BtftS§£ m m BBSS! Hi I H ■ HH LI B R.ARY OF THE UNIVERSITY Of ILLINOIS 621.3^5 IX655te no. 3 1 - 3& cop. < The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN APR 18 MAR 2 8 L161 — O-1096 ANTENNA LABORATORY Technical Report No. 33 A UNIDIRECTIONAL EQUIANGULAR SPIRAL ANTENNA by John D. Dyson 10 July 1958 Contract AF33 (616)-3220 Project No. 6(7-4600) Task 40572 WRIGHT AIR DEVELOPMENT CENTER Electrical Engineering Research Laboratory Engineering Experiment Station University of Illinois Urbana, Illinois ? 2 /. 3CS CONTENTS Page Illustrations m Summary 1 Introduction 2 The Antenna 5 Experimental Results 10 Input Impedance 16 Conclusions 19 Acknowledgements 19 Distribution List ii Digitized by the Internet Archive in 2013 http://archive.org/details/unidirectionaleq33dyso ILLUSTRATIONS Figure Number Page 1. The Planar Equiangular Spiral Antenna 3 2. The Balanced Conical Antenna with Coordinate System 6 3. Antenna As Etched on Teflon Impregnated Cloth and As Assembled with RG 141/U Cable 8 4. Antennas with Variation in Arm Width and Feed Cable 9 5. Radiation Patterns as a Function of 4 1 11 6. Radiation Patterns of Balanced Conical Equiangular Spiral at Mid-Band Frequencies, 4* = 20° 12 7. Radiation Patterns of Balanced Conical Equiangular Spiral, 4" = 30° 14 8. Polarization of Radiated E Field off Axis of Antenna 15 9. Standing Wave Ratio on 5 ohm Line Terminated with Balanced Conical Antenna 17 10. Approximate Boundary Circles of Impedance Loci as a Function of ^ 18 iii 1. SUMMARY Circularly polarized unidirectional radiation over essentially unlimited bandwidths is obtainable with a single antenna. The antenna is constructed by wrapping a balanced equiangular spiral on a conical surface. The non-planar structure so constructed retains the desirable qualities of the planar models and in addition, provides a single lobe pattern off the apex of the cone. Practical antennas have been constructed with radiation patterns and input impedance essentially constant over band- widths greater than 10 to 1 . 2. INTRODUCTION The equiangular spiral antenna originally proposed by Rumsey was demonstrated to be the first of the essentially "frequency independent" (2) structures . This antenna defined by the equation for the equiangular spiral curve, as in Fig. 1, was a balanced planar structure. For all frequencies such that the arm lengths are greater than one wavelength, it provides radiation patterns that, except for a rotation about the axis of the antenna, are essentially constant with frequency and a,n input impedance that has converged to a characteristic value. The radiation pattern is bidirectional with two circularly polarized lobes perpendicular to the plane of the antenna. Practical size structures have been constructed with pattern and impedance bandwidths greater than 20 to 1. Carrel investigated an unbalanced conical version of this antenna (3) fed with the apex of the cone at a ground plane, and demonstrated the basic unlimited bandwidth of this structure. The unbalanced antenna exhibited a tilt of the radiation pattern off the antenna axis and since the pattern had the characteristic rotation with frequency the structure was of limited use. The balanced model he investigated was fed through a ground plane with the apex of the cone on the ground plane. The patterns did not appear encouraging. In the spring of 1957 the author investigated several balanced expanded (4) and conical structures. alone and in combination with planar structures. 1. Rumsey, V.H., "Frequency Independent Antennas", National IRE Convention Record, 1957. 2. Dyson, J.D., "The Equiangular Spiral Antenna!' Paper submitted to IRE for publication 11 June 1958. 3. Carrel, R.L., "Experimental Investigation of the Conical Spiral Antenna", Technical Report No. 22, 25 May 1957 Antenna Laboratory, University of Illinois, Contract AF 33(616)3220. 4. Dyson, J.D., "The Equiangular Spiral. Antenna" . Technical Report No. 21, 15 Sept. 1957, Antenna Laboratory, University of Illinois, Contract AF 33(616)3220. b. The pl£ nar antenna FIGURE 1 THE PLANAR EQUIANGULAR SPIRAL ANTENNA. Although these antennas appeared to have promise the investigation was temporarily suspended because of the problems involved in precisely constructing the non-planar models. Since that time equipment for constructing "printed circuit antennas" has become available, making possible a simple and precise method of construction. This paper is concerned with a balanced equiangular spiral wrapped on the surface of a cone and fed at the apex of the cone by carrying the coaxial feed cable along one arm. It demonstrates that unidirectional rotationally symmetric radiation patterns, with a maximum on the antenna axis off the apex of the cone, can be obtained over bandwidths matching those of the basic planar antenna. 3. THE ANTENNA Design principles for the planar structure of Fig. 1 are given in a (2,4) previous paper. The conical spiral structure is defined as in Fig. 2. The radial distance along the surface of the cone to the outer edge of one arm is given by ^ (a sin -)0 b P 1 = e = The inner edge is defined by The second arm by and P 2 = e = K p x " a7r P 3 = P l G ^4 = K ^3 Hence for an included cone angle, 4*, of 180 (the planar structure) the antenna is defined by P y - e and as this antenna is wrapped on a cone it spirals more rapidly „ This 1 rate of spiral is given by the exponent "a sin — " . The "angular width" 2 of the arm is specified by the constant K. The previous investigation of the planar antenna indicated that except for the fact that the more tightly wound antennas had somewhat smoother and slightly more rotationally symmetric patterns, the rate of spiral rotation had little effect on the i shape of the pattern and a secondary effect on the input impedance. The non-planar antennas were constructed by drawing the arms on the development of a cone. This drawing is transferred by a silk screen process Feed CaLk FIGURE 2 THE BALANCED CONICAL ANTENNA WITH COORDINATE SYSTEM to a 2 mil copper clad teflon impregnated glass cloth .010 inches in (5) thickness. After etching the metal arms, the base material was formed into a cone and the arms soldered along the joint. Figures 3 and 4 show the antenna as printed and the completed structure. The teflon cone is supported by a cone turned from block styrofoam. The arms must be terminated a finite distance from the cone apex and are fed in a balanced manner by carrying the feed cable along one (2 4) arm. This method of feed ' is possible because of the rapid attenu- ation of the near fields on the arms, and for frequencies such that these fields have attenuated to negligible values at the arm ends. the outside of the cable does not carry a significant amount of antenna current. However, as the frequency of operation is decreased a point will be reached where the presence and location of this cable alters the radiation pattern. A dummy cable is placed on the opposite arm to main- tain physical symmetry. The properties of the antenna were investigated as a function of arm width, and cone angle ^. 5. Continental Diamond Fibre, "Dilecto" , type No. GB112T, 00 . I> 00 xi o t» • o oo >* o ^ O iH CO K § *§ S3 10 4. EXPERIMENTAL RESULTS Initially, a planar antenna defined by the constants a = ,303, and K = .925, with arms 150 cm in length was constructed. The effect on the radiation pattern of wrapping this antenna on a conical surface is indicated in Fig. 5. There is a marked increase in front to back ratio for *\> smaller than 60 . The absence of back radiation for 4* = 20° is evident in Fig. 6. There is no basic tilt to the pattern and the lobe is rotationally symmetric. The pattern rotates with frequency but this rotation is masked in the symmetrical structure since the pattern beamwidth is independent of the angle . The beamwidth of the patterns at 2000 mc. in Fig. 6 is 70° - 2° for E polarization and 90° - 3° for Ejl polarization for any angle 0. The average beamwidths of the same antenna on a 30 cone are approximately 80° and 100°. The lowest useable frequency is determined by the arm width and length, and cone diameter. The upper limit is determined by the precision of construction at the apex. For a termination of the apex at a one inch diameter the upper limit is approximately 4500 mc. The effect of arm width is evident in Table 1. Eb E

\ V i I J \» V f/ rl \V \\ u i) sj y^- v**\ ft % 1 1 / If f 1 /I \V /' II II II \» FIGURE 5 RADIATION PATTERNS AS A FUNCTION OF + K = .925 L = 150 cm ( .303 sin ~) 2000 MC * unsymmetry in front and back lobe at t = 180° due to mount 12 {±680 r= 105 F/S>25db {--80Q r= i.o7 F/B>25Jb f=looo N.09 F/B>25db f^200<9 r*L23 F/B>25db ^O -- £* ^--<9£ > / ft \ X / T Y\ / \v \ J \ ^""""■^^ yS^s -i ___^ X ' v A / / >^ \ / \l / \y\ ¥ \ J \ FIGURE 6 RADIATION PATTERNS OF BALANCED CONICAL EQUIANGULAR SPIRAL AT MID-BAND FREQUENCIES . L = 150 cm D = 16.6 cm r = axial ratio b = .053 K = .925 ^ = 20° L3 Table 1 Effect of arm width on patterns at lower frequencies of operation, 4 1 = 30 , Arm length 92 cm, Cone Diameter 15 cm. ARM WIDTH APPROXIMATE FREQUENCY AT WHICH FRONT TO BACK RATIO BECOMES CONSTANT ARM LENGTH MAXIMUM CONE DIAMETER ,050" (micro- dot cable only) .140" (RG 141/U cable only) K = .925 (With RG 141/U) K = ,85 (with RG 141/U) 1000 MC 1000 MC 900 MC 750 MC 3.1 X 3.1 X 2.7 X 2.3 X .5 X .5 \ .45 X .38 X It is of interest that antennas constructed of narrow, constant width arms, actually consisting of the feed cable only, had acceptable patterns although they did not have as low a frequency capability for any given antenna size as the wider, true equiangular spiral structures. For 4 1 of 20 and K = .925 the front to back ratio appeared to be approximately constant for frequencies such that L = 3.25 X and D = . 35 X. The bandwidth potentialities are demonstrated in Fig. 7. The 10 to 1 band can be extended by a suitable increase in arm length. This extension leaves the pattern at the higher frequencies unchanged. The polariza- tion of the field off the axis, shown in Fig. 8, is approximately circular for more than - 60 off -axis at mid-band frequencies, 14 ■0 f«450 /=L28 F/B>l7db f--600 F/B>l2db f=IOOO r=ui F/B>l4db S-ZOoo r--i,3l F/B> /4db f-4550 M.56 F/B>|2dfc ^>=c9£ FIGURE 7 RADIATION PATTERN OF BALANCED CONICAL EQUIANGULAR SPIRAL L = 150 D = 25.4 cm H * 42.5 cm r = axial ratio b = .078 K = .85 i|i = 30° L5 9 9 7 ' 1 L_ ' i t - <+ou n ~ I =2 ? A c 6 5 v A n_ 1*7^ A Ls m^J 0^ ^ ^s *> • * 2 S&"'0*9O ^r^ M -^ — """ "" 9 /O zo 30 40 SO (SO 00 80 90 ^b 9 & % ^ 7 f=2000MC - L*IOA r\ t-rr \ 7 * 5 5 5 ^4 u- /.-/A D rh-t 1^ 2 y c \ ** ** 0>--fcy /0 20 30 40 SO 60 TO 80 90 & m Decrees FIGURE 8 POLARIZATION OF THE RADIATED E FIELD OFF AXIS OF ANTENNA,^ = 30° , K = .85, b = .078 16 5. INPUT IMPEDANCE The input impedance of the antennas remains relatively constant over a wider frequency range than the useable pattern bandwidth. The standing wave ratio presented to a 50 ohm line by an antenna with 4 1 = 20 , K = .925 and fed with RG 141/u cable is shown in Fig. 9 over a 20 to 1 variation in frequency. The mean impedance level appears to slowly decrease with decreasing cone angle. The variation in the measured impedance over the frequency range from .5 to 2.5 Krac is indicated in Table 2 for four cone angles . Table 2 Measured input impedance of balanced conical antennas as a function of 4 1 . (K = .925, L = 150 cm, b = ( a Sin 4/2) Y APPROXIMATE MEAN IMPEDANCE MAXIMUM SWR REFERRED TO MEAN 20° 129 -n- 1.9:1 30 147 1.9:1 60 153 1.95:1 180 164 2.1:1 The impedance is influenced by the construction at the terminal region. Since these antennas were fed with a coaxial cable of .140 inch diameter, this cable dominates the terminal region and contributes to the mean impedance level. However, this appears to be the only practical method of feeding these structures if the full bandwidth potentiality is to be realized. Hence the input impedance with a practical size feed cable bonded to the arms is of interest. It may be expected to change with a change in cable but its stability with frequency is apparent. 17 Q O H & a s OS o w m g II .J S n o o O m M CO o B" FIGURE 10 APPROXIMATE BOUNDARY CIRCLES OF IMPEDANCE LOCI AS A FUNCTION OF iJj K = .925, L = 150 cm, b = (.303 sin |) 19 6. CONCLUSIONS An experimental investigation of the balanced equiangular spiral antenna projected on a conical surface has shown that unidirectional circularly polarized single lobe radiation patterns may be obtained over bandwidths in excess of 10 to 1. The input impedance remains relatively constant over the pattern bandwidth. The antennas are of practical form and may be constructed of metal arms formed on a conical surface or by printed circuit techniques. 7 . ACKNOWLEDGEMENT The author is pleased to acknowledge helpful discussions with Dr. P.E. Mayes and the assistance of R.L. 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