CA1186049A - Antenna having a closed standing wave path - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

An antenna for transmitting or receiving electro-magnetic radiation, comprising a conductor configured to establish a closed standing wave path, and to inhibit the velocity of propagation of and support a standing electro-magnetic wave.

Description

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 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 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~

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~

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 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~

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 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~

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~

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.

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~

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 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 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 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~

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 - ~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 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~

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 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 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)~

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 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 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 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 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 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 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 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 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 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 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 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.

Claims (25)

I claim:

1. An electromagnetic antenna including first and second con-ducting paths for supporting the propagation of first and second electromagnetic waves, respectively, wherein said first and second conducting paths are configured to inhibit the velocity of propagation of said first and second waves, respectively, and are disposed on the same multiply connected surface.

2. The invention according to claim 1 wherein said first con-ductor is circumferentially disposed about an axis, said axis having a closed geometric shape, a portion of said conductor lying within said shape.

3. The invention according to claim 1 wherein said multiply connected surface is toroidal and said first and second con-ducting paths comprise elongated first and second conductors helically disposed on said surface.

4. The invention of claim 3 wherein said first and second conductors are disposed in bifilar relation to each other.

5. The invention according to claim 4 including phasing means for controlling the relative phases of said first and second waves.

6. The invention of claim 4 wherein said first conducting path includes frequency adjustment means for altering the frequencies at which said antenna may support a standing wave.

7. The invention of claim 6 wherein said frequency adjustment means comprises a variable reactance connected to said first conducting path.

8. The invention of claim 3 wherein said first and second con-ductors are disposed in contrawound relation to each other.

9. The invention of claim 1 wherein said first and second con-ducting paths are each elongated conductors contrawound on said multiply connected surface.

10. The invention of claim 1 wherein said first and second con-ducting paths comprise a plurality of conducting ring elements disposed on said multiply connected surface.

11. The invention of claim 10 wherein said multiply connected surface is toroidal.

12. The invention of claim 10 wherein said conducting paths further include conducting bridge elements electrically connect-ing said ring elements.

13. The invention of claim 12 wherein said conducting paths are electrically divided into four substantially identical sections of ring and bridge elements, said sections being electrically connected in parallel.

14. The invention of claim 1 further including a second antenna having a third conducting path for supporting the propagation of a third electromagnetic wave, wherein said first and third con-ducting paths are disposed relative to each other for inducing propagation of said third electromagnetic wave in response to propagation of said first electromagnetic wave.

15. The invention of claim 1 further including electrically driven antenna means for generating a third electromagnetic wave, wherein said first conducting path is disposed relative to said antenna means for inducing propagation of said first wave in response to generation of said third electromagnetic wave.

16. An electromagnetic antenna comprising a plurality of con-ducting ring elements disposed on a toroidal surface.

17. An electromagnetic antenna comprising a plurality of con-ducting ring elements electrically connected by conducting bridge elements, said ring and bridge elements being disposed on a to-roidal surface, wherein said conducting elements are divided into four substantially identical sections of ring and bridge elements and said sections are electrically connected in parallel.

18. A process for radiating or receiving electromagnetic energy comprising conducting first and second electrical currents, re-spectively, through first and second conducting paths configured to inhibit the velocity of propagation of waves propagating along them, to establish, in response to the flow of said currents, first and second standing, inhibited-velocity waves along said conducting paths.

19. The process of claim 18 wherein said conducting paths are elongated conductors disposed in bifilar relation and including the step of controlling the relative phases of said first and second currents.

20. The process of claim 18 wherein said conducting paths are elongated conductors disposed in bifilar relation and including the step of altering the frequencies of said first current at which a standing wave may be established along said first con-ducting path.

21. The process of claim 20 wherein said altering step comprises altering the value of a variable reactance connected to said first conductor.

22. The process of claim 18 wherein said first and second con-ducting paths comprise a plurality of conducting ring elements and a plurality of conducting bridge elements electrically con-necting said ring elements, including the steps of electrically dividing said conducting elements into four substantially identi-cal sections of ring and bridge elements and electrically con-necting said sections in parallel before conducting said first and second currents.

23. The process of claim 18 further including inducing the flow of a current in a second antenna spaced from said first conduct-ing path in response to the flow of said first current.

24. The process of claim 18 further including creating an electromagnetic field by driving a second antenna spaced from said first conductor and inducing said first current to flow in response to said field.

25. A process of radiating or receiving electromagnetic energy comprising electrically connecting in parallel four substantially identical sections of a conducting path, said path including a plurality of ring elements electrically connected by conducting bridge elements, said ring and bridge elements being disposed on a toroidal surface, conducting a current through said sections and establishing, in response to the flow of said current, a standing, inhibited-velocity wave along said path.