TRs SPIRBL AwTZNNA*

R. Bawer and J. J. Wolfe Aero Geo Astro Corporation

Alexandria, Virginia

summary A simplified description of the radiation me-

chanism of the spiral antenna is given, and the e f f ec t s of the various parameters on the charac- t e r i s t i c s of t he cavity-backed Archimedian spiral are discussed. Experimental data illustrating the e f fec t of cavity diameter, cavity depth, conductor loading, and s p i r a l r a t e of growth are offered as design guides. Finally, a spiral antenna and ba- lun feed are described. Over an octave frequency range, e l l i p t i c i t y r a t i o s of less than 3 db have teen maintained over azimuth angles greater than -60 degrees, boresight errors have been v i r tua l ly eliminated, and standing wave r a t io s of less than 2:l have been realized.

- I. Introduction The sp i ra l has been extensively used in ar-

rays and sc anning12tennas as well as an i so la ted radiating element . I n s p i t e of i t s wide use, however, there are many f ace t s of i ts o eration which still remain unexplained. Curtis E , and more recently Rumsey7, have attempted a mathematical description of these antennas, but their results a r e f a r from the form which might be readily used by engineers.

Since the spiral antenna was introduced by E. M. Turner a t WADC i n 1954, i ts development has been completely empirical and its theorg is almost e n t i r e l y i t a t i v e and based on the band theory of B u r d i n e I n r e c e n t y e a r s , numerous a r t i c l e s on spiral antennas have appeared i n t h e l i t e r a t w e . With the exception of Eysonb9 work on the loga- rithmic spiral antenna, all of the investigators have been primarily concerned with applications which make use of t he unique properties of the Archimedian sp i r a l antennas.

After studying the available l i terature, it soon becomes evident that some of the basic char- a c t e r i s t i c s and l imi ta t ions have been overlooked and the re ex i s t s a de f in i t e need t o review the s t a tus of t h e s p i r a l antenna. It should be c l e a w ly understood that many of the ideas presented are not new, but have appeared in one form or other among the col lect ive works of many authors. What is new, however, i s the a t t empt t o j u s t i fy t he ex- perimental results i n t e r n of t h e s p i r a l antenna band theory. The m a i n j u s t i f i c a t i o n f o r this action (and possibly the only val id one) is the in tu i t ive ins ight in to the opera t ion and t h e de- sign problems which results.

.................... *"he work reported i n this paper was sponsored @ t he Airborne Instruments Laboratory, Division of Cutler-iIammer,Inc., P.O.No. 6468 under Air Force Contract No. AF'33(600)-37829.

The purpose of this paper is four-fold: -(1) To present experimental data can-

p i led fran many antennas operating under a wide var ie ty of conditions and to i n t e rp re t t hese re- sults i n l i g h t of t he band theory,

parameters which s igni f icant ly a f fec t the oper- a t ion of t he antenna,

(3) To place the spiral antenna i n its proper perspective with regard t o w h a t character- i s t i c s may be reasonably expected in prac t ica l si tuations, and f ina l ly ,

(4) To emphasize some of the questions which arise in explaining the antenna behavior in the hope tha t sane of the readers may par t ic ipa te in furthering the understanding and c lar i fy ing some of the uncertaint ies in the design of these antennas.

(2) To emphasize those aspects and

11. Theory - O f the var ie ty of possible spiral configura-

tions, only three have received wide attention: the logarithmic or equiangular spiral, the Archi- median or ar i thmetic spiral , and the rectangular counterpart of t he Archimedian sp i ra l . These shapes, formed by photo-etching the geometric form on a copper-clad d i e l ec t r i c base material, are il- lus t ra ted in Figure l. The radiating element may consist of e i t h e r one o r two conductors t o form a single or double spiral. "he dual-ann s p i r a l is samewhat more predictable, having better charac- te r i s t ics than the s ing le ann antenna, and is generally preferred at frequencies below about 5000 mc. A s the operating frequency i s increased, however,.the physical size of the antenna becomes so small t h a t mechanical considerations finally favor the single arm configuration.

When excited frm a balanced two-wire trans- mission line, these configurations exhibit broad- band character is t ic with respect to input impe- dance, radiation pattern, and circular polar iaatkn of the radiated field. Since the dual-ann Archi- median spiral possesses the greatest symmetrg, on ly this form is discussed; many of the results, however, a re d i rec t ly appl icable to the o ther shapes.

Although there is no mathematical basis f o r the % a n d 1 ' description of radiation from the Archimedian sp i ra l , two f ac to r s have contributed t o its acceptance. First, the theorg is i n good accord with experimental observation; and second, the theory.is easily understood and compatible with intuitive reasoning. The point of view is taken that the dual-ann spiral antenna behaves as though it were a two-wire transmission l ine which% gradually transfonned into a radiating structure. Allowable radiation bands exist f o r all c i r c l e s whose circumference is an in tegra l number of wave- lengths; only two radiation modes will be

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discussed, one which produces a single lobe radi- at ion pat tern with a m a x i m u m along the axis of the spiral , whi le the second produces a split-beam pattern with a n u l l on-axis. The fundamental or normal mode will be described first.

Consider an isolated, tightly wound, dual- arm s p i r a l element i n which t h e two arms are ex- c i ted by currents of equal amplitude and 180 de- grees out of phase (Figure 2). I n t h e v i c i n i t y of, and f o r some distance removed from the origin, the currents in adjacent conductors are out of phase so t h a t l i t t l e o r no radiation occurs. As one proceeds fu r the r away from the origin along the curves, t he phase relationship between the cur- rents in adjacent conductors becomes random so that the net radiated energy in this region is small. Th i s s i t ua t ion pe r s i s t s un t i l a diameter corresponding t o a c i r c l e of circumference equal t o one wavelength i s approached. In t h e neighbor- hood of t h i s diameter the current i n adjacent arms are i n phase . a n d the condi t ion for eff ic ient radi- a t ion e x i s t s .

Let the vectors A and A' of Figure 2 represent differential current elements a t two diametrically opposite points on the same conduc- to r , such tha t the a rc l ength A A I i s exactly equal t o one-half wavelength. The current vectors A and A I a r e i n phase since the vector A' is directed opposi te to the vector A by v i r tue of t he geometry plus an additional 180 degrees due t o the a rc l ength AA'. Corresponding t o t h e c u r r e n t

. element A, there i s an element B on the second conductor having the same re l a t ive phase. The element B i s diametrically opposite element A and equidistant from the origin. It therefore fol lows that the different ia l current vectors A, A' , B, and B' a re co l inear and of t he same direction. On .extending this reasoning, it fo l - lows t ha t t he re i s a band of f inite breadth having a mean diameter of X/n i n which the current ele- ments in adjacent conductor are in phase, or near- l y so. This i s the first radiation band.

To each group of different ia l current e le- ments lying within the radiating band and on a diameter, there exists a corresponding group which is i n time and space quadrature t o t h e first; therefore, the radiation i s circular ly polar ized.

In summary, a s p i r a l antenna i n which the two arms are excited by currents having 180 degree phase relationship will radia te from a band of mean diameter equal t o X/n, the radiation pat- t e r n will be b id i rec t iona l and circular ly polar- ized according t o t h e winding sense of the spirals . This i s the normal or fundamental mode and i s t h e one i n which nearly all spiral antennas are designed t o operate.

A similar line of reasoning can be used t o describe the second radiation band. This mode of radiation w i l l be dominant when the input termin- als of t he sp i r a l a r e exc i t ed i n phase as i l l u s - t r a t ed i n F igu re 3. For t h i s case, efficient radiation will first occur from a band whose mean circumference is 2h. In contrast to the previous case, differential current elements diametrically

opposite are out of phase since the elements are now separated by one wavelength. Moreover, t he primed and unprimed current elements are out of phase, hence the radiat ion pat tern has a n u l l along the axis normal t o t h e plane of t h e spiral. And f ina l ly , the rad ia t ion is circular ly polar ized i n t h e v i c i n i t y of the spiral a x i s and e l l i p t i - cally polarized for off-axis angles.

I 111. Antenna Parameters

For t h e dual-arm Archimedian spiral, fou r curves define the boundaries of t he two conductors. The equations are of the fonn

p = a e + b

where p and 8 are conventional polar coordin- ates, and a and b are arbitrary constants. A l l four curves have the same va lue for the rate of growth parameter a, but dif ferent values of the parameter b. In general, the second conduc- t o r i s generated by ro ta t ing the first conductor 180 degrees about the origin. If b l and b2 are the parameters of two curves which define one ann of the sp i ra l , then W = I b2 - b l i i s the width of t he conductor. In general the parameters a r e chosen so t h a t t h e antenna is se l f complemen- tary, i.e., the conductor width is equal t o t h e spacing between conductors. For th i s case a and kr sa t i s fy the re la t ionship a = 2W/n.

The most common applications of s p i r a l an- tennas have occurred where f lush mounting, l a rge bandwidths, c i rcular polar izat ion, and small s ize a re needed. In near ly all of these applications the bidirect ional radiat ion pat tern of t h e s p i r a l element i s undesirable. For this reason, t he most familiar configuration consists of a spiral ele- ment mounted at the mouth of a closed-back cavity. From a design point of view the problem is t o es- t ab l i sh t he optimum parameters, i.e., conductor spacing, spiral r a t e of growth, s p i r a l diameter, cavity dimensions, and feed structure. Unfor tu- nately, a complete solution has not been obtained; ins tead , the e f fec ts of the various parameters are described i n terms of t he band theorg, and sane experimental verification i s given. The experi- mental data, together with consistent explanations, should serve as a guide t o f u r t h e r performance im- provements.

A. Cavity or Spiral Eiameter - --- For sp i ra l d iane ters smaller t h v l X/n, t he

simple band theory tel ls us t h a t t h e antenna gain should be low, increasing with diameter, and assymptotically approaching some upper limit f o r diameters much greater than X/n. This i s i l l u s - t r a t ed i n F igu re hA i n which the absolute on-axis s p i r a l antenna gain, r e l a t i v e t o a l i nea r i so t ro - pic source and normalized t o t h e average axial ra t io , is shown for various diameter over wave- length ra t ios . The curve represents a compil- a t ion of data taken on a la rge number of s p i r a l antennas operating over the frequency range of about 200 t o 4000 mc/sec.

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When the spiral outer terminals are e i t h e r short-circuited or l e f t open-circuited the band theory tel ls us tha t t he axial r a t i o should become progressively larger as the spiral d iameter is re- duced, approaching l inear po lar iza t ion as the spi- ral degenerates to a simple dipole. This e f fec t i s i l l u s t r a t ed i n F igu re b.

By way of explanation, recall that energy t ravers ing the sp i ra l outward from the or igin will be radiated as circular polarization, say clock- wise. The percentage of the input energy which is radiated on this "first pass" i s r e l a t e d t o t h e physical diameter of the sp i ra l . That energy which i s not radiated proceeds on to the t e rmina ls where it i s re f lec ted and directed back t o t he origin. O f the energy reflected, some is again radiated (but in the reverse or counter-clockwise sense) and the remainder appears at the input terminals. The s i tua t ion now exists i n which the s p i r a l is radiat ing c i rcular ly polar ized energy of a clockwise sense and at t h e same tine i s radiat- ing energy of a counter-clockwise sense. The net e f f ec t is tha t t he r e su l t an t f i e ld w i l l be e l l i p - t i ca l ly po la r i zed , o r i n t he extreme case in which D .e X/n, essent ia l ly l inear .

It i s in te res t ing to cons ider the e f fec t of terminating the spiral outer ends with resistors or absorbing material. The most dramatic result i s the improvement i n a x i a l r a t i o f o r small D/X r a t i o s as shown in Figure 5. Note t h a t t h e an- tenna gain i s unaffected by the loading. T h i s re- sult i s primarily due t o t he manner i n which the gain was normalized; i.e., it was normalized t o the average axial ra t io . The explanation of these resu l t s fo l lows d i rec t ly from the previous discus- sion. The poor ax ia l r a t i o results from "second pass" radiation which i s of the reverse sense. For a given polarization, this f i e l d e i t h e r adds t o o r subtracts from the main or first pass radiation, a l t e r ing t he axial ratio while leaving the nomal- ized gain unchanged.

Thus fa r no mention has been made of t he actual cavity diameter. Certainly, the cavi ty diameter must be equal t o o r g rea t e r t han t he sp i - r a l diameter and, i n f a c t , n e a r l y a l l s p i r a l an- tennas are bui l t wi th equal spiral and cavity diameters. If the cavity diameter i s made too large, higher order coaxial and/or waveguide modes nay be exc i ted in the cav i ty which would result i n pa t t e rn de t e r io ra t ion i n t he v i c in i ty of t h e cavi- t y resonances. S t i l l +o the r l imi t a t ion on the spiral diameter i s the th i rd rad ia t ing band which appears when the circumference is 3X. Using the same reasoning as before, one can describe i ts radiation, and then determine the nature of the net pat tern which would result if both first and third band radiation exist.

I n summary, it can be s ta ted that : (1) The cavity diameter should be cho-

( 2 ) Too small a cavity diameter results sen equal t o t h e s p i r a l diameter.

i n reduced gain, increased VS'& and increased e l l i p t i c i ty r a t io .

(3) Too great a cavity diameter results i n pa t t e rn d i s to r t ion due to higher order mode ex- c i t a t ion of the cavi ty and/or the third radiat ing band.

B. Cavity Depth - -- The e f f ec t of cavity depth on the gain of t he

spiral antenna is i l l u s t r a t e d i n F i g u r e 6; again t h e measured gain has been normalized t o t h e aver- age axial r a t i o and is corrected for input V W R . This da ta c lear ly i l lus t ra tes the second limita- t i on of the operating bandwidth of a cavity-backed s p i r a l antenna. In terms of tolerable reduction i n g a i n a t the band edges, say 3 db, the usable antenna bandwidth is limited t o about 3.3:1 due t o the cavi ty depth.

The e f f ec t of the cavity depth on the behav- i o r of t he spiral antenna is seen t o be analogous to the dipole over a ground plane. I n terms of the dipole behavior, the on-axis gain is propor- t i o n a l t o sin(2rrD/X), where D i s the d ipo le t o ground-plane spacing. Thus, the gain gradually increases to a maximum a t a spacing of Xh and thereaf ter decreases to a minimum a t a spacing of X/2 - corresponding t o a split beam pattern with a null on-axis.

- ---- C. Sp i r a l Rate of Growth It will be reca l led tha t the development of

t h e simple theory merely required that the spiral be t i gh t ly wound; i.e., a small r a t e of growth. Intuit ively, one might expect that for an annular r ing of given width and mean diameter equal t o X/., an increase percentage of the input power w i l l be radiated f rm this r ing as the number of tu rns is increased. Less power i s then available at the mter terminals of t h e spira3, and conse- quently, the total energy i n the radiated f ie ld having a reversed sense is reduced. The axial r a t i o should, therefore, be reduced as t h e s p i r a l is wound more t igh t ly .

The reduced ax ia l ra t io has been experi- mentally verified. The chief question which still remains relates t o t h e e f f e c t of increasing the number of tu rns on the antenna gain; the reduced axial r a t i o could a lso be a t t r i b u t e d t o t h e ad- d i t i ona l loss associated with the increase in the e lec t r ica l l ength of t h e antenna. Measurements made on several spirals having different rates of growth have not shown suf f ic ien t ly d i f fe ren t ga ins t o warrant a positive conclusion.

It appears that a conclusion compatible with the intuit ive reasoning can be drawn f romthe da t a shown i n Figure 7. These curves were obtained by very careful ly probing the e lectr ic f ie ld a long the surface of two s p i r a l antennas. Note t h a t f o r a given radial distance, more energy is associated with the spiral having the greatest number of turns; therefore, the reduction in axial r a t i o is not associated with a corresponding reduction i n gain.

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- D. Dielectric Material There has been some confusion as to the char-

a c t e r i s t i c s of the dielectr ic base material which should be used for these printed circuit antennas. In pa r t i cu la r , it was observed that f o r a given aperture s ize and number of turns, lower axial ra- t i o s are obtained using epoxy f iberg lass (tan 6 = .02) as opposed t o t e f l o n f i b e r g l a s s ( tan 6 = .002).

One explanation of these observations follows d i r ec t ly from the previous discussion. We have already noted that axial ra t ios g rea te r than unity have been a t t r i bu ted t o r e f l ec t ions from the spi- ral outer terminals which are radiated with the "wrong" sense. Consequently, increasing the loss in the para l le l t ransmiss ion l ine w i l l reduce the energy available for reflection.

St i l l another explanat ion i s based on the fact that an increased l o s s tangent i s generally associated with an increased dielectric constant. Consequently, t h e phase velocity of the surface wave might be reduced, thereby effectively enlarg- ing the e lec t r ica l s ize of t h e antenna.

There are two fac to r s which tend t o f a v o r t h e former postulate. First, data on spiral antennas printed on high dielectric constant material have indicated only very small reductions in antenna size. And second, the phase velocity of t he printed two-wire transmission l ine formed by t he s p i r a l conductors i s not s ign i f icant ly d i f fe ren t from t h a t of free space regardless of the dielec- t r i c cons t an t of the base material. If the con- ductors were completely embedded in the d ie lec t r iq the s i tua t ion would be somewhat d i f fe ren t ; how- ever, any improvement would probably be more than of fse t by the decrease in antenna gain.

In order to obtain experimental verification of t he above reasoning, a check was made a t 1000 mc on two s p i r a l antennas which were ident ica l ex- cept for the dielectr ic base mater ia l . The t e f lon fiberglass antenna appeared to have about 1/2 db more gain than the epoxy f iberg lass unit (X?D!A grade G10). Since t h i s measured difference might well be within the limits of experimental error, a t h i r d antenna was fabr ica ted in which the sp i r a l was printed on both sides of the tef lon base material. The resul t ing increase in gain of one db over the epoxy unit i s s igni f icant and lends fu r the r credence t o t h e f i rs t explanation.

E. Conductor FJidth and Spacing - O f all t h e s p i r a l antenna parameters, t he

conductor width and conductor spacing appear t o be the least c r i t i c a l ; t h e major consideration being to ob ta in t he m a x i m u m number of turns within the allocated space. In general , the spirals are con- structed so that t h e r a t i o of conductor width t o conductor spacing is unity; i.e., the antenna is self-ccnnplementary. For the most par t , it seems th is choice i s based on precedent, and probably stems from the f ac t t ha t t he i npu t impedance of t h i s c l a s s of antennas has been calculated t o be about 180 ohms. Since the antenna is generally

fed from a 50 ohm l ine , it appears that a r a t i o other than unity would be more desirable . In other words, the impedance matching problem might be greatly simplified if the input impedance of the spiral antenna were reduced by making the ra- t i o of conductor width t o conductor spacing some- what greater than unity.

F. Antenna Feed - -- The entire operation of t h e s p i r a l a n t e m a i n

its noma1 mode was postulated on the bas i s of an ideal, balanced, two-wire feed structure. Kow consider the effects of a prac t ica l feed system and assume tha t the feed itself does not radiate. For i f the feed does radiate as a monopole, t h e far f i e ld pa t t e rn will consist of the feed radi- a t ion ( l inear polar izat ion) and the spiral radi- a t ion (c i rcular polar izat ion); the resul tant pat- t e rn will be ell iptically polarized, asymmetrical with respect to the spiral axis, and with appreci- able boresight error.

There are two cases which should be con- sidered: (a) The case i n which the two-wire l i n e s are carrying currents 180 degrees out o f phase but of unequal amplitudes; and (b) The case i n which the currents are of equal amplitude but with a phase relationship other than 180 degrees. Both of these can be t rea ted by r eca l l i ng t he first two sp i ra l rad ia t ing modes: the noma1 mode a r i s ing from an odd excitation (plus-minus) and the sp l i t - beam mode a r i s ing from an even excitation (plus- plus). Two current vectors of a rb i t r a ry amplitude and phase can always be resolved in to four vec- to rs , two which a r e i n phase, and two which a r e i n phase opposition. Therefore, any amplitude or phase e r r o r i n t h e f e e d can be treated as a l i n e a r superposition of even and odd excitations.

The energy i n t h e odd exc i ta t ion w i l l r ad ia te a t a diameter of X/n, while the energy i n t h e even exc i ta t ion will radia te a t a diameter of 2X/n. If the diameter of the spiral i s l a rge e- nough t o support both modes, the result ing radi- a t i o n f i e l d will be the supemosi t ion of a nom-al beam and a two-lobed beam with a nul l on-axis. Since the relative phase of t h e e l e c t r i c f i e l d i n the lobes of the two-lobed pa t te rn i s 180 degrees, t h e f i e l d s of the two modes will tend t o add on one s ide of t h e axis and cancel on the other. The e f f ec t is that the pa t t e rn cu t s a r e no longer sp- metrical with respect t o t h e axis, but are skewed t o produce a boresight error or pattern squint.

In the event that the spiral d iameter i s not la rge enough t o support the split-beam radiation mode, tha t por t ion of t h e energy contained i n t h e even exc i ta t ion will be reflected and appear a t the input as an increased VSWR unless it i s ab- sorbed a t the spiral outer tenninals .

In summary, improper exc i ta t ion of t he spiral antenna can give rise t o p a t t e r n dissymmetry and pattern squint. Squint w i l l occur i f the feed l i n e s themselves radiate or i f t he two-wire feed l i n e is not balanced. In the la t ter case, however, squint will be observed only i f t h e s p i r a l diame- t e r is suf f ic ien t ly l a rge to suppor t the sp l i t -

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.

beam mode. T h i s s i t ua t ion is easily recognized by noting a sylrrmetrical pa t te rn a t the low frequen- c ies with a gradual dissymmetry occurring at the higher frequencies.

G. Square Versus Round Spi ra l - ---- In all of the previous discussions only t h e

conventional Archimedian or round spiral was con- sidered. It i s w e l l known, however, that similar arguments can be used t o describe the behavior of the square counterpart of t he Archimedian sp i ra l . 'Zistorically, work on square spirals considerably lagged the circular configuration. This resulted, no doubt, from the per fec t ly normal aversion t o the tremendous number of apparent discontinuities i n t h e square configuration. However, the magni- tude of these discont inui t ies i s small, and t h e spacing between them is small and progressively d is t r ibu ted in the reg ion pr ior to the rad ia t ing band. Within the radiating band, the discontinui- ties are spaced very nearly one-quarter wavelength apar t so that the re f lec ted components cancel.

A comparison of a square and round s p i r a l i s shown i n Figure 8. The d i f fe rence in measured gains may be explained by r eca l l i ng t ha t t he first radiation band occurs when the circumference of t h e s p i r a l is one wavelength, corresponding t o a diameter D = h/n f o r t h e c i r c u l a r spiral and a width W = l./L for the square spiral . Comparable gains are obtained when the width of the square s p i r a l i s about 75 per cent of the diameter of t he c i r c u l a r s p i r a l as can be ver i f ied from the figure.

IV. Antenna Characterist ics - - A. Experimental Results

We have previously considered the various de- sign parameters as they affect the behavior of t he cavity-backed Archimedian spiral antenna. In this section experimental data are presented t o i l l u s - t r a t e t he t ype of performance which might reasona- bly be expected from these antennas operating i n a r e a l environment, and subjected t o t h e c o n s t r a i n t s imposed by fabrication techniques and mechanical considerations. The spiral data presented are typ ica l of that obtained on many di f fe ren t models at frequencies ranging from 200 mc t o LOOO mc; frequency bands considered were of the order of two t o one. The specific data presented were ob- tained with a unit three inches in diameter, one inch i n depth, and printed on epoxg f iberg lass NEMA grade G10.

Data showing the frequency dependence of the input impedance, axial ra t io , and beamwidth of an S-band s p i r a l antenna are given i n Figure 9. It should be noted that over the octave range the on- a x i s e l l i p t i c i t y r a t i o i s less than 3 db, the in- put VSWR is less than 2:l and t h e beamwidth varies between 60 and 80 degrees. These values appear t o represent a comfortable goal f o r t h e antenna de- signer and a reasonable specification for q&em design purposes. One should not conclude that more stringent requirements could not be met, but ra ther that any fu r the r improvement would require appreckably greater mechanical tolerances and uni-

formity of the d ie lec t r ic base material.

Figure 10 i l l u s t r a t e s t he t spe of rad ia t ion pa t te rns which have been obtained. The data were taken for two orthogonal cuts with the antenna im- mersed i n microwave absorbing material t o simulate freespace operating conditions. There are three important points which should be emphasized. The first r e l a t e s t o t h e range of azimuth angles over which t h e e l l i p t i c i t y r a t i o (E@/Ee) remains comparable t o t h e on-axis r a t io ; f o r the case il- lus t r a t ed , t he e l l i p t i c i ty r a t io remains less than 1 db over an azimuth angle of greater than 2 60 degrees. In l i g h t of the da ta shohm i n Figure 9, it i s obvious tha t there are other pat tern cuts which are not quite s o dramatic as the ones se- l ec t ed fo r i l l u s t r a t ion . However, i n no case did the e l l ip t ic i ty ra t io wi th in the angles of 2 60 degrees exceed the on-axis r a t i o shown i n t h e f igure .

In most l i t e ra ture dea l ing wi th c i rcu lar ly polar ized antennas, e l l ipt ic i ty ra t io i s taken as one of the primary c r i t e r i a f o r judging the quali- t y of t h e antenna; reference i s seldom made of the corresponding f igu re f o r off-axis angles. Tlhereas this prac t ice might be adequate f o r many t p e s of antennas, on-axis data alone can be very mislead- ing when app l i ed t o t he flush-mounted s p i r a l an- tenna. It i s q u i t e c m o n t o observe a low on- axis rat io while having excessively high ellip- t i c i t y r a t i o s f o r off-axLs angles well within the usable antenna beamwidth. Lvproper feed, 'higher order band radiation, or a combination of the two w i l l coctribute t o this effect .

The second p o i n t r e l a t e s t o t h e symmetry of the pat terns about the axis of the antenna; the beam i s aligned with the antenna boresight axis. The importance of a well-designed balanced feed i n mbimizing boresight cannot be overemphasized. Without a well balanced, non-radiating balun, it is vifiually impossible to achieve zero boresight error.

Finally, a word of caution. The symmetrical pa t te rns shown were obtained i n a simulated free space environment. The presence of even a la rge ground plane may adversely affect these patterns. For example, t h e same antenna when f lu sh mounted i n a square ground plane approximately 10 wave- lengths on a side exhibited non-symmetrical dif- f ract ion lobes a t an azimuth angle of about 60 degrees. Increasing the size of t he ground plane or using a cy l indr ica l s t ruc ture w i l l , of course, move t h e a s p m e t r y t o even greater angles. The important point, however, is t o recognize that the spiral antenna i s a broad beam radiator, and as such i ts pa t t e rn can be adversely affected by t h e presence of a ground plane.

B. - By fa r t h e most important single parameter i n

obtaining satisfactory spiral antenna performance i s the antenna feed or balun. The discussion would, therefore, be incomplete without some men- t i o n of the type of b a l m s which can be used; and in par t icular , the balun which was used i n t h e

88

experimental antenna described.

The l l i n f in i t e balun1t, widely used with equi- angular spirals, i s not par t icular ly appl icable here but i s worthy of mention because of i t s u t t e r simplicity and excellent performance. It cons is t s of nothing more than a coaxial l'ine which follows the curve of one sp i r a l am; the outer conductor i s soldered t o this ann and the center conductor i s soldered to the second arm which generally con- t a i n s a dummy coax ia l l i ne fo r symmetry.

The most comon method of exci t ing the Archi- median s p i r a l i s from a small section o f r i g id co- axial transmission l ine extending into the cavity structure; the center conductor is fastened t o one arm of t h e s p i r a l and the outer conductor i s fas- tened to the other . properly taper ing this cc- axial l i n e , s u y r i s i n g l y g o d impedance and ax ia l r a t io cha rac t e r i s t i c s can be obtained over an oc- tave frequency range. The main d i f f i cu l ty , how- ever, stems from the f ac t t ha t t he f eed i t s e l f radiates , g iving r ise to considerable pat tern dis- symmetry and correspondingly large ell ipticity ra- t i o within the beamwidth of t he antenna. Bore- s igh t e r rors in the o rder of 15 degrees f o r some polar izat ions are not a t a l l uncmxon.

Obviously, any and all baluns such as might be used to exc i t e a dipole o r a two-wire trans- mission l i n e can be used with a spiral . These ba- luns are wel l descr ibed in avai lable l i terature and will not be discussed here. Instead, a novel p r i n t e d c i r c u i t b a l d @ i s briefly described which affords much i n t h e way of ease of fabrication, miniaturization, and f l ex ib i l i t y . The exploded view of a sp i r a l antenna assembly shoTm i n Figure 11 i l lus t ra tes the s impl ic i ty and compactness of the feed design, while a simplified draming of t h e balun i s sham i n Figure 12.

A s seen from the f igures, the balun i s fabr i - cated in unshielded strip transmission l ine; the photo-etched c i r c u i t i s sheared t o t h e p r o p e r s i z e and so ldered d i rec t ly to the sp i ra l and balun holder. The en t i r e assembly i s then dropped into a keyed ho le i n t he bo t tm of the cavity.

It can be seen that two types of transmission l i n e s a r e involved. First, the conventional un- balanced, unshielded s t r ip t ransmiss ion l ine con- s i s t i n g of the thin ccnductor over the ground plane. And second, the balanced line formed by t h e s p l i t ground plane,

The re su l t s of t he work on these pr inted c i r - cuit baluns will soon be published i n t h e PSfTT.

It i s s u f f i c i e n t t o say that the feed has been successfully used with spiral antennas a t frequen- cies ranging from 200 mc t o over bo00 mc with ex- cel lent resul ts . Over an octave frequency range, e l l i p t i c i t y r a t i o s o f less than 3 db have been maintained over azimuth angles greater than 2 60 degrees, boresight errors have been v i r tua l ly e- liminated, and standing wave ratios of less than 2:l have been realized.

References

1. J. A. Kaiser, tlScanning Arrays Using F la t Spi- ral Antenna,!! Naval Research Laboratories Re- por t 5103, March 1958.

2. J. A. Kaiser, !!Spiral Antennas Applied t o Scanning Arrays,l! Electronic Scanning Symposi- um, Air Force Cambridge Research Center, Apr i l 1958.

3. J. R. Donnellan, "An Eight Spiral Doublet Electromechanical Scanning Array," Naval Re- search Laboratories Report 5383, April 1959.

11. S. R. Jones and E. M. Turner, rlPolarization Control with Oppositely Sensed Circularly Polarized Antennas,!! National Conference on Aeronautical Electronics, Dayton, Ohio, 1959.

5. E. M. Turner, '!The Impact of the Spiral An- tenna and Its Derivatives on the Design of Antennas and the Weapon System,!! National Conference on Aeronautical Electronics, Dayton, @hio, 1958.

6. W. L. Curtis, !!Spiral Antennas,11 K.S.E.E. The- sis, University of Washington, June 1958.

7. V. H. Rumsey, Informal Presentation given a t the URSI International Symposium on Electro- magnetic Theory, University of Toronto, June 1959.

8. B. -H. Burdine, "The Spi ra l Antenna,11 Massachu- s e t t s I n s t i t u t e of Technology, Research Laboratory Technical R e D O r t , April 1955.

9. J. D. Dyson, "The Equiangular Spiral Antenna,!! University of I l l i n o i s Antenna Laboratory Technical Report KO. 21, September 195'7.

10. R. Eawer and J. J. I+Jolfe, "A Printed Circuit Balun f o r Use with Spiral Antennas,!! i n t e rna l report, Aero Geo As t ro Corporation, t o be pub- l i shed i n IFE Trans on Microwave Theory and Techniques.

89

Fig. 1. Dual arm spiral antenna geometries.

Fig. 2 . The normal mode or first radiation band.

90

ry 0

- 2

91

0

-2

v 8 -h

3 -6 e

-12

- X X Terminals Loaded e Teminals Open-Circuited

-

- / /

I .23 .25 -27 .29 .31 .33 .35

cavity nismeter ( n h )

.23 .25 .27 .29 .31 .33 .35

cavity Diameter ( ~ h )

Fig. 5. Effect of loading the spiral conductors at the outer terminals.

0.0 0.1 0.2 0 . 3

Cavity Depth (Sh)

Fig, 6. Effect of cavity depth.

92

0 .5 .? .9 1.1 1.3 1.5 1.7 1.9 2 ;1

P.adial Distance (Inches)

Fig. 7. Field distribution along spiral surface for two growth rates.

.23 .25 .27 .29 .31 .33 .35 .37

3 -0

2.5

2.0

1.5

1.0

z '23 .a5 .27 .29 -31 .33 .35 3 7

Cndty Mameter ( O h ) or A d t h (Wh)

Fig. 8. Comparison of square and round spiral antennas.

93

0

R N <

P

94

Fig. 11. Exploded view of spiral antenna showing printed-circuit balun.

L

Dielectric

conductor

SECTIm' A-A

Fig. 12. Simplified drawing of the printed circuit balun.

95