JO URNAL OF RESEARCH of the National Bureau of Standards- D. Radio Propagation Vol. 66D, No.1, January- February 1962

A Survey of the Very Wide Band and Frequency Independent Antennas-1945 to the Present

John D. Dyson

Contribution from University of Illinois, Urbana, Ill.

(Rece ived August J 6, 196J )

Thc last few years havc \\'itnessed major developments in t he field of a ntenn as whi ch are suitab le for use over a ran ge of frequ en cies. Operatin g bandwidths t hat \\'ere co nsid ered an impossibility as little as seven years ago are now readi ly ava ilable.

To trace t hese developments, a brie f historical survey of t he li terature in th is fi eld since the Second World War, is presented .

1. Introduction

Th e PltSt two decades haNe witnessed a rapid ex-t tension of that portion of th e eledromagnelic fr e­

q uenc.\· spectrum that is useable 1'01' cOlllmlmicaLioll purposes . Wi th t his portion of Lhe spectrum ex­pand ed to a range of oveL' 10 7 to one, and with presen t applications r equiring eonLinuous coverage of large portions of this specLrum, it is not surpl'isinf! tha t a gL' eat dNtl of time and efIor t havc been directed Lowa.rd the developmcnt of the p hysical equipmen t to provide this coverage . One 0[' Lbe serious clraw­b/1.cks to a.ny simpli6 ed solu tion has been the ex­trem!" limi ted bandwid ths obtainable wilh boLh Lh e receiving and transmitting equipment and th e anten­nas r eq uired to successfully lau nch and receive Lhe electromagnetic r H,diation. R ecent developments , of which the tr/weling wave tubes a rc of Hote, h ave so mew)m t alleviated th e first por tion of this problem.

I Th is survey is concern ed with the latter portion of t he problem, the development of antennas which are cl1.p/1. ble of being operated over a very wid e range of frequencies.

As 'World War II came to n close, the ge ner al stt"tLus of r esearch and development in the field of l1.l1.tennas had led to a fe'''" structures that wer e capa­bl e of being operated over a 2 to 1 or sligh tly greater range of fr equencies wi th acceptable radinLion an d impedf1.l1.ce characterisLics. In a majority of cases, it was the radical changes in the radiation pnttern wi t h cht1.nges in op en"tLing fr equency, which limited the usefuln ess of' antenn as Lo somewhat less than this range. Antennas had been developed with an input impcdance that remained relatively constant with n change in fl'equenc~7 .

In a discussion of an tennas intcnd ed to be used OVe L' a m nge of' fr equencies one is immediately faced wiLh a problem in terminology. Such an tennas have been referred to as " broadband antennas." The term broadband, however, is a rather nebulous term. It has been l1.l1d is still b eing very loosely applied. In t he usual sense it has been appli ed to antennas whose rad iaLion and inpu t impedance chnracteristics

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were acceptable, alLhoug h noL nec essfl,l'ily constant, over 11, f reque nc~' r/1.nge LhaL may be anyLhing from 17~ to 2 to 1.

In con tn1.s t Lo these antennas, this survey has been limiLed to a ll te nnas which /"Lt'e useful over f1t least n 4 01' 5 to 1 r ange of frequencies . Thus, nl though this is cer tn.inly 11, broad bf1.nd of frequencies it might be pref ermble to ref or Lo them n.s "vc ry wid e ban d" an Lenn as.

2. Discone

Probabl~' olle of the firs t of th e Ycry wide band antennas was the cliscone anten na proposed by Kandoian [1946]. IL wa a departure from prior antennas in that it could be used over approximately a 4 01' 5 to 1 range of frequencies. However, advances in the field during Lhe next 7 or 8 years, were, in the main, limi ted to increasing the band­widtb of existing types of ant.ennas by a few percent. The one exception during Lhis period was a modified helical antenna investigated by Springer [1949] and later by Chatterj ee [1953, 1955]. These unbalanced conical helical structures fed agains t a ground plane had acceptable pattern bandwidths of' 4 or 5 Lo l.

3. Archimedes Spiral

In 1953 a major step forward \ms taken wben Turner [1955] proposed the first spiral antenna. This antenna consisted of two flat, rather narrow, constant width m etalli c arms, wound in Lhe form of an Archimedes spiral. Fed at the center in a b alan ced m anner it radia tes a broad circularly polarized lobe on each side 0[' Lhe plane of tbe an­tenna. Subsequent investigations and development of this antenna produced forms that had stable pattern and impedance characteristics over band­widths up to 10 to 1 [Burdine and M cElvery, 1955; Bmdine and Zimmerman, 1955: Jones and T mner, 1959; Curtis, 1960 ; Kaiser, 1960; Bawel' and Wolfe, 1960 ; Donnellan, 1960, 1961; Donnellan and Close, 1961].

4. "Frequency Independent" Antennas­Equiangular Spiral

In 1954, Rumsey, applying a theory that an antenna specified entirely by angles would have characteristics which are independent of frequency, suggested that an infinite length structure based upon the equiangular or logarithmic spiral could be specified completely in terms of angles. He pro­posed that a finite structure be studied. Subsequent investigation of a balanced planar antenna based upon these curves disclosed the equiangular spiral antenna to be the first antenna to have, in a practical size, the characteristics which could be associated with an infinite structure [Dyson, 1955, 1957J . Thus it became the first of a class which might b e called "frequency independent antenn3s" [Rumsey, 1957J.

The introduction of the term "frequency inde­pendent" adds to the terminology problem . It is b eing used, however , by the author and others, in the sense that, since the upper and lower frequencies at which these antennas Imay b e operated are determined by independent parameters, the band­width over which the radiation pattern and input impedance ch aracteristics are essentially contstant is theoretically unlimited. In actuality it is limi ted only by practical considerations of construction, and antennas have b een constructed to operate over a b andvvidth of more than 42 to 1. There is no fundamental reason ",,-hy this could not b e extended.

The general philosophy behind the equiangular spiral antenna is to design a radiating structure such that successive applications of a scaling factor results in structures which ar e identical with the original, or which at most , differ by some rotation about an

FIGUR E 1. Balanced planar equiang1tiar or logarithmic spiral slot antenna.

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axis through the origin of the original structure. Al­though the structure must be infinite in size to fulfill the scaling condition of exact equivalence, it has been found that forms based upon the equiangular (or logarithmic) spiral curve may be truncated to a finite size and still retain, over an extremely wide range of frequencies, the char acteristics that would be as­sociated with the infinite structure.

5. Logarithmic-Periodic Antenna Shortly after the investigation of the equiangular

spiral geometry was initiated, DuHamel proposed that it should also b e possible to force radiation from otherwise angular structures by the use of periodic discontinuities [DuHamel and I sbell, 1957; DuHamel, U.S. Patent No. 2,985 ,879J. This led to a form of linearly polarized antenna which had pattern and im­pedance characteristics which would repeat periodi­cally with the logarithm of frequency. Thus al­though these "logari thmic-periodic" an tennas scale exactly at only certain discrete frequencies, they can be designed so that t he radiation characteristics do not change appreciably over the period between these frequencies. H ence they also exhibit nearly fre­quency independent characteristics.

6 . Versions of the Equiangular Spiral Many versions of these log-spiral 1 and log-periodic

antennas have been developed in the last few years. The planar log-spiral antenna shown in figure 1, is a bidirectional antenna, radiating a broad circularly polarized beam on each side of, and perpendicular to , the plane of the antenna. The antenna may be made unidirectional by an orthogonal proj ection of the b al­anced spiral arm s upon the surface of a cone as shown in figure 2 [Dyson, 1958a, 1958b , 1959 ; Dyson , U.S. Patent No. 2,958 ,081]. For included cone angles less than about 45 deg, radiation is confined to one broad circularly polarized lobe wi th maximum radia­tion off the apex of the cone. The antenna is a balanced structure with the feed voltage applied between the two arms at the apex of the cone. This feed voltage may be supplied by a conventional balanced line carried along the axis of Lhe cone or by a coaxial line and balun. The characteristics of these antennas permit a third m ethod. The feed line, a coaxial cable, may be carried along and soldered in con tact with one of the arms. Because the ampli­tude of the antenna curren ts on the arms (and also on the outside of the cable) fall off rapidly with dis­tance from the apex, the ends of th e arms where t he cable enters carry negligible antenna current. This optional feed conveniently and automatically pro­vides a frequency-independent b alun, permitting feeding the balanced antenna by means of an un­balanced line.

Conical log-spiral antennas h ave been constructed to operate over more than 40 to 1 band wid ths. Again this bandwidth is at the discr etion of the designer. The upper useable frequency being deter ­mined by the truncated region at the ap ex which

1 A convenient abbreviation for logarithmic spiral. a synonym for equiangular spiral.

FIGURE 2. Balanced conical logarithmic spiral antenna with feed cable carried along one ann.

must remain sillall in terms of wavelengths (less than ~~ wavelength). Th e lowest u cable frequency by the base diameter of the cone which must be on the order of 0.4 wavelength [1,t the lowest fr equency o [ opera tion.

A highly practical version of the conical log-spiral antenna, can be constructed by allowing the expo­nentially expand ing arms to degenerate into rather narrow constant width structures following the logarithmic spiral curve as shown in figme 3. For fairly tightly wrapped spirals this version has characteristics "which are very similar to those of the original antenna. This "wire" version is simple to construct and if th e " infinite balun" feed referred to above is desired, the feed cable itself can become one of the arms with a dummy cable becoming the second arm of a balanced structme.

It is interesting to note that Nussbaum [1958] and Barsky [1959] proceeding from Chatterjee's work in an independent investigation developed a different version of an unbalanced conical helix an tenna. This antenna consists of a single helical conductor formed into a cone and fed against a small disk at the apex of the cone. It radia tes a broad circularly polarized lobe directed off the apex of the cone. This pro­jection of a cylindrical helix, with a judiciously chosen variable pitch angle, onto a coaxially oriented conical surface, r esulted in an antenna which is con­structed in a logarithmic spiral cmve and thus the antenna is usable over very wide bandwidths. 2 The

2 If this antenna were constructed as a hifilar structure with one arm fed against the other it would be identical to the wire ,'ersion of the antennas as reCerted to by D yson.

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FIGU RE 3. Wir e version of balanced conical logarithmic spiral antenna fed with coaxial line and balun along axis of cone.

unbalanced antenna however ha a slight pattern tilt and does not have the excell ent ci.rcular polar­ization off the axis of the antenna, or the sta ble input impedance that is characteristic of the balanced two arm conical log-spiral antenna.

Multiarm versions of the balanced conical log­spiral n.ntenna cn.n be constru cled to provide opera­tion in several distinct modes [Dyson n.nd :Mayes, 1960a, 1960b, 1960c; D yson, 1961a]. Thus n. four arm symmetricn.l structure may be cxicted to radiate an n.xial beam with an e± j</> variation. i.e., the phase of the far field varies linearly with the azimuthal angle <p , around the antenna. 'It may also be exietecl to produce a conical bemn with an e±j2</> and f1 conical beam with an e± i3</> variation. Since the orientation of th e maximum of the conical bemn may be con­trolled by a variation in the rate of spiral of the antenna arms, it may be positioned perpendicular to the axis of the antenna to provide a simple very wide band circularly polarized omnidirectional source.

The complex coefficien t of coupling and charac­teristics of the conical log-spir al antennas in simple arrays have been investigated [Dyson, 1961b].

7. Versions of the Log-Periodic Structure The log-periodic antennas have been extensively

investigated [Mayes, Isbell, and Carrel, 1958]. ] sbell [1958] demonstrated that the planar antenna could

J

be modified to provide unidirectional patterns by forming the two clements of the antenna into a "V." DuHamel and his associt),tee developed a wire version of the log-pcriodic antennas and demonstrated their capabilities in ;LI'I'a~TS ;md as feeds for' reflectors [DuHflmel and BelT~', 1958, 1959: DuHfJmel and Ore, 1958, 1959]. Isbell [1959a] constructed a log-periodic feed for a 28-[t parabola. The near fields on the log-periodic structure were studied by Bell, Elfving, and Fmnks [1960]. Elfving [1961] has considered the des ign of these structmes.

A simple form of log-periodic structure is the log­periodic dipole army proposed by Isbell [1959b]. In this alTay shown in figure 4, t he length of each ele­ment bears a fixed ratio to the length of the preceding element [tnd the adjacent element spacings bear the same ratio ODe to [tl1otbel'. From the principle of scaling, the pa ttem and imped;mce characteristics of the array at [requenc~T f n, such that the nth element is resonant, will be repeated at a higher frequency ! n+ l, which makes the ,11 + 1)t11 element resonant. The characteristics l'epea,t periodically at all fre­quencies given by Tnf, where 11 is an integer and T the ratio or the lengths ol ;Ldjacent elements. When excited with a 180 0 phase shif t between elements it radiates a single-lobe linearl." polarized beam direct.ed toward the apex of the an·a.,' . An analysis and design information fo]' this arm." h,lS been pres en ted by Carrel [1960 , 1961].

In an extension of this work, Berry and Ore [1961] investigated a log-periodic monopole array in which they have used simple reactive networks to produce the proper monopole current, amplitude, and phase

FIGURE 4. Logarithmic periodic dipole a1·ray.

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distributio n for unidircc(,ioJ1fll f]'equenc~'-independcnt operation.

The log-periodic resonant-F al'm~' shown in figure 5, developed by .\IIayes and Carrel [1960a], was designed to operate ill several different modes . In the lowest order modc the perfornmnce is approxi­matel.,' that of the log-periodic ;tl'l'ay. The active portion of the an(,el1lltt cen tel'S around those dements whose lengths are ne,),l' H baU-wave-lengtll at the frequ ency of opemtion. As the rrcquenc~' of opera­tion is in creased this active region moves toward the apex. The ,tlltellll<1. Ill a.,' be designed such t llHt as the 'A j2 region moves ofi' the a.pex or the antenna the large clemen ts on the othe r eud are approaching fI 3'A j2 1'eS011ancc. Thus rts the frequency of operation is increased s till further the active region moves through the array in the3A/2 wavc modil, then in the 5t..j2 mod e, etc. This scheme permits useable band­widths up to 20 to 1 or more with only relatively small uns(,able intervals interspaced throughout this range about the mode-traneition frequencies. The forward tilting of the individual elements insures a . unidirectional beam and provides increased direc- i tivity.

It has beell demonstmtecl t hat lllrtny of the log­periodic designs may be optimized to operate over It

moderate bandwidth of 2 or 3 to 1 with a significant increase in directive gain [Ma~ 'es and Carrel, 1960b]. Directive gains in excess of 10 db over isotropic can

FIG U RE 5. Log-periodic 1'esonant- r array.

FIGURE 6. 1-el·tically polari zed IO{I-periodir: zigzag antenna.

bo achieved over broad band wid ths using a small log­periodic zigzag structmo ovor a ground plane, and on the ord er of 18 db over isotropic in the higher order modes of the log-periodic r eso nltnt T1lw tennas. Th 0

zigzag structure was also co nsidered by Carr [1961). Gl'eiser an d M ayes [J 961) have investigated a ver ti­cally polarized log-periodic zigzag stru cture over a ground plane a s hown in figure 6.

8. On the Theoretical Analysis

The new class of antennas which have been termed "frequency ind epend ent" have opened up a new em in wid o band antennas. Operating bandwidths that were considered to be an impossibili ty as little as seven ~-ears ago are now readily available. How­ever , in view of the com.plex geo Llletery involved it is perhaps not surprising that the exp erimen tal a nd empirical developmen t of these antennas ]MS far outstripped the theoretical analysis. The t heor etical problem of the log-spiral antenna hits been attacked by Mast [1958) who calculated the field s due to a logari thmic spiral filament and by Rumsey [1959) who consid er ed the fields produced by an infinite number of planar Jogaritlunic spiral filaments. Copeland [1960) h as obtained an approximate analy­sis for the radiation patterns of the log-spiral antenna with an assumed current distribu tion and Wh eeler [1961) has considered a semicircular geom etry to approximate the spiral cmve. The impedance of ll1ultiterminal antennas was studied by D esch amps [1959) and that of the log-periodic dipole arrays by C<1.rrel [1961).

A new approach which holds promise is to consider the log-periodic antenna as a locally periodic struc­ture whose period varies slowly, incr easing linearly with distance to the origin or apex [M ayes, D es­champs, and Patton, 1961). Such an approach indi­Clttes that th e basic ingredients for a fr equenc~-­independent antenna are a slow-wave transmission med ium and a series of radiating elements satisfying the similarity condition, and which are coupled to th e transmission medium at points spaced in geometric progre s ion . Proper design of such a structure can produce a wave substantially radiated toward the feed point with charac teris tics which vary little as the frequency of operation is varied over extremely wid e bandwidths .

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9. Conclusions

In consid erabl.v less than a decade major changes h ave been wrought in accepted concep ts concerning the usable bandwid th of antennas. Th ere is a great deal yet to be learned about th ese new an tennas but i t can be said that the path has b een opened for fu ture investigation .

Figures 4 and 5 are reproduced with the kind per­mission of R. L . Carrel and figure 6 with the per­mission of J. W . Gl'eiser .

10. References

Barbano, N., Phase center di sLribuLions of spiral antennas, IRE WESCON Cony. R ecord 4, pL. 1, 123- 130 (1960).

Barsky, !-T . S., Broadband con ical hr li x antennas, IRE Kat. Cony. R ecord 7, pt.l, 130- 146 (1959).

Bawer, R ., and J. J. Wolfe, The spiral antenna, IRE Inter­naLional Cony. Record 8, pL. 1,84- 95 (1960).

Bell, R. L ., C. T. E trving, and R . E. Franks, Ncar- fi eld meas­urements on a 10gariLhmically periodic antenn a, IllE Trans. AP- 8, 559- 567 (Nov. 1960) .

BeITY, D. G., and F . R. Or e, Log-periodic monopole array, IRE I nternational Cony. Reco rd 9 (1961).

Burdine, B. H ., and R . M. McElve ry, Sp ira l a ntenna, MIT Research Laboratory of E lectron ics, R eport No. 1 (Mar.

""'1 955) (unpublished). Burdine, B . H ., a nd II . J . Zimmerman, The spiral antenna, ~ MIT R esearch Laborator y of E lectronics, R eport No.2

(Apr. 1955) (u npub li shed). Carr, J . '-IV ., Some variations in log-pe riod ic an tenna struc­

Lures, IRE Tran . AP- 9, 229- 230 (Mar . 1961). Carrel, R. L ., An ana ly is of log-period ic dipole antenn as,

Proc . T enth Sy mposi um , USAF Antenna R esearch and D evelopment Program, Allerton P ark, Monticello, Ill. (Oct. 1960) .

Carrel , R . L ., The design of 10.'2;-periodi c dipole antennas, IRE Internation a l Cony. R ecord 9 (1961).

Chatterjee, J . S., Radiation fi eld of a con ical helix, J. App!. Phys. 24, p. 550 (May 1953) .

C hattcrjee, J . S., Radiation characteristics of a con ical helix , of low pi te h angles, J . Appl. Phys. 26, 331- 335 (Mar. 1955). Copeland, J . R ., Radiation from the balanced conical equi-

angu lar spi ral antenna, T ech. R epo rt No. 903- 12, Con­tract AF 33(616)6211., D cpartment of E lectrical Engineer­ing, Ohio State University (Sept . 1960) (unpubl ished).

Curtis, W. L ., Spira l a ntenn as, IRE T rans. AP- 8, 298- 306 (May 1960).

D escha mps, G. A. , Impedance p roper t ies of co mplementary mu lt i-termi nal p lanar structures, IRE T rans. AP- 7, 3371-3378 (D ec. 1959).

Donnellan, J . R, Second-mode operation of t he sp iral an­tenna, IRE Trans. AP- 8, pp. 637 (Nov. 1960).

Donnellan, J . R ., A spiral-doublet scanning array, IRE T rans. AP- 9, 276- 279 (May 1961).

Donnellan, J. R ., and R . T . Close, A spiral-grating a rray, IRE Trans. AP- 9, 291- 295 (May 1961).

DuHamel, R. H ., U.S. Patent No. 2,985,879 (1958). DuHam el, R . H ., and D . G. Berry, Logarithmi call y periodi c

anten na arrays, IRE WESCON Con". Record 2, pt. 1, 161- 174 (1958).

DuHamel, R. H ., an d D . G. Berry, A new co ncept in high frequ ency antenna designs, IRE Nat. Co ny. R ecord 7, pt. 1,42- 50 (1959).

DuHamel, R H. , and D . E. I sbell , BroadbandlO!l;arithmically periodic antenna structures, IRE Nat. Cony. Record 5, pt. 1, 119- 128 (1957) .

DuHamel, R. H ., a nd F. R Ore, Logarithmically periodic designs, IRE Nat. Con" . R ecord 6, pt. 2, 139- 152 (1958).

DuHamel, R . H ., a nd F . R . Ore, Log-peri odic feeds for lens and reflectors, IRE Nat. Cony. R ecord 7, p t. 1, 128- 137 (1959) .

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D yson, J . D ., The equiangular spiral antenna, Proc. Fifth Symposium on t he USAF Antenna Research and Develop­ment Program, Allerton Park, Monticello, Ill. (Oct. 22, 1955) (classified).

Dyson, J . D ., The equiangular spiral antenna, IRE Trans . AP- 7, 181- 189 (April 1959); also Antenna Laboratory T ech. R eport No. 21, AD- 145019 Contract AF33(616)-3220, D epartment of Electrical Engineering, University of Illinois (Sept. 15, 1957) .

D yson, J. D., U.S. Patent No. 2,958,081 (1959) . D yson, J . D ., The unidirectional equiangular spiral antenna,

IRE Trans. AP- 7, 330-334 (Oct. 1959); also Antenna Lab­oratory T echnical Report No. 33, Contract 33(616)6079, D epar tment of E lectrical Engineering, University of Illinois (10 July 1958a).

D yson , J. D. , The non-planar equiangular spiral antenna, Proc . Eighth Symposium, USAF Antenna R esearch and D evelopment Program, Allerton Park, Monticello, Ill. (Oct . 1958b) .

Dyson, J . D ., R ecent D evelopments in spiral antennas, Proc. IRE Nat. Aero . Elect. Conf., pp. 617- 625 (May 1959).

D yson, J. D. , Multi-mode logari thmic spiral antennas- p os­sible applications, to be published in Proceedings National E lectronics Conference, vol. 17, pp. 206- 213 (1961a).

Dyson, J . D ., The log-spiral antenna in simple arrays, Proc . 11th Symposium, USAF Antenna R esearch and D evelop­ment Program, Allerton Park, Monticello, Ill. (Oct. 1961b).

D yson, J . D :, and P. E . Mayes, New circularly polari zed frequency independent antennas with conical beam or omnidirectional patterns, IRE T rans. AP- 9, No.4, 334--352 (July 1961); also Antenna Laboratory T echnical Report No. 46, Contract AF33 (616)3220, D epartment of Electrical Engineering, University of Illinoi s (July 1960a).

D yson, J. D., and P. E. Mayes, The lo~-spiral omnidirectional circularly polarized antenna, URSI- IRE Sprin~ M eeting, Washington, D .C. (May 3 1960b) (unpublished).

D yson, J. D ., and P. E. Mayes, Multi-arm logarithmic spiral antennas, Proc. T enth Symposium, USAF Antenna Re­search and D evelopment Program, Allerton Park, Monti­cello, Illinois (Oct. 1960c).

E lfving, C. T ., D esign cri teria for log-periodic an tennas, IRE WESCON Cony. R ecord (1961) .

Greiser, J. W. , and P. E. Mayes, Vertically polarized log­periodic zig-zag antennas, Proceedings National E lec­t ronics Conference, Vol. 17, pp.193- 204 (1961).

I sbell, D . E ., Non-planar logarit hmically periodic antenna structures, Proc. Seventh Symposium, USAF Antenna Re­search and D evelopment Program, Allerton P ark , Monti­cello, Ill. (Oct. 1957); a lso Antenna Laboratory T echnical R eport No. 30, Contract AF33 (616)3220, E lectrical E ngi­neering D epart ment, University of Illinois (Feb . 1958).

I sbell, D. E., A log-periodic reflector feed, P roc . IRE <17" No. 6, 1152- 1153 (June 1959a).

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I sbell, D. E ., Log-periodic dipole arrays, IRE Trans. AP- 8, 260- 267 (May 1960) ; a lso Antenna Laboratory T echnical R eport No. 39, Contract AF33(616)3220, D epartment of E lectrical Enginering, University of Illinois (June 1959b).

Jones, S. R ., and E. M. Turner, Polarization control with oppositely sensed circularly polarized antennas, Proc. IRE Nat. Aero. E lectronics Conf., pp. 588- 595 (May 1959) .

Kaiser , J . A., The Archimedean two-wire spiral antenna, IRE Trans. AP- 8, 312-323 (May 1960).

Kandoian, A. G., T hree new antenna types and t heir applica­t ions, Proc. IRE 35, pp . 70w- 75w (Feb. 1946).

Mast, P . E., A theoretical study of the equiangular spiral an­tenna, Antenna Laboratory T echnical Report No. 35, Contract AF33 (616)3220, D epartment of E lectrical E ngi­neering, University of Illinois (Sept. 1958) (unpublished).

Mayes, P. E., and R . L . Carrel, Log-periodic resonant l' arrays, IRE WESCON Cony. R ec., 1961 ; a lso Antenna Laboratory T echnical R eport No. 47, D epartment of E lec­t rical Engineering, University of Illinois (July 1960a) .

M ayes, P . E., and R. L. Carrel, High gain log-periodic an­tennas, Proc . T enth Symposium, USAF Antenna R esearch and D evelopmen t Program, Allerton P ark, Monticello, Ill. (Oct. 1960b) .

Mayes, P. E., G. A. D eschamps, and vV. T . Patton, Back­ward-wave radiation from periodic structures and applica­t ions to t he design of frequency-independent antennas, Proc. IRE <19, No.5, 962- 963 (May 1961).

Mayes, P. E ., D. E. Isbell, and R. L. Carrel, Antennas with periodic and pseudo frequency independent performance, National T elemetering Conference R ecord, pp. 279-28-! (1958) .

Nussbaum , M ., Designing broadband conical helix antennas, E lectronic D esign (Sept. 3, 1958) .

Rumsey, V. H ., Frequency-independent antennas, IRE Nat. Conv. Record 5, Pt. 1, 114-118 (1957) .

Rumsey, V. H ., A solution to t he equiangular spiral antenna problem, IRE Tra ns. AP- 7, pp. S- 117 (D ec. 1959).

Springer, P. S., End -loaded and expanding helices as broad band circularly polari zed radiators, Proceedings National E lectronics Conference, vol. 5 (1949).

Turner, E. M ., Broadband radiators, Proc IRE Nat. Aero. E lectronics Conf. (1958).

Turner, E. M ., Spiral slot antenna, "Vright Air Development Center, Dayton, Ohio, T ech . Note WCLR- 55- 8 (June1955) unpu blished.

Turner , E. M., The scimitar antenna, Proc IRE Nat. Aero. E lectronics Conf. (1956).

'Wheeler, M. S., On the radiation from several regions in spiral antennas, IRE T rans. AP- 9, 100- 102 (Jan . 1961).

(Paper 66D 1- ] 68)