(efo-Joy ANTENNA LAB&RATQJ&& Technical Report No. 2 l'.'.l'.' J ' " ILLINOIS UfiOlS uo .WJi. *» V ' JPLEASE RETURN WlTHIIi /rf/,. THE EQUIANGULAR SPIRAL ANTENNA by John D. Dyson 15 September 1957 Contract No. AF33(61 61-3220 Project No. 6(7-4600) Task 40572 WRIGHT AIR DEVELOPMENT CENTER ELECTRICAL ENGINEERING RESEARCH LABORATORY ENGINEERING EXPERIMENT STATION UNIVERSITY OF ILLINOIS URBANA, ILLINOIS Antenna Laboratory Technical Report No. 21 The Equiangular Spiral Antenna by John D. Dyson 15 September 1957 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 CONTENTS iii Page Acknowl edgement Abstract List of Symbols I Introduction II Definition of the Antenna 2,1 The Design Principle 2„2 The Equiangular Spiral 2.3 The Antenna 2.4 Physical Construction of the Antenna III The Radiation Pattern 3.1 The General Far Field Pattern 3,1a The Typical Antenna 3„lb The Pattern Bandwidth 3.2 Variation of Antenna Parameters 3.3 Pattern Beamwidth and Pattern Rotation 3,3a Pattern Rotation 3, 3b Pattern Beamwidth 3.4 Polarization of the Field 3.5 Variations in the Basic Antenna 3,5a Designing for a Specific Band of Frequencies 3,5b Effect of Construction with Thick Arms IV The Near Fields 4.1 The Tangential Field in the Slot Arms 4.2 The Normal Field on the Arms 4,2a General Considerations and Theory of Measurement 4,2b Adjustment of Equipment 4,2c Measured Fields 4.3 Estimation of Error V The Input Impedance VI Efficiency of the Basic Antenna 6.1 Method of Measurement 6.2 The Experimental Investigation 6,2a Measurement of Surface Resistivity 6,2b Ratio of Power Inputs 6, 2c A Check on the Current Distribution 6, 2d Measured Efficiency VII The Cavity Backed Antenna 7.1 Efforts toward a Unidirectional Antenna 7.2 Antenna with Absorbing Termination 7.3 The Antenna over .a Conventional Cavity IX XI 1 3 3 7 13 17 17 17 18 28 41 41 42 53 55 55 56 68 68 81 81 82 84 100 101 112 112 114 114 116 117 117 124 124 127 133 iv CONTENTS (CONTINUED) Page VIII Conclusions 138 Bibliography 140 Appendix A — Table of Physical Parameters of the Specific Antennas Referred to in the Text 141 Distribution List Digitized by the Internet Archive in 2013 http://archive.org/details/equiangularspira21dyso ILLUSTRATIONS Figure Number Page 1. The Equiangular Spiral 6 2. Defining One Arm of an Equiangular Spiral Antenna 9 3. Outline Drawing of Antenna 10 4. The Arm Length from Feed Point to Termination 11 5. The Balanced Spiral 12 6. Antenna 2M-15 with Modified Feed Sections 15 7. Enlargement of the Terminal Portion of Antenna 2M-15-3C 16 8. Polarization, On Axis, of the Radiated E Field of Antenna 2M-15C 22 9. Minimum Arm Length in Wavelengths Necessary to Produce Circularly Polarized Radiated Field 23 10. Ground Screen Pattern Range, Viewed from Above 24 11. Polar Coordinate System for Pattern Measurements 25 12t13. Radiation Patterns of Antenna 2M-15C, a = .30, K = .62 26,27 14t15. Radiation Patterns of Antenna 2M-18, a = ,415, K = .49 29, 30 16-17, Radiation Patterns of Antenna 2M-21 , a = .415, K = .75 31,32 18-19. Radiation Patterns of Antenna 2M-22, a = .415, K = .875 33,34 20-21, Radiation Patterns of Antenna 2M-16C, a = .28, K = .75 35,36 22-23, Radiation Patterns of Antenna M-5, a = . 35 , K = . 68 37,38 24-25. Radiation Patterns of Antenna 2M-32, a = .45, K = .75 39,40 26. Rotation of Radiated Field with a Change in Frequency 44 27, Patterns Obtained by Simultaneous Rotation of Antenna and Increase in Frequency 45 28, Pattern Rotation for a Given Change in Frequency 46 29. Beam Width at 1/2 Power Points, Antenna M-10 47 vi ILLUSTRATIONS (CONTINUED) Figure Number Page 30. Pattern vs. Azirauthal Angle, Antenna 2M-16C, a = .28, K = .75 48 31. Pattern vs. Azimuthal Angle, Antenna M-10, a = .30, K = .75 49 32. Pattern vs. Azimuthal Angle, Antenna 2M-38, a = .35, K = .75 50 33. Pattern vs. Azimuthal Angle, Antenna 2M-21 , a = .415, K = .75 51 34. Pattern vs. Azimuthal Angle, Antenna 2M-32, a = .45, K = .75 52 35. Polarization of the Radiated E Field of Balanced Planar Slot Antenna M-10 54 36. On Axis Polarization of Radiated Field of Antenna 2M--28C 58 37-38. Radiation Patterns of Antenna 2M-28C, a = .2, K = .69, Feed Slot, 3 cm 59-60 39. Dimensions of Feed Structure of 2M-28C at Upper Cutoff of Pattern Bandwidth 61 40. Pattern Bandwidth for Various Size Feed Slots 62 41. Full Size Drawing of the Feed Slots of Antennas 2M-15C, 2M-15-3C, 2M-15-4C. 63 42. Radiation Patterns of Antenna 2M-15-3C 64 43. Radiation Patterns of Antenna 2M-15-4C 65 44. Antenna 2M-5W 66 45. Radiation Patterns of Antenna 2M-5W 67 46. Experimental Setup for Measuring Electric Field in Slot Arms 71 47. Amplitude of Tangential E Field along Slot Arms of Antenna 2M-I0 72 48-51, Probe Points and Orientation of Dipole Probe for Maximum Response, Antenna 2M-10, f = 1000, 1500, 2000, 2500 MC 73-76 52-55, Orientation of Probe for Maximum Response at 1.31, 1.53, 2.09, 3.58 X from the Feed Terminals 77-80 vii ILLUSTRATIONS (CONTINUED) Figure Number Page 56. Equipment for Measuring Amplitude of Normal Component of the Near Field 86 57. Experimental Setup for Measuring Phase of Near Field along Antenna Arms 87 58. Comparison of the Null Obtained by Two Methods of Measurement of Relative Phase 88 59-60, Amplitude of E n Field along Arm of Antenna 2MA-15, a = .30, K = .62 89-90 61-62. Amplitude of E n Field along Arm of Antenna 2MA-10, a = .30, K = .75 91-92 63. Relative Amplitude of E n Field along 2MA-15C with Arms 2.5 and 18.7 X Long 93 64. Relative Amplitude and Phase of E n Field along Arm of 2MA-15C with Arm Length of 18.7 X 94 65. Relative Amplitude and Phase of E n Field along Arm of Antenna 2MA-15, a = .30, K = .62 95 66-67. Relative Amplitude and Phase of E n Field along Arm of Antenna 2MA-10, a = .30, K = .62 96-97 68. Contours of Equal Amplitude of E n Field, Antenna 2MA-15 98 69. Contours of Equal Phase Of E Field, Antenna 2MA-15 99 70. Input Impedance of Slot Antenna 2M-8, a = .30, K = .85 104 71. Input Impedance of Slot Antenna 2M-10, a = .30, K = .75 105 72. Input Impedance of Slot Antenna 2M-15, a = .30, K = .62 106 73. Input Impedance of Balanced Planar Slot Antennas as a Function of K 107 74. Standing Wave Ratio of Antenna 2M-10 with Various Feed Cable Arrangements 108 75. Standing Wave Ratio of Antenna 2M-28C 109 76. Standing Wave Ratio of Antenna 2M-15-3C 110 viii ILLUSTRATIONS (CONTINUED) Figure Number Page 77. Standing Wave Ratio of Antenna 2M-15-4C 111 78. Experimental Setup for Measurement of Attenuation Constant 119 79. Standing Wave Ratio Measured on One Pair of Shotted Coaxial Lines 120 80. Equipment for Measuring Ratio of Input Power to the Antennas 121 81. Efficiency of 2MA-15 Constructed of Brass 122 82. Line Drawing of One Arm of the Balanced Antennas Used for Efficiency Measurements 123 83. Conical Bottom Cavity 126 84. Planar Equiangular Spiral Antenna Backed with an Expanding Conical Equiangular Spiral 126 85. Antenna 2M-15C Mounted over a Resistive Cavity 128 86-87. Radiation Patterns of Antenn 2M-15C with and without a Resistive Cavity 129-130 88. Relative Gain at 9 = of Antenna 2M-15C with an Absorbing Cavity to Antenna without Cavity 131 89 . Standing Wave Ratio of Antenna 2M-15-3C Mounted over a Resistive Cavity 132 90. Polarization of the Field on Axis of Antenna 2M-15C over a 13 Inch Square Cavity with a Flat Bottom 134 91-92. Radiation Patrterns of Antenna 2M-15C Backed with a Flat Bottom Cavity, 13 Inches Square 135-136 93. Standing Wave Ratio Presented to a 50 Ohm Line by Antenna 2M-15C When Placed over a 13 Inch Square Cavity, 3/4 Inch in Depth 137 ix ACKNOWLEDGEMENT The author has become indebted to many individuals during the course of this investigation. He is pleased to acknowledge the advice and suggestions of his adviser, Prof. V.H. Rumsey, to whom must go full credit for the original concepts leading to this antenna. Appreciation is extended to Dr. R.H. DuHamel , Dr. P.E. Mayes, and Mr. W.L. Weeks for many fruitful discus- sions, to W.E. Kennedy and other members of the laboratory who assisted in the measurements, and to Mr. V.P. Rash who performed many of the measurements and who fabricated the more than 50 odd antennas investi- gated. Mention should be made of Mr. E.M. Turner, Wright Air Development Center, whose original work on the Archimedes Spiral Antenna undoubtedly gave impetus to further thought in terms of spirals and who has been an enthusiastic supporter of this investigation. ABSTRACT A new antenna is described which makes possible radiation pattern bandwidths previously considered to be impossible. The design of the antenna is based upon the simple fundamental principle that if the shape of the antenna were such that it could be specified entirely by angles, its performance would be independent of wavelength. Since all such shapes extend to infinity it is necessary to specify at least one length for an antenna of finite size, This principle can be used as a basis for practical antenna design, because in some cases the antenna performance is practically independent of wavelength, provided this one length is very large compared with the wavelength of operation. Each arm of the equiangular spiral antenna is defined by two identical equiangular spiral curves, one rotated through a fixed angle around the origin with respect to the other. Thus the antenna is completely described by two angles and one specified arm length, It is remarkable in that this one length need only be comparable to one wavelength to obtain operation essentially independent of frequency, It is the first antenna to exhibit, in a practical size, the characteristics associated with an infinite structure. The investigation is concerned with the planar balanced antenna which radiates a broad lobe perpendicular to the plane of the antenna over a practical range of parameters. The radiation is bidirectional with equal beams radiated from the front and the back of the structure. The beam is circularly polarized on its axis, over the useable bandwidth. There is no basic tilt to the lobe of the symmetrical antenna. > 1 It is shown that a change in wavelength is equivalent to merely rotating the antenna through a fixed angle, Hence the pattern of the infinite structure would be independent of frequency, except for a rotation of the radiated field about an axis perpendicular to the antenna, Within the necessary limitation imposed by the one fixed length, this is shown to be true for the finite size structure. For frequencies such that the antenna arms are very short in terms of wavelength, the radiated field is linearly polarized. As the arm length is increased (or frequency increased) the field on the axis perpendicular to the plane of the antenna becomes elliptically and then circularly polarized. Since there are no distinctive changes in pattern shape, this change in field polarization is used as a criterion for specifying the cutoff of the pattern bandwidth. The upper and lower cutoffs are independent, the upper being determined by the fineness of construction of the spiral at the feed point and the lower by the arm length. Pattern bandwidths in excess of 20 to 1 have been recorded and there is no indication that this bandwidth could not be extended indefinitely. Radiation patterns are presented for a wide range of antenna parameters. The input inipedance is shown to converge rapidly with increasing frequency and for the antennas of most interest the slot version is rarely mismatched more than 3 to 1 to a 50 ohm line, and is usually 2 to 1 or better over the radiation pattern bandwidth. The near fields on the antenna were probed and the amplitude and phase distributions are presented. The efficiency of the basic antenna (constructed without lossy dielectrics) is approximately 98% over the useable band of frequencies. xii LIST OF SYMBOLS a Constant determining rate of spiral where curve is defined by /3 - e ^ A Angle between radius vector and tangent to curve b Constant determining rate of spiral of orthogonal curve e Naperian Base E Normal component of the electric field n k Constant which determines physical starting point of curve when (p z. -aS K = e 1 Arm length r Axial ratio 6f the polarization ellipse of the recorded voltage polarization pattern 8 Constant angle inner curve of arm is delayed behind outer curve 9 Conventional spherical angle measured from the perpendicular to the plane of the spiral > = J n JL (2.2) 4 as in Fig. 1. p and

■-« (2 . 13) and P 4 = ke a *-"- 6 Up 3 . (2,14) These two conductors constitute a balanced antenna of infinite length. To specify a finite size structure, one fixed length, the arm length, must be specified. Figure 3 is an outline drawing of a practical antenna. It should be noted at this point that this antenna can be completely specified by the two angles, 0'and 6, the arm length, and the size of the terminal region. This arm length could be defined in several ways. As used in this report it refers to the spiral length along the center line of the arm, where the center line is defined by the equation p -¥"i= ¥* a *' < 2i5 > as in Fig. 4. If the arm is terminated in an arc of a circle as in \ ^ Fig. 4(b), the length along any spiral filament in the arm is the same, I i.e., the length along the outer curve up to the circular arc is equal to the length along the inner curve (except for a usually negligible difference which will be due to the way in which the spiral is terminated at the center) . The constant K, defined in Eq. 2.12, is a convenient measure of the "angular width" of the antenna arm, the width along the radius vector. A practical balanced antenna imposes a lower bound on K if the space between the arms is to remain open. Thus in Fig. 5, it can be seen that if P 2 * e~ a6 p 1= K p x (2.16) P 4 = KP 3 (2.17) and -alT n P 3 = 6 P l it must be specified that and P 3 < P 2 —&1T e < K < 1. (2.18) ,,-ke* Arc of o circle with center at origin. Figure 2 Defining one arm of an equiangular spiral antenna 10 'gure 3 Outline drawing of antenna i 2MA-r23 a = .35 K = .597 k = .2 inch 11 Pz =K Py L = .254 rrv «w> o ) + p o cm, where p and p are in inches/10 ' o Figure 4 The arm length from feed point to termination Arm — 12 Curve Curve 2 K Pz_ P*_ P\ ~~ P* Figure 5 The balanced spiral 13 2 . 4 Physical Construction of the Antenna The investigation with which this report is concerned has been confined to the balanced, planar, equiangular spiral antenna with a balanced feed. Two forms of this antenna have been used, the plane conductor antenna, i.e., metallic arms suspended in free space, and the slot antenna, which consists of spiral slots cut in a large conduct- ing sheet . The slot is the complement of the plane conductor antenna and is itself an equiangular spiral. Fig. 6 shows three of the slot antennas investigated. The slot antennas are shown cut into a 14 inch, square of 1/32 inch copper, which is bolted into a larger ground plane. The antennas were fabricated by plotting them on polar paper and trans- ferring these curves with carbon paper to the sheet copper. The arms were then cut, using fine blades in a scroll saw. The slot antenna is a most useful form because it makes it possible to feed the balanced structure in a completely balanced manner by simply embedding the coaxial feed cable in the ground plane, or soldering it to (5) the ground plane, as shown in Figs. 6 and 7, This method of feed, which might be referred to as an "infinite balun," is the only form of balun presently in use which will permit the fullest use of the infinite imped' ance and pattern bandwidths of this antenna. The only disadvantage to this type of feed is that it requires leaving sufficient ground screen between the slot arms to carry the feed cable. This imposes a require- ment that the spiral be terminated at the center in a fairly large feed section, as can be seen in Fig. 6, if a large coaxial feed cable is required. This large feed section will place an upper frequency limit on the antenna; however, antenna 2M 15-4 in Fig. 6, which is fed with 14 RG 87A/U cable (a teflon dielectric cable equivalent in size to RG 9/U) has good patterns as high as 3000 mc. The other two antennas pictured may be operated at much higher frequencies. This point will be developed more fully in Section 3.4, If the width of the metal on which the cable is mounted approaches the diameter of the feed cable, it may be necessary to mount a dummy cable on the opposite arm, as has been done in Fig. 6, to maintain sym- metry of construction and to prevent tilt of the radiation pattern. Throughout this report, reference will be made to the patterns or characteristics displayed by certain spiral antennas. In nearly all cases the physical parameters, which describe the antenna, will be includ- ed on the appropriate figure. In a few cases the antenna may be referred to by a model number. To facilitate a rapid identification of the antennas and to provide a cross reference between the model number and the param- eters a tabulation of these antennas is included in Appendix A. • • * • 9 m ... • « Figure 6 Antenna 2M-15 with modified feed sections 16 Figure 7 Enlargement of the terminal portion of antenna 2M-15-3C 17 III. THE RADIATION PATTERN 3.1 The General Far Field Pattern 3.1a The Typical Pattern Using Equation 2.1, note that if the unit of length is chosen as the wavelength, X, and if p equals the radial coordinate measured in wavelengths, or ' ad) e T X ,./ In Xw = e p / = /<*'-<> ./ In X where - — ^o a (3.1) Since the electrical performance of the antenna depends only on the shape of the antenna measured in wavelengths, the effect of changing X is equivalent to changing the angle (!) . This indicates that the o pattern of the infinite structure would be independent of frequency. Within the necessary limitation imposed by the one fixed length, i.e., the arm length, this has been found to be true for the finite size structure. The radiation patterns of more than 40 spiral slot antennas have been investigated with the parameters a and K varying, . 2 A g. uj C 1 5 3 .NZ.5 *E O £ 2 O O S Sl< 3tl .er tgth 95 X Axial Rat o i j .5 .6 .7 .8 .9 1.0 1.5 2 2.5 3 Frequency in Kmc 6 7 8 9 10 12 Figure 8 Polarization, on axis, of the radiated E field of antenna 2M-15C 23 1 1 /^3 i CM II a. J/ x^^n^^ «* q a ) oo r-. «? •H m •H T3 a u -a 0) N •H Si cci r-l a >> rH fn Cd iH 3 O ?H ■H O CD 3 T3 u ft +-> >> Sh CtS co CO CD CJ CD Pi CO Xi j-> bJO ,<*N fl LO CD W c3 £ a3 •H V/ CM J3 • -p bO ««. a CO CD ■H iH X Rj -P n H o CO H s 3 CM s •H VI Pi •H h en Si bD CM X/l 24 Figure 10 Ground screen pattern range, viewed from above 25 cut (on axis of feed slot) 2 nd arm is continued to a symmetrical structure. 4>-0 cut Figure 11 Polar coordinate system for pattern measurements ?*595Mc f*800 1*139 f-OOO ril04 -X4400 S^^f^^ "Sv>. WIj04 x /I/ \ 4 --90 26 jr '/"■*. __, *" s ' ^ >v X ^ v. x /x ' / \ > \ / X / x r r* X \ 1 ^^ yC ' \ 1 I N- X ' S ] \ 1 " v X ** 1 —f-^T^\ S » /■ 1 >. 1 \ /X * / / X V \ 1 /\ / \» / fv\ s* 1 \ / / ^\ / * 1 \ 1 X X.* \ 2^. £<" \ X f ( V ^>v / ^\' ( \\ /\ / \ j/f \ 1 vx Figure 12 Radiation patterns of antenna 2M15-C a = .30 K = .62 (all patterns in this report are voltage plots \ r = axial ratio _ _ £ ■e E 6 =o c f=2800Mc r=l.05 f=3950 r=l.07 f=5600 r=l.07 f=9027 r= 1.07 f=l2,000 r=l.24 <£ = 90 c 27 /z' N ^\\ A // \ \ yX If \ /7 \ / v\ / sl \ 1 i v\ r*+ i 1 Figure 13 Radiation patterns of antenna 2M15- C a = .30 K = .62 28 3.2 Variation of Antenna Parameters ) Since the pattern of the Equiangular Spiral Antenna is expected to rotate with frequency, a detailed study of pattern change with frequency would require a corresponding antenna rotation for every shift in frequency, (this point will be fully developed in a later section). In most normal operations, the antenna will be in a fixed mount, and the pattern response with respect to that fixed mount is desired. Hence the patterns in, the preceding section and those in this section are displayed as a function of frequency, without regard to any pattern rotation. As will be shown in the next section, this accounts for most of the apparent variation in the patterns over these frequency ranges. Although the radiation patterns of the balanced spiral antenna are relatively insensitive to variations in parameters, a study of the patterns indicates that the more tightly spiral ed antennas, and the antennas with wider arms, (a and K small), tend to have smoother and more uniform patterns. This is apparent in Figs. 14 through 19, which show patterns for antennas with a constant rate of spiral but with various arm widths, and in Figs. 20 through 25 and Figs. 16 and 17, which show patterns for antennas with approximately a constant angular width but with a variation in the rate of spiral. The pattern J'ears" apparent on some of the patterns become evident for antennas with the larger a and K values. The ''ears 11 on these particular patterns do not become deeper, but tend to slough off, and slide down the side of the pattern. However if a' and K are allowed to become much larger, the pattern does tend to lobe. <£=0 <£=90° 29 f = 680Mc r = 2 i / V \ /' \>^ / / >^ / • f = IOOO r = L2 f=3O00 r=LI3 f = 2000 > ^^^ s~ ^,\\ r=l.26 A \(: vS \\\ V \ y v ^^^*~ ^>w ^ ir \ 1 / 1 V / / ^ \^ / / I 1 ^ N ^S /' • \ ^---' ^F^^ — /^ j / r A. < ) x\ / \. t /-**/" ~ *""X ' / \ / /vs. / / v\ v\ I - 3 *£* m ^^^^ sN. M X / \1 V\ // \ Z^ \ Figxire 14 Radiation patterns of antenna 2M-18 a = ,415 K = .49 E 30 <£ = £ f = 4000Mc r= II f=5000 r=T.I8 f=IOOOO r=l.l5 f=l2000 r=l.28 f=7000 r=l.06 A i V t V x i Wi ) \S \ ' X \ /I \ \\ X *X X. (£=90° Figure 15 Radiation patterns of antenna 2M-18 a = .415 K = .49 — E Q <£=0 C f=860 Mc r= 1.94 f = l500 r=l.5 r= 1.34 f=3000 r = l.28 f=IOOO ^ — >^~ ^=^^^ r=l.75 / \ '/ \ vx >X A \ 1 V X * ^ x / / 1 1 r ^ —J oo ^7=*\ 4 /A" \ ^\ X / x \\ \ XX / ' \\ y\ / \/' \\X \ / v\ / 1 N X 1 X X / / / \ ^=90° 31 X i "**> A/ jA / V 7\ Y \ 1 ~s x ' y 1 AJ i ""V .X \ NX / i ^\ / 1 \\ / n // / \ X ' / \ X> 1 \ Figure 16 Radiation patterns of antenna 2M-21 a = .415 K = .75 "9 E £ <£=0 C (£=90* 32 f = 4000 Mc r = l.09 9 ^^^ \ N s\. / f ^\ / \ V X / V v X / *» X / * \ \ SSI \ / Si \ ^^--^*^%."* ^v f=5000 s't ^^^~ ^ \\ r=l.09 / X / Y/x v Vx / ft \ / / / \ \\ \y X s */ \ f=7000 r=l.07 A "^^s ^"\ ^* X XV \ f=IOKmc r=l.l f = l2Kmc r=l.48 Figure 17 Radiation patterns of antenna 2M-21 a = .415 K = .75 E0 <£ = 0* f=l020 Mc r=2 rr" A (*' \ \ / X ' / x ' 1 i *\. / / *\ /< ) \ f=l500 r=l.59 f=2500 r= 1.26 f=3000 r=l.26 f=2000 * v " N /^ / ^\ r=l.29 / /^ y\ X / \ /\ \ I \ X 1 v X V \ ""-X. /i J \ / > f \ <£=90« 33 xX f ' / X ! 7 / XL/ \ v/\ /M \ / v* ^\. / // \ Figure 18 Radiation patterns of antenna 2M-22 a = .415 K = .875 <£=0< f = 4000 Mc r= 1.2 j^ZZ^^ ex* ' C ^5^V A v x X 1 <\ / V X X 1 l\ / 1 N X. X / \ / \ 1 v X X / / \ / v xC •* ^^ r=L02 /> p*»_ V ry Y\ \ \ V X v X \\ \ x\ 'x / \ /X / \ \ r"X ) ^ X x X ^*^X x > x^ \ X S X 1 f=l0000 r=l.39 X f /v^ \ 1 ? Mi "V \ | / \ 1 J y< \ / "y x^ \ / / y' \ <£=90< 34 A <'"*/** u. \ X / X X / yx X l /\ XM \ / / S \ / # ^ \. / / ^ X / / v X 1 v X / / 1 \ / / s \ / /' \ \ X* j ll ^^»"" r XX 'l ~1 ^\ 1 * x\ V y\ / x. A / X v / X 1 1 / x\l / / \ n/ \ / \ x^^ N - ' \T X XX rL V " /^ Ad l X /\(/^ \l J H w ~>/\ / [\\ / \ N X / x N X X ^/ \ / \ x X. y S 1 \ / ^ x X. y * ^ y \ 1 ■*» X II "^ f-s il Figure 19 Radiation Patterns of Antenna 2M-22 a = .415 K = .875 E0 — - E <* <£ = C f=8IOMC r = \3 f=IOOO r-\A f=2488 r=l.09 f=3380 r= l.0>7 )o ^7^ / M l I \*\ />( \ f = 1500 P^\ r= 1.05 , iV\ T\ K \ \ v\. / ■/} \ <£=90 c 35 ) X / X/ - ^ / / N \ 1 \ Figure 20 Radiation patterns of Antenna 2M-16C a = .28 K = .75 ^ = 0* f=5040Mc r=l.37 f=6887 r=l.33 f=IOKmc r=l.28 f=ll.8Kmc r=l.38 ^=90* 36 y^ — C^ A f f~\ \X / Qc^ TMi \ / \l\ /l ' \ / N V x / ^\ \ • ^ // \ / ^s. / Jr 1 Figure 21 Radiation patterns of antenna 2M-16C a = .28 K - .75 E 4> (£ = 0° f=IOOOMc r = 2.1 f = 3000 r= 1.33 f;4000 r = l.22 CJL . — "~r~ Xx ' ( 1 X X / X. / v / \ A I \ / \ ' \ / MX / '**» X v»X X--— "^ «X"1 I <£ = 90° 37 XX r i ■*s — -\ ^^ 1 ^^ l s\ \ / Jx' \ X \ y \ \ / i X / \\ 1 ^ X y j ^"-"C^'" - -_ ^*****w^ ./^ ^ . \X X ^ ^Z" \ \ x\ / XiV \jX \ / h\ X / \ / \ \ X / \ / I "* X / S \ 1 ! 1 ">»X ^_ ' 1 S<- X ^V >X X'' X \ \ x / ' \\ X XX // X X /' / \/f \\ y\ / /x /i i \ /* i \ / I ^\ X / \ X"' 1 ^ — ' s z r "\"^"\ X // ~\\ ^\ x // A> X A /{ / XII V /\ 1 i X \ / X ' 1 / x\ I X \ / vS. x/ \ 1 ^^. x^ \ X" 11 Figure 22 Radiation patterns of antenna M-5 a = .35 K = .68 f = 5800Mc r= 1.12 f=6600 r=l.03 f=7500 r = 1.1-7 f=8000 r = l.05 f=9780 r = 1.17 <£ = 0° = 90 ( 38 A if / x ' / XV I/\ ^" /I \ y \ ^ r rf i ^^^a % ^C^Nv / vi / S / f \ / 1 / \ / J' \ X \ /^.■sy \ /x ( / u / 1 \ / \ X // ; \ / ^ vs. / ^ vs. / ^ X // / \ Figure 23 Radiation patterns of antenna M-5 a = ,35 K - .68 E0 H <£ = 0< f = 1000'Mc r = 234 y^ J \^^\ / 1 1 X s\ 1 ^ H, k /\ / \y / / / \ j"\ \ i ^ %^ /' \ \ f= 1180 Mc r= 1.76 -N ~* \ s\ / \ ) J ^ s / \ / X <* \ 1/ \ / x/ i y\ \ / 1 \ /> \ \ * N X 1 V.X f=l500Mc r=l.09 f=2000 Mc 35 ^-^Tl y^ f / X/ ' / K 1 ( >} \ / \v\ 1 N ^ X f=2500Mc r=l.45 5 ^^r t^»\ X i f ■> •* \ i X / \ Vf \ / / \ / \M // \ / nI K \ / vJ wr \ / v\ /^r \ 1 V X ss J \ -v \ X X i /\ 1 ■ 1 ' • \ \/ \ \vX /s\ 1 / X / <*"* ~^\ \ / \l ' \ / K y / U X />/ \ / V^ x / \ "n x /'J \ 1 v v JS 6-** ' y/S vX f X ~^~ \/\ /( vX / \ X f N. / S ' 1 / s 1 Figure 24 Radiation patterns of antenna 2M-32 a = .45 K = .75 E * 4>--o ( f = 3000 Mc r=l.05 f=4000 15 ^Kr?\ ^7 1 )v\ / \\ / \ \ \ * 1 \ f=5000 r = l.03 f = 7000 r= 1.03 f = 10000 r =1.24 <£ = 90< 40 / /y /\I' ^XX V\\ / 1 X / 1 \ X y^ > \ / V v X / * ) \ / \ ^ X / ' / \ / \ 'V X / y I \ 1 ^ \ / s i 1 ^"^"^ ***+ "V> ^ s f / \ s ^^ ^ ' / \ \ X /X i / / X i / \ ) x\ Figure 25 Radiation patterns of antenna 2M-32 a = .45 K = .75 E : 6 t 41 3.3 Pattern Beam Width and Pattern Rotation 3.3a Pattern Rotation Any discussion of pattern beam width must be prefaced by an understanding of the manner in which the radiated field rotates about the axis of the antenna. It was shown earlier that a change in wavelength of operation is equivalent to merely reorienting the antenna, or shifting it through some angle around the 9=0 axis. If the radiated field were independent of (f), this reorientation would ) leave the pattern unchanged. ' When viewed from different points on the 9 r 90 plane, the field of the practical structure may have a beamwidth which varies 40 degrees or more. Thus if operation is confined to a fixed frequency, an observer moving around the antenna will note a variation in beamwidth such as that of curve A, Fig. 26. Since the antenna is symmetrical, the variation is periodic every 180 degrees. Now if the observer remains fixed with respect to the orientation of the antenna, and the frequency of operation is increased, he will observe this same variation of beam width. Consequently, we see from Eq. 3,1 that, if the frequency of operation is changed, the observer must also move around the antenna a fixed angular distance to make the pattern he sees remain unchanged. An examination of Eq. 3.1 indicates that this angle may be expressed as s - In \ o a A^^-lfl^iln-^ . (3.2) Since there are few distinctive pattern changes with frequency, a check of this pattern rotation must be made by a repetition of pattern 42 beam width at the new frequency. Figures 26 and 27 indicate two experimental checks on this rotation. In Fig. 26 we see that the variation in beam width, observed through a variation in (p from to 210 degrees for fixed frequency operation, is repeated quite closely by observing at a fixed angle (f>, and increasing the frequency from 2472 to 7505 mc. The deviation at the low end is traceable to some end effect. In Fig. 27 observe that the variation in beamwidth is held within four degrees by an antenna reorientation, when the frequency was varied from 2 to 5.18 kmc. This is to be compared with the variation of approximately 50 degrees indicated in Fig. 26 over the same band of frequencies without reorientation. Equation 3.2 has been plotted in Fig, 28 to facilitate the determination of the rate of pattern rotation with frequency for some representative spirals. 3„3b Pattern Beamwidth It has been shown that the pattern of the antenna stays relatively constant with a change in frequency, except for a rotation which gives a cyclical variation in beamwidth: for a particular pattern cut. As will be shown later, there is a very rapid decay of the near fields along the antenna arms. This decay is approximately a constant function of the arm length expressed in wavelengths. This has the effect of constantly shortening the active arm length as the frequency is increased, resulting in an effective adjustment of antenna aperture size, even though the physical aperture remains constant, This is observable in Fig. 29, which is a plot of beam width versus frequency for two polarizations at two pattern cuts. There is some end 43 effect in evidence but no tendency for the beam width to become narrower with increased frequency. The antenna aperture expressed in wavelengths appears constant, U> 2 $^ U ^4 A^M** The average beam width is relatively insensitive to variations of the antenna parameters, but the tighter spiral ed antennas and antennas with wider arms tend to have more uniform patterns which exhibit smaller variations in beam width. The beam width as a function of the orientation angle at the frequency for which the arm length became four wavelengths. These patterns should be representative over the main portion of the pattern bandwidth\ of that antenna. The frequency was then decreased to the lower cutoff of the pattern bandwidth of that antenna and the antenna rotated through a suitable angle so that the patterns at the two frequencies are comparable, except for the end effect at the lower frequency. It was observed that the variation in beam width is much smaller in Figs. 30 and 31. The pattern "ears" which are characteristic of antennas with a loose spiral and rather narrow arms are in evidence in Figs. 33 and 34. 140 S so 3 o 40 v CD 20 44

en CO ro CM lO 0> fO — i?r CD CD CO * * m o CO in o m Frequency in Mc (dashed line) Figure 26 Rotation of radiated field with a change in frequency (antenna M-10-3 slot length, 33 cm) 45 4~--\ (2000 Mc) c/> = l36° ^^^Z> f = ..5 (£ = 212° sS^f?^ \ / BW = 65° Ny / \ / BW = 67{°\ / f -7-= 1.95 •0 <£ = 262° 's -7-= 2.59 TO _ c/> = 316° ^^/^^ \ / BW = 69° N. / \ y^BW = 68° \. / Figure 27 Patterns obtained by simultaneous rotation of antenna and increase in frequency, (antenna M-10) rfi polarization 46 .45 .40 .35 .30 .25 .20 .15 .10 07 f / / / ' it T 2 °7 o/ / ) / *> C i / o w 5. CO o o 1 o ^ / 11 ^ //// ///// ill///// 2 3 4 5 Frequency Ratio f/fo 8 9 10 Figure 28. Pattern rotation for a given change in frequency (N = number of revolutions of the pattern*, N = 1 when A = 77) 47 I & a a a a> -p a a 10 -p •H o a t o a ■P -P i a) CQ 05 1 / \ / X / ^ A \ / I X y 1 \ / 1 ^x X / l 1 v o* Ss ' \ (f>- 336.6 ^*"~*. H ^^X. "v*l ^^ yV ^ ""» \ XV XX /« M /\ / NE! / (x / \ \ X / \ \ X S* J 1 I ' v X •> ' 1 = 6.6° =36.6° Figure 30 Pattern at a given azimuthal angle ant. 2M-1GC, a = .28, K = .75 49 f = 1000 Mc f=3490Mc (L=4\) Figure 31 Pattern at a given azimuthal angle ant. M-10, a = .30, K = .75 50 f = 993 Mc f = 3240Mc (L=4\) Figure 32 Pattern vs azimuthal angle ant. 2M-38, a = .35, K = .75 51 f = 850 Mc f*2950Mc U=4X) Figure 33 Pattern vs azimuthal angle ant. 2M-21, a = .415, K = .75 52 f = 1160 Mc f=38IOMc (L=4\) Figure 34 Pattern vs azimuthal angle ant. 2M-32, a = .45, K = .75 53 3.4 Polarization of the Field Having defined the pattern bandwidth in terms of the polarization of the field on the axis of the antenna, it is of interest to determine the polarization 9f the field off this axis. This was measured by mounting the antenna in the ground scrrten of Fig. 10, moving the boom through successive steps of the angle 9 and rotating the receiving antenna with respect to the fixed spiral. The results for one antenna are shown in Fig. 35. This antenna becomes circularly polarized on axis at 1000 mc and the bandwidth extends somewhere beyond 12,000 mc. Note that around the center of this band the field is circularly polarized 75 degrees off axis, an included angle of 150 degrees. Over more than 80% of the band it is circularly polarized 40 degrees off axis. If the polarization of the field very far off axis is of importance for a specific application, it should be investigated for the particular antenna design. Some antennas have been investigated which exhibit a sudden rise in the polarization ratio when some 30 or more degrees off axis. The ratio rises above two and then may fall back. This is usually detectable from the relative amplitudes of the crossed polarization patterns, although obviously this is not necessarily true, since the polarization information depends on both phase and amplitude of the field components. 54 a. UJ c o o ft f=2000 mc // // // r -^s^-— * sr-S-S^ <^' — — """" o a. o o < 7 g f = 5000 mc e /| •» / o 2 / / ■ — — — ; ' 1 20 30 40 in degrees Figure 35 Polarization of the radiated E field of a balanced planar slot antenna (M-10) 9> = 90°cut "*-2 Turns 9=0° cut ) 55 3.5 Variations in the Basic Antenna 3.5a Designing for a Specific Band of Frequencies Many applications Will not require the ultimate in antenna bandwidth. A specific band of frequencies such as 1 to 3 kmc or 0.3 to 3 kmc may be desired. It is usually advantageous to design for the upper cutoff first. Thus the maximum length of tapered feed slot may be determined. To obtain a circularly polarized field, as previously defined, the feed slot should be no greater than one half wavelength at the highest frequency. Since all equiangular spiral curves converge to the origin, the arm width becomes narrower as the origin is approached. The feed slot is merely a straight slot which passes through the origin and connects the opposite spiral arm. Referring back to Fig. 6 we see that for any given spiral structure, a longer feed slot causes the ground screen between the slot arms to be wider at its narrowest portion. If this ground screen is to carry a feed cable, the v size of the cable will determine how wide it must be at its narrowest point. Thus, this required ground screen arm width, together with the chosen feed slot length will determine how tightly the antenna arms may be spiral ed. With the rate of spiral chosen, the required arm length necessary to meet the lower cutoff frequency will determine the antenna diameter. The pattern bandwidth of one antenna designed for an upper cutoff of approximately 5000 mc is indicated in Fig. 36. The antenna was arbitrarily terminated at a 10 inch diameter, which gave an arm length of 59 cm. The measured bandwidth is slightly greater than 9 to 1. A recalculation of the tightest practicable spiral with this feed slot 56 and " Microdot" feed cable indicates the lower cutoff of this antenna could be extended to approximately 500 mc in the same diameter, a diameter of approximately 0.43X. Patterns of this antenna are shown in Figs. 37 and 38. Note that beyond the upper cutoff (r>2) the pattern shape has not deteriorated, although the field polarization ratio is rising. Figure 39 is an enlarged drawing of the feed slot with dimensions in wavelengths at upper cutoff. The bandwidths of the three antennas previously pictured in Fig. 6 are shown in Fig. 40. The three antennas are identical except that the feed slot is progressively enlarged and the antennas fed with corespondingly larger cable. The feed sections are drawn to full scale in Fig. 41. The patterns of antenna 2M15C were previously shown in Figs. 12 and 13. Those for the other two versions are pictured in Figs. 42 and 43. An inspection of Fig. 6 indicates that the minimum arm width on antenna 2M-15-4C could be reduced further and carry the RG 9/U size cable. This would make the feed slot shorter and extend the upper frequency limit. In addition, the feed gap, i.e., the distance across the feed slot, can be increased for power handling purposes without affecting the patterns, as long as it is small compared to a wavelength. 3.5b Effect of Construction with Thick Arms All of the patterns shown thus far have been for antennas cut into thin metal, 1/32 inch sheet copper. The soldering of feed cable onto the ground screen between arms has the effect of making the arms thicker, particularly as the feed point is approached. Although thin metal antennas can be used in many applications, it may be necessary 57 for structural reasons to construct the antenna of a heavier metal. It becomes immediately apparent that the thickness of the arm introduces one additional parameter and that this fixed dimension will place some limitation upon the bandwidth of the antenna. Antenna M-5, which was originally constructed of 1/32 inch copper, was modified as indicated in Fig. 44 by adding 1/4 inch walls around the slot arms, simulating \ an antenna cut from 1/4 inch material, The radiation patterns in / Fig. 45 show that, although there is some change in beamwidth at the lower frequencies, the patterns are useable up to 4 or 5 kmc. Above 5,000 mc the patterns tended to break up as indicated by the pattern for 10,000 mc. These patterns are to be compared with those in Figs. 22 and 23, which are for this antenna with no walls. The original antenna had a slightly shorter arm length, which accounts for the difference in the polarization ratio at the lower frequencies. If the antenna had been designed for a lower band of frequencies it is probable that a thickness of only 1/4 inch would have had little effect on the radiation patterns. A slightly wider feed gap would also tend to reduce the effect of the thick arms. 58 o> a. uj c ,o o N *c o £ p o o = ()< <£=90< 59 MX / V 1/1 \ ( v/7 ) \ /'' \ Figure 37 Radiation patterns of antenna 2M-28- C a = .2 K = .69 feed slot = 3cm f = 3000 Mc r = l.24 f=4000 r= 1.51 f =5000 r= 1.78 f=5500 r=2,3 f=6900 r = 2.39 ^ = 0^ ° ^-^zs / X 1 ' " — -s * / y \ / X 1 lis \ / vl \y \ <£=90° 60 _ -^ ^v. yr *• ^\ / S A / S ' s - L -\. V >. / \ 1 / X 1 \\ /\ / *s Jn \ / V V 1 ^"^ A- 1 ^^*~~ ^^ ■> ^^^"^. // v x / J \ X /\ ' \ X / X ' / x * > / \ \ / \ / X » / 'Vs. i V^X Figure 38 Radiation patterns of antenna 2M-28- C a = .2 K = .69 feed slot = 3cm E e 61 Figure 39 Dimensions of feed structure of 2M-28-C at upper cutoff of pattern bandwidth (not to scale) 62 4.0 30 2.5 Antenna 2MI5C '5 1.0 .4 .5 .6 .7 .6 .9 1.0 1.5 2 2.5 3 4 5 6 7 8 9 10 12 Frequency in Kmc 4.0 0) M .9- 30 5 2.5 c o 2MI5-3C — tio of Polariza 9 bi <: , ^ -4 .5 .6 .7 .8 .9 1.0 1.5 2.0 2.5 3 4 5 6 7 8 9 10 12 Frequency in Kmc o 4.0 'x < 3.0 — — _. 2.5 2MI5-4C 2.0 1.5 1.0 -""' 1-5 2 2.5 3 4 5 6 7 8 9 10 12 Frequency in Kmc Figure 40 Pattern bandwidth for various size feed slots (see Fig. 41 for dimensions) 63 .050 Cable (Microdot) Figure 41 Full size drawing of the feed slots on antennas a. 2M-15C b. 2NKL5-3C c. 2M-15-4C f=595 Mc r=2.0 f=IOOO r=l f = l950 r = l.06 f=3950 r <£ = 0° -*-\ X \ / /\ ' v s\ \ / \ X' V x 1 \ y \ \ / l X Sf ' \ i \\ yx II N.N II x yr \vX 5 /^^ ^^v^^x s ff N\ X /\ /' A yX \1/ \ /\ J/ / m\ / \\\ /*»■ T J <£=90° 64 , "4»^'" "^.^ / / /x / / V ^N '/ \ / IV >X /' 1 ■ \V\ jr J* On \ jC O t I X /\ }* *"( \ X\. / XT > / N jf \ / i X / nX //' \ / l sX / • I i > / // VV-Xv / / / Tl X X / / v X / X / i!/ \ / Us. /# \ / \\\ // \ / A. X / // \ / s' ( i 1 " > /--" I *-"% >^ ^ % ^*\ \ \ X \ X \ ] 1/ \ 1 X yi \ / ^Yv A i \ / AX 'J * \ / N v\ r ' i 1; ^^ -A Figure 42 Radiation patterns of antenna 2M15-3C (see Fig. 41 for dimensions of feed) E * f=595Mc r=2.06 f=800 r=l.34 f=2835 r=2.03 =O c /j /i X r<~~ ^"1 n y\ /\fs 1 (X vr/ \ / I *\ / \ X X 1 ^x Ss 1 f=l200 r=l.l3 X ^nV, ^x ^s X M \ \j l \ \\ 1 ^\ /s / \ /> - J f=2000 / r=l.35 /\ ( r ' Nil Vx ^ = 90' 65 x If**— M \ / I X / , < ^ X / * ) \ / y / I /s 1 s^r^" 3^ \ / rj /\ r V / \ / \K y/j \ / \v\ \ X. \ A / A X /r \ 1 ^ s - /^ j Figure 43 Radiation patterns of antenna 2M15-4C (see Fig. 41 for dimensions of feed) 66 Figure 44 Antenna 2M-5W <£=o e f=IOOOMc r=l.63 f=2000 > // ' r=l.37 /\ / / 1 * / \ //\ \ f*3000 r*UO / S/7 "* r>^^v \\ \ ^ X / / \ /SI \ f=5000 r=l.45 f= 10,000 <£ = 90 e 67 /^/ v\ yy / \ \ /x ' /^ \ 1 /\ / /\N /I \ / | V • 1 \ -X. A. S" / x / X N X \ y\ / \l\ At \ / l N I s.\ ^^^^- /s^ \V X/ / \X / f\f // l\ 1 1 ^\ / / \\ / \ ^ X / I \ / ^ X 4" \ /** Figure 45 Radiation patterns of antenna 2M-5-W. 1/4 inch walls around slot arms) (antenna M-5 with 68 IV THE NEAR FIELDS 4.1 The Tangential Field in the Slot Arms. To gain a better understanding of the operation of the antenna, experimental facilities were set up to measure the fields on the antenna arms. The first attempt was to measure the tangential compo- nent of the electric field in the slot antenna. A probe carriage was constructed that would allow the precise placement of a probe with three degrees of freedom, at any point within a 12 inch square and at any point within six inches of the plane of the square. The carriage was constructed to carry several different types of probes which would protrude through a four inch thick section of hair absorbing material. A .14 inch dipole probe was constructed, fed with miniature rigid wall coaxial cable and a split drum balun. The dipole was checked by probing the fields immediately in front and just inside an open-end waveguide. The guide was constructed to be 3/8 inch by 2 3/4 inch and was fed from normal S band guide through a tapered section. The probe was positioned 1/4 inch inside the guide mouth and rotated, and the relative amplitude as a function of angle was recorded. It was then withdrawn in 1/4 inch steps and this procedure repeated for five steps. The minimum and maxi- mum probe response was at all times within three degrees of the expected probe orientations and the minimum response was greater than 40 db below the maximum. To allow a precise and repeatable placement of the probe along the arms, the desired positions were calculated and plotted on thin polar graph paper, which was then lightly stuck to the face of the antenna. 69 The antenna was bolted into a five foot square ground screen- The probe was positioned at the surface of the slot and rotated for maxi- mum response. Figure 46 is a block diagram of the equipment, and the amplitude and probe orientation, as recorded along the arm for four frequencies, is indicated in Fig. 47. These curves confirmed several things which had been observed in pattern and impedance measurements. The decay of the fields along the arms is very rapid. Further, this decay is essentially independent of frequency. It is also interesting to note that the reflected wave is small in magnitude and quickly damped. Figures 48-51 are full size outline drawings of one arm of the antenna, showing probe points and the probe orientation for maximum response. The probe orientation did not coincide with the anticipated direction j of the electric field, i.e., along the orthogonal curve, and since the direction of the electric field in the slots of the infinite length antenna was of interest, a new and larger antenna was constructed. Antenna 2MA-15C was extended to an arm length of 280 cm, a diameter of 54 inches. The arms were cut out of 1/32 inch copper and mounted on a polyfoam support. The antenna was fed with a balun perpendicular to the plane of the antenna. Since the larger antenna would permit making the measurements at a lower frequency, a new and larger dipole probe was constructed. This increase in probe size made possible more accurate construction. Figures 52 through 55 are full size drawings of the probe paths, showing the required orientation of the dipole for maximum response. The orientation of the probe in the center of the slot corresponds to 70 that in Figs. 48 through 51, indicating that the displacement of the field from the orthogonal curve was not entirely due to the end effect of the shorter antenna. The tangential electric field in the slot does not appear to be oriented along the orthogonal curve and the deviation from this curve increases as the distance out along the slot away from the feed point is increased. 71 Ground Screen HP 415 A SWA Figure 46 Experimental setup for measuring electric field in slot arms 72 o I I CD o ■p o T3 -p SP o p 4 5 (1) u fafl •H qp u; apn;j|diuv i r i i i ! r jt i i n i > / x X Figure 48 Probe points and orientation of dipole probe for maximum, (probe not to scale) ant. 2M-10, f = 1000 mc 74 Ny -/" V- V S \f / I H \ 'i V \ ; i Figure 49 Probe, points and orientation of probe for maximum, (probe not to scale) ant. 2M-10, f = 1500 mc 75 / / / / \ V* w h '/. / Y I \ \ \ \ \ Figure 50 Probe points and orientation of probe for maximum, (probe not to scale) ant. 2M-10, f = 2000 mc 76 Figure 51 Probe points and orientation of probe for maximum (probe not to scale) ant. 2M-10, f = 2500 mc. 77 Metal Arm Scale Drawing of Slot and Dipole Probe 31 X from Feed Point (Slot Width J7\) r Metal Arm legrees > o o -30 f =525 MC X = 572cm Arm Length = 4.9 X -6-4-2 o 2 4 Distance from Center of Slot in cm, Figure 52 Orientation of probe for maximum response, 1.31\ from feed 78 -6-4-2 2 4 Distance from Center of Slot in cm f =525 MC X = 57.2 cm Arm Length 4.9 \ Figure 53 Orientation of probe for maximum response, 1„53\ from feed. 79 w -10 u 4> -30 -6-4-2 2 4 Distance from Center of Slot in cm f = 525 MC X= 57.2 cm Arm Length 4.9 X 2.09 X from Feed (Slot Width. 27 X) Figure 54 Orientation of probe for maximum response, 2„Q9\ from feed 80 3.58 X from From Feed (Slot Width .473 X) f = l050MC X= 28.57 Arm Length 9.8 X -4-2 2 4 Distance from Center of Slot in cm Figure 55 Orientation of probe for maximum response, 3.58X from feed. 81 4.2 The Normal Field on the Arms. 4.2a General Considerations . and Theory of Measurement It appeared desirable to continue the study of the near fields by measurements of the normal component of the electric field on the sur- face of the plane conductor form of the antenna. This component can be measured by an open-end coaxial probe, which can be constructed much more accurately than a very small dipole and balun. Therefore the antenna was constructed with 1/32 inch copper arms mounted on a two inch thick slab of "Styrafoam". It was fed with a balun brought out perpendicular to the plane of the antenna and was positioned approxi- mately 50 cm in front of a 10 inch thick absorbing screen. The probe consisted of a rigid coaxial line constructed by pushing the center conductor and teflon dielectric from RG 141 /U cable into a .140 inch outside diameter silver tube. As before, the probe points were plottedi on polar paper which was fixed to the surface of the arms. The probe was again connected by a flexible coaxial cable to a tuner and coaxial bolometer mount and the output read on a standing wave amplifier. The cable was carefully selected from one of several for minimum amplitude and phase variation with flexing, and the amplifier spot-calibrated with fixed attenuators of known accuracy. Figure 56 is a block diagram of the equipment as used for amplitude measurements. The relative phase of fields along the arms was measured by the I use of a balanced detection method. A coaxial hybrid junction was (9) constructed following that proposed by Morita and Sheingold and used in the circuit of Fig. 57. Fundamentally the method consists 82 of putting a reference signal into the series arm (4) and the signal to be measured into the shunt arm (3) of a hybrid junction. The vector sum of these signals is impressed across the load connected to output no. 1 and the vector difference across the load connected to output no, 2 of the junction. A balanced input adapter was constructed to pro- vide proper bias for the bolometers and to take the difference of the signals from the hybrid junction. When the reference signal is adjusted to be 90 degrees out of phase with the test signal, a sharp null is observed. A study of Fig. 58 indicates one advantage of this method; it provides a good null for considerably different amplitudes of the test and reference signal. The method which requires the addition of a reference signal 180 out of phase with the test signal requires approxi- mately equal amplitude signals for an easily measured null, since the null becomes increasing broad as the difference between the signals increases. This requires a variable attenuator carefully calibrated for both amplitude and phase. 4„2b Adjustment of Equipment Barretters 1 and 2 are tuned by breaking the circuit of Fig. 57 at C and at D and applying a modulated RF signal to each barretter in turn. Resistance R is turned so as to remove its resistance from the circuit to the barretter in use, and the tuners are adjusted for maximum output on the tuned amplifier. The outputs of the detectors were within 1 db of each other. Points C and D are reconnected and the circuit broken at points A and B. Point A was connected to input no. 3 and a tunable detector and tuned amplifier were connected to B. Thus any signal leak- ing through the hybrid junction from 4 to 3 is modulated; detected, and 83 indicated on the amplifier. The tuner "t" is adjusted for minimum leak- through. It is not difficult to get 60 or 70 db of decoupling between the two junction terminals, although the decoupling is very sensitive (8) to the balance of the loads connected to terminals 1 and 2. Mc Coy has estimated that as long as the null is maintained down 70 db, a conservative estimate of error due to leak-through is about one per cent. After nulling the hybrid junction points A and B are disconnected, a 50 ohm load is connected to terminal 3 and the oscillator is modulated at 1000 cycles. Resistor R is adjusted for a minimum output on the amplifier. The system is reconnected as shown in Fig. 57 and is ready for measurements . For measurements, the probe signal is modulated rather than the oscillator signal, since this imposes fewer requirements on the audio (8) null obtained at R. Even though the unmodulated reference signal , which may be large compared to the probe signal , is present at the detectors, the result is only a DC input to the transformer. The only error due to the reference signal will be due to that leaked through the hybrid junction and this is reduced by a null of potentiometer R. The probe is positioned at a chosen point and the reference signal varied in phase until a null is obtained. This is repeated along the arm, giving the relative phase on the antenna in terms of the known phase in the slotted line. The system, exclusive of the probe, was checked by measuring the phase along a different slotted section. The variation from a straight line was entirely negligible. The probe was checked by constructing one which had one-third the original diameter and the results were negligibly different; however the useable amplitude range was decreased. 84 4.2c Measured Fields The normal field on one antenna was measured at 12 frequencies from 125 mc to 8000 mc . This represented a variation in length from 0,16 to over 10 wavelengths. The measurements at lengths of .3\ and shorter revealed too much reflection from the arm end to be of use in establishing a trend. However, it is significant to note that for an arm length of only one-half wavelength, the trend of the normal rate of decay is discernable. The rather large reflection from the end quickly dies out, as it does for longer lengths. Figures 59 and 60 show the trend of the decay of the normal fields for frequencies up to 2500 mc. Above this frequency there was no great change in this trend, but it was felt that the size of the probe in wavelengths would leave the measurements open to question. Figures 61 and 62 depict the near fields as a function of arm length on a narrower arm antenna. Several conclusions can be drawn from these graphs. As was evident in the previous curves of the tangential field in the slot, reflected waves from the antenna end are soon dissipated. The fields on the antennas with the narrow arms tend to decay at a somewhat slower rate and it appears to take longer for the reflected wave to die out. This was evident in the radiation patterns, where it was noted that the antennas with narrower arms required a slightly longer arm length for stabilized patterns . Figure 63 indicates the relative amplitude of the normal field along antenna 2MA-15 when it was 2.5 \ in length and when extended to 18.7,3. (the 54 inch diameter antenna referred to in the previous section). 85 Figures 64 and 65 show the relative phase of the fields along the arm under these two conditions. Figure 64 indicates two items of interest: (1) The fast initial decay of the fields along the arms appears to slow down as the arms become wider in wavelengths. This point was evident in the previous figures and particularly in Fig. 47. (2) The average phase velocity over the first three wavelengths approaches a v/c ratio of approximately 1.7, indicating a fast wave which is consistent with the rapid dissipation of energy by radiation. The v/c ratio of the short antenna appears to be lower, although still greater than one. Figures 66 and 67 indicate the relative phase of the fields along a narrower armed antenna at two frequencies. The relative amplitude and phase was measured along the inside and outside of the antenna arms and along several spiral paths along the arm, These measurements have been combined into a full scale map of equal amplitude and phase contours along the antenna arm in Figs. 68 and 69. 86 AIL Osc HP 211 A SW Gen Absorber Antenna on Poly foam Balun i 1/ Y Absorber Mounted on Probe Carriage Barreter Coaxial Probe 4 ^ HP 4I5A SW Amp Figure 56 Equipment for measuring amplitude of normal component of the near field. 87 Absorber 20db Coupler j- Antenna on f Polyfoam -VyV- Filter (LP) 6R 874-GA .Allen, 14 FXR Freq Mtr r* 1 VTVM Scope 12/if —I Barreter i No.lj Bias ^250 ohms Bias o I2^f Coaxial Probe 1000 Cycle Modulator '**- Barreter No. 2 HP 4I5A SW Amp Figure 57 Experimental setup for measuring phase of near field along antenna arms 88 E T -Er E T E t +Er 1.0 .75 UJ 1 i- Ul —.25 ^ v. Er = .25, \ \ \. .5/ \ l.0> 2.0 1.5 oe UI 1 \ Ef - = I.Q t / 1 1- Ul — 1.0 1 5 a UJ t.5 UI ^25 90 120 150 180 210 240 270 9 in degrees 30 60 90 120 150 180 6 in degrees Figure 58 Comparison of the null obtained by two methods of measurement of relative phase 89 -40 1.0 1.5 Length along Arm in X. Figure 59 Amplitude of E. T field along arm of antenna 2MA-15, a= ,30, K=.62 N 90 o CM IO CO II « « o CO m oJ II cd . m 1 o |j CM CM a c (< C c ' — ' cd E i_ «H *>« o — • o c 6 o fc o 0$ JC ?f +- P o> O c 0) _J cd •d o iH (1) m o m Csl 1 Csl 1 o qp uj dpnjjidujv 9Aip|ay o CD ■a -p & o CO •H 91 .o x» a> ■o a> 0) a: \ -5 \\ \ -10 \ \ \ ■• r \ V^ -15 -20 -25 / > s"~ S/ -30 1 - 1 50 MC f=IOOO Mc -3S -40 -45| 1.0 1.5 Length along Arm in X 20 2.5 Figure 61 Amplitude of E field along arm of antenna 2MA-10, a = .30, K= .75 92 / 1 J / 808 ( 10 9 « 1 1 1 II II — «*-«♦- ! 1 ^ y ■ ! 1 / ^■* ^~. ^**^ / X / s / f I 1 1 \ \ 1 > I--- r~ */ /< // Ss j yX ^ 'i/ r // 4 1 / f / . «/ JV £r / ^ in k5 i> 11 M O 10 n CO cm c E »_ <; c o « SI — '.e o> c in m I 10 m in m CM 1 CM 1 tn 10 1 1 1 o I N a a •p § S3 o 4 •H o •o ■3 +> •H a to a> u be El qp ui 9pn|i|dujv 9AijD|ey 93 f = 2000 Mc X= 15cm Arm Extended to I8.7X \ \l \ I \ \ / { 1 / V / ■* *^ — s / / I / 1 1 / J t / i y jy c 9 ^ CM .S o a. 15 £ a> o c o in m I O T ID I o CM I IO CM I O to I IO O I bo a o A t> 00 c m CM w 8 u a in CM ■o w a> a a> o u. r^T ClJ E o T3 i_ iH *- •H +» ed rH CO to a •H fa qp u| apn^idujv ©Ai^iey 94 Sd9j5ep ui asotid 3AijD|ay o ID O CvJ 1 W 1 1 io to I o io u N IO at 8 IO a M 1 *< bo § c <•- c ■o O £ 0) M 0) •H £ if E Q> m IO O a C o (A 'a 5 tude and 18.7 X. o lative ampli m length of to M qp ui 3pni!|diuv 9AijD|9y sadj6ap uj asogd 9AijD|8y 95 o in o CM 1 M 1 IO 1 in I O I o 0) CO a ft •o & cd •d 3 • +> ! •H a. II > •H •M cU H es IO to u fa qp ui epnijidaiy SAijoiay 96 saajbap in asDq m i w o m O 1 CM 1 ro I o I m ^- I qp ui 9pru!|dtuv 3Ai|D|aa 97 S99j6ap U| aSOL)d 9A!|D|3y o CO o r-i I •H H t > •H -P cd H CD ft! M u qp uj epru!|duj\/ aAi|D|8y Figure 68 Contours of equal amplitude of E„ T field with reference to N points marked by x^ant 2 MA-15 99 Figure 69 Contours of equal phase of E field on ant. 2 MA-15 100 4.3 Estimation of Error The errors introduced by the sampling probe have been discussed in 11 the literature. The checks made on the dipole probes, the coaxial probe, and the phase measuring setup have been discussed in Sections 4.1 and 4.2. The largest source of error appeared to be due to the reflection of energy by the absorber-covered probe carriage. It is extremely difficult to probe a circularly polarized radiating source, and it was found that the antenna was inducing currents on the outside of the coaxial probe. These fields apparently propagated down the probe to the carriage, were reflected back, and returned to the antenna to distort the original field. This effect was small near the feed point because of the strength of the original field, but became apparent when the probe was moved out along the arm to the point where these original fields were down 25 to 30 db. A one quarter wavelength movement of the probe carriage toward the antenna, without changing the position of the probe itself, produced changes of as much as 5 and 10 db in the measured fields. This was extremely difficult to overcome but was minimized by moving the carriage to a distance of approximately 49 inches from the antenna, monitoring the reflection coef- ficient of the spiral antenna, and placing a quarter-wave choke on the rigid wall coaxial probe. This choke was positioned along the probe until the carriage could be moved through ?/4 without introducing a substantial change in the monitored field. It is estimated that the measured fields are within 10% for the first 20 or 25 db of decay and within 207o farther out on the arms. 101 V. THE INPUT IMPEDANCE The input impedance of the planar balanced equiangular slot antenna converges rapidly as the frequency is increased. For frequencies such that the arm lengths are greater than one wavelength, or slightly less, the impedance remains reasonably constant. The measured impedance of three typical antennas is shown in Figs. 70, 71, and 72. These antennas were constructed of 1/32 inch copper with a .150 inch diameter coaxial cable (RG141/U) bonded to the ground screen between the slot arms. An inspection of these three impedance plots indicates that there is a relationship between the arm width and the impedance, i.e., the narrower slot arms present a lower input impedance. This relationship is shown graphically in Fig. 73. This curve is only an approximation to the impedance, since variations in the physical construction of the antenna will bring about changes in the input impedance. From the symmetry of the structure the characteristic impedance is known for one width of arm. It is easy to show that for 5 = 7T/2 the antenna arms and the space between the arms are identical in shape; thus the antenna is identical to its complement and its impedance is independent <7) of frequency and equal to 607T = 189 ohms. The antenna of finite thick- ness does not have a uniform characteristic impedance (since it is a non- uniform transmission line) but the input impedance does settle down to a reasonably constant value for relatively thin antennas. It is of interest to note that the characteristic impedance of a transmission line which is carrying a wave in the TEM mode can be shown to be inversely proportional to the capacitance per unit length. While it appears that there may not be propagation of energy in the normal TEM 102 mode along the spiral, the antenna behaves in many respects as if this were true. Thus any finite antenna thickness would increase the capacitance between the arms and decrease the measured impedance. The measured impedance of the antennas tested is considerably below the theoretical impedance of an infinitely thin antenna, due in part to the thickness of the metal and the presence of the feed cable. The measured impedances on which Fig. 73 is based were for antennas constructed of 1/32 copper, with k = .2 inch, with a feed cable equivalent to RG 58 AT, and without a dummy cable on the opposite arm of the ground screen. The use of a dummy cable of this size will lower the measured impedance approximately 10%. The input impedance of the antenna can be lowered still further by increasing the thickness of the metal. This will be -done at the expense of some pattern bandwidth, as was indicated in Fig. 45. Increasing the thickness of the arms of antenna 2M-5 to one -fourth inch lowered the measured impedance from approximately 57 or 60 ohms to approximately 38 ohms . The use of a miniature cable such as "Microdot'" lowers the capacitance between the arms and raises the measured impedance by approximately 20%. The effect of the feed cable is evident in Fig. 74. Antenna 2M-10 was originally constructed with feed cable and with a dummy cable of RG 141 /U on the opposite arm of the ground plane to balance the structure. The standing wave ratio as a function of frequency was recorded. The dummy cable was removed and the measurements were repeated. The feed cable 103 was removed and the "Microdot" cable substituted and again the measure- ments were repeated. The structure of the antenna itself was not altered. The antenna fed with the "Microdot" cable presents not only a higher average standing wave ratio but also considerably greater variations in the standing wave ratio. The latter effect may be due to irregularities in the miniature line after soldering it to the ground screen. The standing wave ratios of several antennas whose radiation patterns have been shown are illustrated in Figs. 75, 76, and 77. 104 Figure 70 Input impedance of slot antenna 2M-8 .303 arm 1 = 44,5 cm, a = K = 105 Figure Tl Input impedance of slot antenna 2M-10 a = .30 arm 1 = 42.3 K = =75 106 Figure 72 Input impedance o:f slot antenna 2M-15 a - . 30 Arm 1 = 39 cm E = .62 Ic r 1 £ /? 107 140 1 ' 120 l \ p yi />, = ke°9 \y\ r z Pz'?P\ 100 d> u o 80 TJ fl> o. E *. SO o. c 40 20 .5 .6 1.0 K Figure 73 Input impedance of balanced, planar slot antennas (constructed of 1/32" copper with .150" coaxial cable bonded to screen between the slot arras) 108 oijDy aADM 6u;puDis s o^ » °Nd <2° K , ■—«*-, (1 I I too « ll J s T C c a c < D 1- ) O i.v- 5 5 > 5 a c c c ? C 7 J u f o •H o> CO * 00 ll t- X i0 (35 CO II m M CM 109 to u CM E u m c — " a> 3 a> u. CO CO ir> o o i oo CM 3 CM cd a g (V -p fl d ^ (V «H H o ,a at O ri "§ CO > be A G +» ■H -H •O £ cd T3 +-> (D fO m CD U 3 bD •H 110 I i J V < i ( 1 1 T C C a c I c c _c c X c a ?cv D D a 5 3 3 j I } \ to CM in >» u c a> 3 cr 0) to o in o CO o 1 E in .E N a § -p o •H •P at U > •H a a$ ■P CO CO t> 0) ?H 3 •H ro M _^ cf iTl ~d jT S* / _^/ , ' I C C t X - c T 5 ? ? { 111 to CV! 10 in o in i in r-H ! u £ E d s: +-> _ c cl IO — aS >» o «H c ai ?■< CD > S3 •H T3 aJ +-> W l> •H tO CM OMDy 9ADM 6uipuD|s 112 VI. EFFICIENCY OF THE BASIC ANTENNA 6.1 Method of Measurement The efficiency of the basic antenna was measured by a method which makes use of antennas constructed of different surface resistivities. The basic antenna is considered to be the metal structure, consisting of slots in a metal plane or metal arms in free space, without lossy dielectric material or any type of cavity backing. The principle of this method, which was proposed by Crowley in (10) 1953, is to supplement the antenna whose efficiency is to be measured with another antenna, identical in every respect except that it is constructed of a metal with a different conductivity. The method and the problems encountered in its use will be considered in some detail, because, although it appears to be no more difficult than any of the other accepted' methods of measuring efficiency, it has certain advantages over some of these methods. Let quantities pertaining to the given antenna be denoted by superscript one and those to the supplemental antenna by two. Then and P R 2 + P L 2 = P I 2 (62) where P is the power radiated, P the power lost, and P the power R LI input to the respective antennas. If K ! " P R 1/P R 2 K 2 * "l 1 ^! 2 K 3 " P L 1/P L 2 113 the efficiency of the given antenna may be expressed as K 3 2 E = A similar expression can be obtained for antenna two. To simplify the measurement of K , K Q , and K , it is assumed that the currents are distributed over the surface of antenna 1 in the same manner as over the surface of antenna 2. As Crowley points out, there are two things that could invalidate this assumption. The antennas may not be physically identical and the different surface resistivities may force the currents into a different distribution. If the first cannot be eliminated by careful construction, every antenna constructed will have a different efficiency, so that another method is required. The second may be reduced by the choice of surface resistivities used. If the assumption is correct, the radiation patterns of the two antennas are identical and K. may be made equal to one by placing a fixed receiving antenna in the field of the antennas being tested and adjusting the power input to the two antennas until equal received voltages are: indicated. Since the currents are assumed to have the same distribution, this adjustment for equal field strength makes the absolute value of the current the same at corresponding points on the two antennas, and thus K„ = l 1 JlVS ds ' P L 2 J,' 1 !'**.- or r K = — = R 3 r 2 114 where R is the ratio of the surface resistivity of antenna 1 to that of antenna 2, K Q can be obtained by using a slotted section in the feed line to the antennas, since in this feed line the product of the voltage maximum and the voltage minimum is proportional to the power absorbed by the load. Hence (E E , ), max min 1 K_ — 2 (E E , )_ max min 2 One of the advantages of this method is that, once the ratio R is obtained, it is a simple matter to measure the efficiency over a wide range of frequencies, since only K need be determined at these frequencies, A second advantage is that it may be carried out in the laboratory, since reflections will not affect the measurements, providing they are not great enough to change the efficiency. 6.2 The Experimental Investigation 6.2a Measurement of Surface Resistivity The ratio of the surface resistivities of the two metals was obtained by constructing two lengths of shorted coaxial lines, using the two metals from which the antennas were to be constructed. This statement needs some qualification. It did not appear to be practical to construct a coaxial line from the sheet stock that was used for the antenna, so commercial cold drawn tubing was used for the lines and cold rolled sheet for the antenna. Although, so far as possible the same metal was obtained, the finishing, (drawing and rolling) may leave the metal with slightly different surfaces, and hence resistivities. As will be noted later this difference may be expected 115 to give only a second order error. It can be easily shown that the surface resistivity of the metal is directly proportional to the attenuation in the air dielectric coaxial line and that the attenuation of a shorted line is inversely proportional to the standing wave ratio on the line. With this in mind it is obvious that the R and hence K_ can be obtained from the ratio of the standing wave ratios on the lines. The first attempt at measuring R was to construct three coaxial lines, 67 cm in length, of steel. The SWR and attenuation were measured at several frequencies between 1000 and 2000 mc. Figure 78 is a block diagram of the equipment used for these measurements. It should be noted that, in theory, the surface resistivity need only be obtained at one frequency; however, as a check on the measuring procedure and to reduce the experimental error that may appear in that one reading, the SWR was measured over a band of frequencies. The theoretical variation of the SWR with frequency was calculated and this curve normalized to the measured data. Values used to calculate R were obtained from the normalized curves. After measuring the standing wave ratio of the steel lines, the lines were silver plated and the measurements repeated. One steel line and that same line, silver plated, constituted one pair of lines for calculating the ratio of surface resistivities of steel and silver plated steel. The three separate steel lines were used to check on the plating process as well as on the measurements. The use of steel and silver plated lines was an attempt to have identical lines, aside from the negligible change in dimensions due to plating. The measurements of the attenuation of the three silver plated lines 116 indicated a variation of as much as 25% in the surface resistivity of the plated metals. However this variation in the silver plated lines caused a variation of less than 1% in measured efficiency of the silver plated antenna. This would suggest that any difference in surface resistivity between the tube stock and the sheet stock of the same metal would be very small in comparison with the difference between metals. Figure 79 indicates the agreement of calculated and measured values of SWR as a function of frequency for one pair of lines. In addition to the silver plated lines and antenna, two brass lines and a brass antenna, and a copper line and antenna were constructed „ The measurements were repeated, pairing the steel antenna with another metal antenna in each instance. 6.2b The Ratio of Power Inputs K, the ratio of the power fed into the two antennas with the radiated power held constant, was obtained with the equipment shown in Fig„ 80. Plane conductor antennas were constructed with arms of 1/32 inch material mounted on two inches of Styrafoam . The antenna was fed by a .140 inch teflon dielectric cable and a balun perpendicular to the plane of the antenna. The probe antenna consisted of a small dipole supported on a block of foam. The power input to antenna 1 was adjusted to some reference value as read on, the meter monitoring the probe. The maximum and minimum values of the voltage in the slotted line were obtained. The antenna arms were unsoldered from the balun and arms of the second antenna substituted. New voltages were obtained from the slotted line 117 after the power input had been adjusted to make the radiated power equal to that of the first antenna. K is obtained from the voltage ratio. 6.2c A Check on the Current Distributions The radiation patterns of the steel, brass, and silver-plated antennas mounted on the foam support were recorded. There was a difference in pattern level, indicating a difference in efficiency but no change in pattern shape. It is recognized that the far field pattern may be insensitive to small changes in the current distribution, but the patterns should provide some check on the distributions over the different antennas. 6. 2d Measured Efficiency The measured efficiency of this antenna (2MA-15 ) at 1200 mc is indicated in Table 1 below. Table 1. Comparison of Measured Efficiencies using Different Metals. Brass Silverplate OFHC Copper Steel 98% 90% 98% 92% 99% 98% The 9% variation in the measured values for the steel antenna is considered to be acceptable in view of the fact that any measurement of efficiency is a difficult measurement and cannot be expected to be any closer than 10% to the actual value. The efficiency of the brass antenna was measured over a range of frequencies such that the arm length varied from .4 to 2.55 wavelengths. These measurements are shown in Fig. 81. For an arm 118 length of .4 wavelength, which is shorter than the antenna which will be used, the efficiency is above 95%. It rapidly rises to more than 98% for all practical lengths. To determine whether this efficiency would deteriorate when the arm width was reduced, the measurements were repeated on an antenna constructed with the same rate of spiral but narrower arms. The efficiency of this antenna was measured at 3200 mc and there was no appreciable difference from that indicated for the original antenna. The arm widths of the antennas are indicated in Fig. 82. 119 Shorted Coaxia&Efrie 1= 67 cm. Amerac Ext. Cav. Klystron LP Filter FXR Z 816 A PS S Mod GR Atten. 20 db # HP 805A SL 6db Bolometer FXR 410 A F Meter i Xtal Micrometer Drive HP 415 B SWAmp VTVM Scope Figure 78 Experimental setup for measurement of attenuation constant 120 70 60 50 o 40 o 5 o» c 30 ■o c o 20 en a «fc- o > 10 Curves Are Calculated Points Are Experimental oJ Steel 1.0 1.2 14 16 Frequency in Kmc 1.8 2.0 Figure 79 Standing wave ratio measured on one pair of shorted coaxial lines. 121 FXR Z8I6A - Gftiflften - GfTSSJen n r 50/1 n r >20db >20db u u Bolometer — U_ HP 415 B SW Amp VTVM Scope f Weston 622 10" of Absorber 51 cm from Ant. Dipole Probe Xtal ^ HP 4I5A SW Amp. Figure 80 Equipment for measuring ratio of input power to the antennas 122 100 k, 1 1 o d 200 Mc 3200 Mc 3 98 I960 Mc 96 "T" 1200 r AC c J? 1 QA c a? '5 66 !00 Mv Ul 99 * Antenna Arms Lengthened 90 88 1.0 1.5 2.0 Arm Length in X 25 3.0 Figure 81 Efficiency of 2MA-15 constructed of brass 123 V I Arm of Antenna f 2MA-I5 >l Arm of Antenna 2MA-8 Figure 82 Line drawing of one arm of the balanced antennas used for efficiency measurements. 124 VII. THE CAVITY BACKED ANTENNA 7.1 Efforts Toward a Unidirectional Antenna The primary objective of the present investigation was to study the characteristics of the basic antenna — the antenna without lossy dielectrics, cavity backing, or other modifications. The usefulness of this antenna is limited to those installations that permit radiation into the two hemispheres that surround the antenna. It has been recognized from the beginning that it might find its widest use as a flush mounted cavity backed antenna. Therefo^ as a secondary objective, some time has been spent in an effort to obtain a backing that will permit the full use of the bandwidth of the basic structure. Such efforts have not been successful as of the present time. An extension of the principle of specifying the structure entirely by angles would lead to some form of conical or spiral structure. Various cavities with conical bottoms, as in Fig. 83, were tried. The cone angle was varied from 5 degrees to 45 degrees without showing promise of a bandwidth greater than two or three to one. Spiral backings, such as that in Fig. 84, were tried. It was possible to suppress the radiation on one side at certain frequencies but the structure was not frequency independent. The expanded antenna appears to be frequency independent, as is the planar structure; however, when the antenna is expanded, the reationship between the arm length and the polar angle q) is altered so that the rate of pattern rotation is altered. A successful combination of the expanding and planar models would, of course, require that the expanding spiral suppress the radiation of the planar spiral in one hemisphere at some frequency and that the two spirals have the same rate of pattern rotation. One could expect this structure to be unidirectional and independent 125 of frequency. Such a structure has not been successfully constructed but would seem to warrant further investigation. 126 Ground Plane Planar Antenna Cylindrical Cavity Conical Bottom Figure 83 Conical bottom cavity Ground Plane Planar** f Antenna Expanded Antenru Figure 84 Planar equiangular spiral antenna backed with an Expanding Conical equiangular Spiral. 7.2 Antenna with Absorbing Termination 127 One solution to a broadband cavity backing has been proposed by (4) DuHamel and Isbell. For some applications, the sacrifice in efficiency brought about by a resistive cavity may not be prohibitive. The cavity, to be completely effective, must absorb one half of the radiated power at all frequencies of operation, leaving the performance of the antenna the same as its free space performance in the hemisphere of radiation. To check the performance of the spiral over one such cavity, a metal hemisphere of radius eight inches was lined with three inches of absorbing material and attached to one side of antenna 2M-15c. Figure 85 is a drawing of the cavity and antenna. Radiation patterns of this antenna with and without the cavity over a 20 to 1 bandwidth are shown in Figs. 86 and 87. The relative gain of the antenna with the cavity to that of the antenna without the cavity is indicated in Fig. 88. The increase in gain at the lower frequencies would indicate an incomplete absorption of the back radiation; however, above 1500 mc the gain at pattern maximum is within 1 1/2 db of the gain without the cavity. The standing wave ratio of antenna 2M-15-3C over this cavity is indicated in Fig. 89. These measurements indicate that it would be possible to obtain good broad band operation with a suitably developed resistive cavity. For certain applications the decrease in efficiency may be overweighted by the need for very broad band unidirectional performance. 128 m _n ..'S* ® X Absorb 3 layer sorb C a> F a> 0) F J. o "5 o Without Covity With Cavity 129 f=595 Mc r=2.00 f = 800 r= 1.37 f=IOOO r=l.l4 f=l400 r=l.02 f=2000 r=l.03 5 ^*r ^^< S/7~* s // /\ Y / Nl / \\ L ^ /s\ \ r = 3.00 r=l.7l r = 2.l9 r = l.08 r = l.04 8 ^ \y \ / \v y/> \ / * V // / \ 1 ) 4 ^^7S ^\N-^\ \\ X A I w/ \ yyi \ / \\ /// \ 1 r\. /X • Figure 86 Radiation patterns of antenna 2M-15C with and without a resistive cavity 4>=o c E * Without Cavity With Covity 130 f=2820 r=l.08 f=3950 r = l.07 f=5590 r=l.08 f=7300 r=l.04 f- 11,960 r=l.28 4 ^^Cr ^^N ^V^V A\ ' * / X /Si/ \ \/\ \y \ / v\ /if \ /St \ / v\ /Jr \ i ^ cs *=^. j/^*' \ r = U7 t y/^ / \~ ^\. /vy v\X / V\ AJ \ 1 1 ^^ //y \ r = UI r=l.l! r = l.09 r = !.30 Figure 87 Radiation patterns of antenna 2M-15C with and without a resistive cavity 4»=o< -H 131 qp ui uidq 9AUD|ay 132 g >1 CD •H > at r- O 0) > 10 •H 0] •H m CD u > +> — o n c ctS a> 3 1_ u. O •H ■p o 03 (x o\ CD > cU ® r-: •H as (0 03 If) CO a> * 3, to ro cvJ OIJDfcj 9ADM 6u|puD4S 133 7.3 The Antenna over a Conventional Cavity Until a frequency independent reactive cavity is developed, it is of interest to determine the behavior of the antenna over a conventional cavity. Antenna 2M15-C, which is 11 inches in diameter and whose patterns Without a cavity termination are shown in Figs. 12 and 13, was mounted over a 13 inch square flat-bottomed cavity. The cavity depth was made adjustable, and patterns were recorded at 3010 mc, where the antenna arms were approximately 4.9X.in length. The patterns were acceptable for a cavity depth from slightly less than 1/8X up to slightly less than 1/2X. Figure 90 indicates the polarization of the field on axis over this range of depths. This indicated that a frequency bandwidth of as much as 3.7 to 1 might be obtained. The cavity depth was fixed at three- fourths inches and the frequency of operation varied. Figures 91 and 92 indicate that acceptable patterns were obtained from 1730 to 6,000 mc, a 3.48 to 1 bandwidth. At 1,700 mc the E pattern on the^> = cut has a 3db depression on axis and at 6,200 mc the F^. pattern on the = 90 cut has two symmetrical minima 3 db down from the pattern maximum. Over the 3.5 to 1 bandwidth of Figs, 91 and 92 these depressions are no greater than 2.2 db. This particular cavity is not necessarily an optimum design but was chosen merely to demonstrate that the equiangular spiral over a simple cavity is a practical antenna. The standing wave ratio of antenna 2M-15-3C over such a cavity is shown in Fig. 93. X34 7 I 6 e Q. UJ c o •^ 3 o N o Axial Ratio of Pol .2 .3 .4 Depth of Cavity in X Figure 90 Polarization of the field on axis of antenna 2M-15-C over a 13 inch square cavity with flat bottom f = 3010 mc d> = 0° f=l730Mc r = 1.38 d=.llX f=l800 r = l.68 d = .N4X f=l980 r =.1.40 d = .l26X f=2500 r = l.49 d = .l6X f=30IO r = 1.14 d = .l9X d> = 90° 135 S J *" ~ A / X ^* / ^ V / \ / X / / N/ \/l \ / X J\ X / \ / \N X J ^ S X Figure 91 Radiation patterns of antenna 2M-15-C backed with a flat bottom cavity, 13 inches square, depth = d = .75 inches (£ = 0° ^=90' 136 f-3950 Mc r=l.2l d=.25X f*5500 r = 1.29 d=.35X f=6000 r = 1.24 d = .38\ y // — x if / \ i \\ X 1 1 / \ / V V \ /y \ Figure 92 Equiangular spiral antenna (2M-15-C) backed with a flat bottom cavity, 13 inches square, depth = d = .75 inches 137 o ac > I c '■B c o Bond Width iH u V- P u \ -o^ ^ >-« N>- J [ ne f r 1.5 3 4 Frequency in Kmc 8 9 10 Figure 93 Standing wave ratio presented to a 50 ohm line by antenna 2M-15-3C when placed over a 13 inch square cavity, 3/4 inch in depth 138 VIII. CONCLUSIONS The planar balanced equiangular spiral antenna has been demonstrated to be the first antenna to exhibit, in a practical size, the characteristics associated with an infinite structure. It is a remarkable antenna in that it makes possible radiation pattern bandwidths previously considered to be impossible. It is truly frequency independent since the bandwidth has been shown to be limited only by the chosen arm length and the precision of construction at the feed point. An extension of the bandwidth is a practical matter since the arm need only be one wavelength at the lowest frequency of operation, and this extension to a broader and broader arm will not affect the excellent efficiency or power handling capabilities. The antenna will provide circularly polarized^ single lobe, bidirectional radiation, perpendicular to the plane of the antenna. The beam width varies with rotation in the plane of the antenna, and since the pattern rotates with frequency, the apparent beam width will vary with frequency for a fixed ^ cut. This variation is typically from 40 to 60 degrees. The more tightly wound spirals and the antennas with broader arms have the most uniform patterns. The input impedance converges with increasing frequency , and for the antennas of most interest the slot antenna is rarely mismatched more than three to one to a 50 ohm line, and is usually two to one or t) et ter over the radiation pattern bandwidth. The structures described in this report are not miniature when compared to many present narrow band antennas. However, the maximum 139 diameter need be only one half wavelength or slightly more. The primary advantage of the antenna is its unlimited bandwidth, circular polarization, and excellent efficiency and power handling capabilities. Additional effort should be expended toward the development of a cavity backed version of the antenna to permit its widest utilization. 140 BIBLIOGRAPHY 1. Kandoian, A.G. "Three New Antenna Types and Their Applications," Proceedings of the I.R.E., Vol. 34, February 1946, p. 70w-75w. 2. Chatter jee, J.S., "Radiation Field of a Conical Helix," Journal of Applied Physics, Vol. 24, No. 5 May 1953, p. 550. 3. Turner, E.M. , "Spiral Slot Antenna," Technical Note WCLR-55-8, Wright Air Development Center, June 1955. 4. DuHamel, R.H. , and Isbell, D.E. , "Broadband Logarithmically Periodic Antenna Structures," Technical Report No. 19, Contract AF33 (616)3220, University of Illinois, Urbana, Illinois. 5. Dyson, J.D. , "The Equiangular Spiral Antenna," The Fifth Symposium on the USAF Antenna Research and Development Program, Robert Allerton Park (University of Illinois), Monticello, Illinois, 22 October 1955. 6. Dyson, J.D. , and Carrel, R.L. , "An Experimental Investigation of the Equiangular Spiral Antenna," The Sixth Symposium on the USAF Antenna Research and Development Program, Robert Allerton Park, (University of Illinois) 22 October 1956. 7. Rumsey, V.H., "Frequency Independent Antennas," Technical Report No. 20, Contract AF33 (616)3220, University of Illinois, Urbana, Illinois, (to be published). 8. McCoy, Donald, "Near Field Measurements of Slot Antennas," Technical Report No. 667-15, Contract AF33 (616)3353, Antenna Laboratory, The Ohio State University Research Foundation, Columbus, Ohio. 9. Morita, I., and Sheingold, L.S., "A Coaxial Magic T, " Technical Report No. 162, Cruft Laboratory, Harvard University, Cambridge, Massachusetts, 10 October, 1952. 10. Crowley, T.H. , "Measurement of Antenna Efficiency by using Metals with Different Surface Resistivities," Technical Report 478-21 , Antenna Laboratory, Ohio State University, Columbus, Ohio, 6 November 1953. 11. Richmond, J.H. , and Tice, T.E., "Probes for Microwave Near Field Measurements," I.R.E. , Transactions on Microwave Theory and Techniques, Vol. MIT 3, No. 3, 1 April 1955. 141 APPENDIX A TABLE OF PHYSICAL PARAMETERS OF THE SPECIFIC ANTENNAS REFERRED TO IN THE TEXT. Antenna* 1 * fc^ 3 \,^x a 6 K Un/LO) M 5 2M-5W* 2) 2M-8 M-10 2M-10 2M-15 2M-15C 2M-15-3C 2M-15-4C 2M-18 2M-21 2M-23 2M-28C 2M-32 2M-38 1 .35 1.087 .684 2 .35 1.087 .684 2 .303 .538 .85 1 .303 .948 .75 2 .303 .948 .75 2 .303 1.57 .62 2 .303 1.57 .62 5. 18 .303 1.57 .62 13. 42 .303 1.57 .62 2 .415 1.705 .49 2 .415 .704 .75 2 .35 1.475 .597 6. 3 .20 1.21 .692 2 .45 .622 .75 2 .35 .823 .75 Arm Max. Arm Length Diam. Term. (cm) (cm) 31.7 25.3 r v 37.7 30.4 r v 36.6 22.8 r v 23.0 22.9 r v 42.3 29.2 r v 38.7 28.4 r v 38.7 28.4 arc 37.1 28.4 arc 32.9 28.4 arc 34.9 36.3 r v 40.7 36.3 r v 27.6 23.5 r v 59.2 25.3 arc 31.5 30.0 r v 37.1 28.4 r v Footnotes: 1. Antennas identified by a model number as listed are slot antennas. To identify those constructed with metal arms in "free space" a letter: "a" is inserted, as 2 MA-15. 2. One- fourth inch walls were soldered along the slot arms — see Fig. 44. 3. Purely ^.s a convenience in plotting, k was maintained in units of inches/10; thus 0' is "always > and P •> 1 , facilitating plotting on conventional polar paper, divided 10 parts to the inch. 4. "rv" indicates a termination along ^the Tadius vector; "arc" indicates a termination along a circle with radius at the origin. 5. The table is not intended to be a tabulation of all antennas tested. DISTRIBUTION LIST (CONT ) AF33( 616) ■• 3220 One copy each unless otherwise indicated page 2 Chief Bureau of Ships Department of the Navy ATTN Code 838D L E Shoemaker Washington 25, DC Director Naval Research Laboratory ATTN Dr J I Bohnert Anacostia Washington 25 : DC, National Bureau of Standards Department of Commerce ATTN Dr. AG. McNish Washington 25, DX. Director ,U,S Navy Electronics Lab. 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