0
-33-
Figures 20 and 21 for two separate resonances of the antenna.
Example 5 - Medium Frequency Vertically Polarized Toroidal
Loop
A 106 turn bîfilar toroidal loop of the form of
Figure 13 was constructed with the following parameters:
a - 5.95 ft.l' b = .95 ft., s = 4 inches. The turns were
measured at the feed point AA' and the results are shown in
Figure 22. The loop was constructed at a mean height of
3.5 ft. above soil with a measured conductivity of 2 milli-
mhos/meter. The graph shows two sets o curves. One setof curves 2201 shows the feed point impedance vs. frequency
for the situation where 40 ~wenty foot long conducting ground
radials were sy~etrically placed below the torus at ground
level. The second set of curv~s 2202 shows the same data for
the case where the ground radials have been removed. What
is interesting is that the conducting ground plane has very
little effect on the feed point impedance. This is to be
expected if the electric current tends to zero and the major
fields are produced by the magnetic current, Im. Howe~er,
the proximity effect of the ground has not been analyzed
theoretically. It should be noted that the measured velocity
factor was Vf = .094 while the theoretical value is Vf = .103.
This corresponds to a difference of about 8.7%. This may be
due to the ground or it may be due to mutual coupling effects
on the bifilar windings. The theory which was developed
above was for an isolated single toroidal helix. I~ would
be applica~le to multifilar helices if mutual effects are
neglectable.
Example 6 - HF Rectangular Toroidal Loop
An HF toroidal loop was constructed in a rectan-
gular shape with 116 equally spaced turns of ~18 gauge wire
wound on a 2 1/2 inch (O.D.) plastic pipe form. The
-34-
recta~gle was 27 inches by 27 inches and the feed point was
at ~he ce~terof one leg of t~e rectangle. See Figure 23.
The feed point impedance was measured and is shown in
Figure 24. The resonant frequency for this structure occu~s
where ~he reactive component o~ the Lmpedance vanishes:
27.42 M~z.
Example 7 - Parasitic Array
A VHF parasitic array was constructed from a
driven resonant quarter wavelength stub (above a 2 wavelength
diameter ground plane) and a parasitically excited toroidal
loop, as in Figure 17. ~he loop had a majo~ radius of 1/10
wavelength and was tuned to resonate at a frequency 1071.
higher tha~ th~ driven linear element. The measured gair~
oves the driven elemen~ alone was 4 db. The array was
constructed at 450 MHz.
Example 8 - Contrawo-md VEIF Toroidal Loop
A structure consisting of t~o helices wound in
opposite direction~ a~ the sa~e radius is called a contra-
wound helix. Slow wa~e de~ices have been constxucted as
. 20 con~rawound helices (operating as non-radiating transmission
lines, or as element~ in ~ra~eling wave tubes ) . See
C . K. Birdsall and r. E . Everhart, "Modified Contrawound Helix
Circuits for Hlgh Power Traveling Wave Tubes", Institute
of Radio Engineers Transac~ions on Electron Devices, ED-3,
October, 1956, P. 190. See Figures 2Sa and 25b. In Figure
25a the arrows indicate the current flows along the inter-
twined helices where the cnnductors cross. Figure 25b s'nows
a ring and bridge slow wave structure described by Birdsall
and Everhart that is electromagnetically related to a contra-
wound helix structure. The current flows at the "cross-overs"
of the structures of Figures 25a and 25b are shown in more
aetail in Figures 26a and 26b, res~ectively. As indicated
in Figure 25b, the currents flow around the rings in the
~ ~ 6~ ~ ~
same direction~ but flow counter to each other across
the brldges connecting ~he rings. These structures mav be
constructed as closed toruses and opera~ed not as trans-
mission lines as in microwave tubes, but as resonant
radiating tcroidal helix antennas. Under ap~ropriate opera-
~ion of a ring and bridge structure as an antenna,
~hese counter curren~s on the bridges will cancel each other
so that no net electrical current flows along the major
circumference of the torus, but a net electrical current
flows around each of the rings of the struceure. This
electrical current flow condition is equivalent to the flow
of a non-uniform magnetic current along the maJor circum-
ference of the torus. Since in this mode of operation the
bridge elements perform no electrical unction they may be
omit~ed from the antenna. An embodimen~ of such an antenna
is shown in Figure 33. Our previous analy~is describes this
mode of ra~iating toroidal heli~ if we le~ I~ = 0 2nd a -
~ . Then, the Ee of equations 50 vanish and ehe fieldsreduce to
~ ~ ~05 ~ J~ (~asi~ t-~R ~ )
(2) E~ i~ n~ ~ e.i (~t~R+~)
The resultant radiation fields will be elliptically polarized.
Such a device was fabricated (by bending the contrawound
25 helix of Figure 25b wound into a ~orus) o 1/16" thick
aluminum, with minor radius 5/8" and majox torus radius of
5~1/4'1. Figure 25b shows three additional useful parameters:
the ring thic~cness "rt1'; the angular arc "aa"; and the slot
width "sw" . The ring thickness was 1/ 2", the angular arc
30 was about 25, and the slot width was 1/4". I~e 78 turn
devic e op era ted as a r es onant ant enna s truc tur e at 8 5 MHz
with a radiation resistance of approximately 300 ohms.
g
- 35a-
Example 9 - Contrawound Helical Torus for Producing Ver~ical
Polarization .
If we could obtain a uniform current distrlbution
over a cor.trawound toroidai helix of resonanc dimensions j we
S wou].d have ~he case where n is effectively equal to zero.
I~is is especially interesting because E~, would then vanish,
lea~ring only the ield given by
t3) E~ ~ _~ Jl(~asin~) ei((~3t ~R~),
This is an omnidirectional ~ertically polari2ed (in the
1(~ az~uthal plane) resonant radiating toroidal heliæ. Here
we have a~ eq~i~ale~ magneti:: curren~ flowing along the
rnaj or circumf erenca of the tor~ls . In this ca~ e ~ it i~
~ ~ ~ 6
-36-
necessary to establish a uniform magnetic current along the
helical structure in order to make n = 0 and cancel out the
E~ component in the radiation field. This mode of operation
is especially appealing for VLF antennas.
Such a device was constru~ted as shown in Figure
27 of #10 gauge copper wire. The major radius of the 32 turn
~oroidal heli~ was 4-3/4", the minor (or ring) radius was
11/16", the slot width was 3/4", the ring thickness was
1/8" and the resonant frequency was measured as 135 MHæ. The
antenna of Figure 27 is made by bending the helix of Figure
25b around into a toroid and then dividing it into four parts
2701, 2702, 2703, 2704. The technîque employed to obtain
the n = 0 mode of excitation for the toroidal helix was to
simulate a uniform loop by exciting the toroidal helix as
the ~our smaller parts 2701, 2702, 2703, 2704 connected in
parallel across a coaxial feedline 2705. This arrangement
is the magnetic current analog to the electric current
" loverleafl' antenna. For a discussion of the electri~ loop
cloverleaf antenna, see Kraus, Antennas, supra, P. 429 and
P.H. Smith, "Cloverleaf Antenna for FM Broadcasting", Pro-
ceedings of the Institute of Radio Engineers, Vol. 35,
PP. 1556-1563, December, 1947. In my toroidal helix, the
feed currents cancel, producing no radiation fields and the
contrawound resonant toroidal helix supports an effective
azimuthally uniform magnetic current which produc~s the
omnidirectional vertically polarized radiation. This
structure would also be appropriate as an element in a
phase array configuration.
Variable Resonant Frequency
Figure 28 shows an embodiment of my invention in
which a variable capacitor 2801 is used as a means for
varying or tuning the resonant frequency of the antenna
without changing the number of turns of the antenna. The
antenna of Figure 28 consists of two toroldal helices. One
~ ~ ~6
-37-
is fed at points AA' and the other at CC'. The variable
capacitor 2801 is placed across the feed points CC'. As
the capacitance is varied, the resonant frequency of the
antenna is varied.
By making use of the slow wave nature of helical
structures and the duality between vertical monopoles and
magnetic loops, we have been able to construct electrically
small, resonant structures with radiation pa~terns similar
to resonant vertical antennas and other antenna arrays. Of
course, one does not get some~hing for nothing. The price
one pays with the toroidal helix is that it is a narrow band
structure (called "high Q") and inherently not a broad band
device. These antennas according to the invention which, by
virtue of their unique construction, possess a greater
radiation resistance than known antennas of similar electrical
size without the slow wave winding feature described above.
The helix on a torus winding feature permits the formation
of a resonant antenna current standing wave in a region of
ele~trically small dimensions, and it permits the controlled
variation of antenna currents, resonant frequency, impedance,
polarization and antenna pattern.
Various toroidal helices fall wi.thin the scope of
the invention. For instance, the helices can havQ righ~-
hand windings, left-hand windings, bifilar windings in the
same direction (both right-hand or both left-hand), or
bifilar win~ings which are contrawound (one right-hand, one
left~hand). The toroidal helices can be used with other
configurations of the conducting means as well.
Although the preferred embodiments described above
relate to various toroidal helix antenna systems, there are
other configurations in which an electrical conducting means
cause the antenna system to function as a slow wave device
according to the invention, with a velocity factor less than
1 (i.e. Vf < 1). The electrical conducting means should be
configured to establish a closed standing electromagneti~
wave path, ~he path inhibiting the velocity of propogation
-38-
of electromagnetic waves and supporting a standing wave at a
predetermined resonant frequency. Such configuration should
have a substantially closed loop geom~try. Such geometry
could be described as being multiply connected. Thus, the
electrical conducting means would not have an essentially
linear shape, and it would not be a simple circle lying sub-
stantially in a single plane (in a strict mathematical
sense, a wire or other elongated conductor would necessarily
be 3 dimensional and extending in more than one plane, but
for the purposes of this discussion an antenna is considered
to lie in one plane if it could rest on a flat surface and not
rise from that surface more than a small fraction of its
length - i.e. a conductor is considered as lying in one plane
if in ordinary parlance it could be described as being flat).
A simple ring shaped conductor 3401 of the type shown in
Fig. 34 would not satisfy the criteria of the invention. In
addition to the toroidal configurations described above, other
configurations function to form wave inhibiting devices
according to the invention. Thusl in Fig. 29, a conductor
2901 has a wavey pattern and extends around a non-conducting
toroidal support 2902. A conductor 3001 is shown in Fig. 30
having a zig-zag shape and is disposed around an imaginary
cylinder. Another zig-zag arrangement is shown in Fig. 31,
where a conductor 3101 lies in a single plane. The con-
ducting means can lie in a single plane so long as it isnoncircular. (It could be circular in projection, if it lies
in more than one plane). The conducting means could have
linear and curved components, such as the con~iguration 3201
in Fig. 32. The conducting means need not be a single
element or even a plurality of physically connected elements;
for example~ the antenna 3301 of Fig. 33 comprises a
plurality of spaced rings 3302 arranged about a circle. Rings
3302 would be inductively coupled in response to the trans-
mission of electromagnetic waves in antenna 3301. The various
antenna arrangements of Figs. 29-33 must be dimensioned and
have the characteristics to fulfill the requirement that they
~ 4
-39-
establish a closed standing wave path for electromagnetic
waves, which path inhibits the velocity of the waves along
the path and supports a standing wave at a preselec~ed
resonant frequency.
The invention has been described in detail with
particular emphasis being placed on the preferred embodiments
thereof, but it should be understood that variations and
modification~ within the spirit and scope of the invention
may occur to those skilled in the art to which the invention
pertains.
