UNCLASSIFIED Securitv Classification DOCUMENT CONTROL DATA- R & D (Security cflsslficntion of ftl!o, hody n,ilf,rist c mtl rt ln dtxlt f dlnltnolll(t/f nm.t hi e onterd,ili, n lio overnll report 1.9 clnAilod) I. ORIGINATING ACTIVITY (Corporate aulthor) 40. REPORT SECU I 1 Y CLASSIFICATION The University of Michigan Radiation Laboratory UNCLASSIFIED 2216 Space Research Bldg., North Campus 2b. GROUP. - Ann Arbor, Michigan 48105 3. REPORT TITLE THEORETICAL AND EXPERIMENTAL STUDY OF ARRAYS OF AXIAL SLOTS ON A CIRCULAR CYLINDER 4. DESCRIPTIVE NOTES (Type of report ind Inclusive dateo) Final, Scientific For Period 1 September 1973 through 30 June 1974 5. AU THOR(S) (First name, middle initial, last ltime) Dipak L. Sengupta Joseph E. Ferris 6. REPORT DATE 7,t. TOTAL NO. OF PAGES 7b. NO. OF REFS August 1974 43 4 8a. CONTRACT OR GRANT NO. 90. ORIGINATOR'S REPORT NUMEIER(S) F19628-74-C-0020 b. PROJECT NO. 012131-1-F 5635-06-01 c.' 61102F'lh. OTHER.REPORT NO(S) (Alny otlhcr ulmbers ( tIot manv 1) r sl inl. 61102F Mcthis report)' d. 681305 A FCRL-TR-74-0420 10. DISTRI BUTION STATEMENT Approved for public release; distribution unlimited. I 1. SUPPLEMLt.< I ARY NOTES 12. SPONSORING MILITARY ACTIVITY Air Force Cambridge Research Laboratories Tech. Other |Hanscom AFB, Massachusetts 01731 Contract Monitor: Otho E. Kerr/LZR 13. ABSTRACT The radiation patterns produced by -arrays of axial slots on a conducting circular cylinder of infinite length are studied theoretically and experimentally. The required phase of excitation of elements to produce a beam in a certain direction are obtained by approximating the array by a section of a circular array of isotropic sources. For the given radius of the cylinder and the frequency band of interest, the approximation is found to yield satisfactory results. Radiation patterns produced by arrays of 2, 3 and 4 axial slots are numerically computed and discussed. Theoretical results are alsocompared with measured results and the agreement between the two has been found satisfactory. DD,O 0 o 14 73.....UNCLASSIFIED

UNCLASSIFIED Security Classification 1 4 * { L. N K A j LINK D l~f^^/^^^^I 14. IKLINIK A LINK 0 LINK C KEY WORDS RO L E WT RfOLE WT ROLE T Single Beam Antennas Slot Arrays on Circular Cylinder Radiation Patterns of Slot Arrays VSWR of Slot Arrays UNCLASSIFIED S".:- r i t v ('l.,I, Ifi';r t i,-,,l

TABLE OF CONTENTS ABSTRACT ii INTRODUCTION1 1.1 Preliminary Remarks1 1.2 General Considerations1 1.3 Outline of the Report 3 II THEORETICAL AND NUMERICAL ANALYSIS 4 2.1 Theoretical Pattern Expressions 4 2.2 Excitation of the Array 7 2.3 Discussion of the Element Pattern Expression 9 2.4 Numerical Results for Single Slot Radiation Patterns 9 2.5 Patterns of an Array of Two Slots 9 2.6 Patterns of an Array of three Slots 14 2.7 Patterns of 4-Slot Array 14 III EXPERIMENTAL RESULTS AND COMPARISON WITH THEORY 24 3.1 Elementary Slot 24 3.2 3-Slot Array 24 3.3 The 4-Slot Array 30 IV CONCLUSIONS 42 REFERENCES 43 iii

I. INTRODUCTION 1.1 Preliminary Remarks The objective of the research reported herein is to determine the best arrangement of elements for an antenna to produce a single beam pattern for applications on electrically small aircraft or missiles. The antenna is to operate in the low VHF range (30 MHz - 200 MHz; X = 10 m - 1.5 m). The electrically small vehicle is approximated by a perfectly conducting circular cylinder of diamter ^ 2 meters and length - 13 meters. For obtaining patterns in a plane normal to the axis of the cylinder produced by elementary slot radiators placed on its surface, the cylinder is assumed to be of infinite length. This assumption simplifies the theoretical analysis considerably. 1.2 General Considerations Let us represent the fuselage of the aircraft by a conducting infinite cylinder of radius a. The coordinate system used and the orientation of the system are shown in Figure 1 where the axis of the cylinder is oriented along the z-axis. We shall refer to the x-y plane as the vertical or elevation plane, the y-z plane as the horizontal plane and the x-z plane as the longitudinal plane. The desired beam produced by the antenna should be normal to the z-axis and be directed as shown in Figure 1. The antenna should also have some directivity in the y-z plane. Ideally, there should not be any radiation beyond the range A 0 AO B0 - 2 <0< 060+ 2 where A o is the beamwidth between nulls in the x-y plane pattern. 1

7^V^ ~ CROSS SECTION OF /a [ ^ AIRCRAFT FUSELAGE / / I \\-> /N^d FZig 1\(' \ Figure 1: Idealized pattern and the coordinate system used. We assume here that the sidelobe levels, if any, should be about 15 to 20dB down from the main beam. The antenna system should have a bandwidth of 5 MHz with a VSWR equal to 3.0:1. This implies that at 30 MHz the required bandwidth would be about + 8 p.c. and about + 1.25 p.c. at 200 MHz. The bandwidth requirements at the lower frequency end appears to be quite severe. From this consideration alone it may be advisable to use antennas such as the log-periodic, the yagi or zig-zag antennas. If circular polarization is acceptable one may also consider the use of flat spiral, conical spiral or 2

helical antennas. However, all these antennas would require an excessive amount of protrusion from the cylinder or require a large amount of cylindrical surface area at the lower frequency end. Because of this we have ruled out the use of such antennas for the present study. To obtain the desired patterns we use the technique of arraying a number of elementary radiators around the circular cylinder. Axial slot radiators are considered for the reason that they need minimum amount of protrusion from the cylinder surface. 1.3 Outline of the Report In Chapter II we derive the expressions for the desired far field patterns produced by arrays of axial slots on a conducting circular cylinder of infinite length. The required phase of excitation of elements to produce a beam in a certain direction are obtained by assuming that the array consists of a section of a circular array of isotropic sources. For the given radius of the cylinder and the frequency band of interest, the approximation is found to yield satisfactory results. Radiation patterns produced by arrays of 2, 3 and 4 slots on the circular cylinder are numerically computed and discussed. Chapter mI discusses the experimental results. The agreement between the theoretical and experimental results are found to be satisfactory. 3

II. THEORETICAL AND NUMERICAL ANSLYSIS In this chapter we develop theoretical expressions for the radiation field produced by a number of axial slots located on the surface of a conducting circular cylinder of infinite length. The far field patterns produced by such elementary radiators are discussed thoroughly in the literature [1 - 3]. Here we write them in a manner suitable for our purpose and use them to obtain the array pattern expressions. The radiation patterns produced by arrays of monopoles or stub radiators located on a circular cylinder have been discussed in our first quarterly report [4] and will not be repeated here. 2.1 Theoretical Pattern Expressions Consider a narrow axial slot of length L located on the surface of the cylinder at 0 = 0e and z = 0 as shown in Figure 2. Let the excitation of the slot be represented by: ifs VT e S S a A s 2a A cos e (1) where, VI ip are the amplitude and phase of the excitation, 2 A is the width of the slot, -iOt e is the assumed time dependence, A eo is the unit vector in the 0-direction. It can be shown [2 ] that the far electric field produced by such a slot of length L = X/2 has only a -component and is given by: 4

z (r,e, )' I Figure 2: Axial slot on a circular cylinder and the coordinate system used. ikr V e cos( cos ) E r 2 X r Vr (ka) sin 0 n, oos~l-8 ~ sm (2) E a (-i) cosn(0-w) sn sin 8 H() (ka sin ) n (2 5

where, k = is the propagation constant in free space, r, 0, 0 are the usual sphereical coordinates, H( represents Hankel function of the first kind and order n, n indicates differentiation with respect to the argument, =1 for n = O n =2 for n 0 For a narrow slot, 0A ( O, so that we can assume rn 0 1 n AO in Equation (2). Thus the far field in the x-y plane (0 = 7r/2) may be represented by: ikr ~ = r P () where, ___ co E(-_1) cosn (n -0 (0)= - 2 Ve n - (4) 2r(ka) n=0 H(1) (ka) I= 0 n | Pi (0)1 is the x-y plane pattern produced by a single axial slot located at 0 = 0,. The pattern produced by an array of such slots located on the cylinder may be obtained by summing Equation (4) over the index i and may be written formally as: P(0)= P(0). (5)

Equation (5) assumes that there is no mutual coupling between the slots which would be a valid approximation as long as the slots are not too close to each other. In our analysis we neglect the mutual coupling between the slots. 2.2 Excitation of the Array It has been assumed in the previous section that the array is obtained by locating a number of axial slots on the cylinder at z = 0 plane and at 0 = 0, the excitation of A-th slot being V e. Within the range of frequencies of interest and for the given size of the cylinder, it appears that the physical extent of the array should be confined approximately to one quarter of the cylinder circumference in order to obtain a desirable pattern. From this consideration it seems that the maximum number of slots that can be used for the array may be 4 or 5. For larger number of slots the mutual coupling effects would become appreciable and the analysis of the array pattern will be very complicated. The array pattern expressions given by Equations (5) and (4) are in the form of double series, one of them being infinite. It is quite difficult, if not impossible, to obtain the array excitation coefficients V, e for a given beam direction from these series expressions. We use the concepts of the section of a circular array of isotropic sources to obtain the excitation coefficients in the present case. Consider a section of a circular array of isotropic sources in the x-y plane, as shown in Figure 3. It can be shown that the far field pattern in the x-y plane is given by: P(-) = V ei -ika cos (0-h) -i [ka cos (0-0 - 6 -X V e e (6)

P(r,+) TYPICAL ELEMENT O' —\ —- X Figure 3: A circular section array with typical elements at 0 =. Let the desired direction of the beam maximum be 0 =.' Equation (6) indicates that the phase of the excitation p must then satisfy the following: kra cos (0o - 0) =' (7) We shall design excitation coefficient Q for the slot array on the circular cylinder on the basis of Equation (7). For example, let us design a 3-slot array which is required to produce maximum field in the direction 0 = r /4. For convenience we assume that the three slots are located at 01 = 0 02= 7r/4 and 03 = r/2. The phase ka of excitation of the slots are then given by I1 -=. /2 = ka and i3 = ka/4F respectively. If the slots are excited with uniform amplitude, V = V2 = V = 1. It may be found necessary to use non-uniform amplitude of excitation to modify the pattern in directions away from the main beam. 8

2.3 Discussion of the Element Pattern Expression The pattern produced by an individual slot element located on the cylinder is given by Equation (4) which is an infinite series. The convergence of the series depends on the parameter ka. Within the range of frequencies of 4 interest the maximum value of ka is - 7T. It has been found that for proper 43 convergence with ka = 4 A, it is necessary to consider at least ten terms in the series. Therefore in all of our pattern calculations we have used the first ten terms of Equation (4). 2.4 Numerical Results for Single Slot Radiation Patterns In this section we discuss the far field patterns produced by an axial slot located on the surface of the conducting cylinder at = 00. The patterns have been obtained by numerical computation of Equation (4) for three selected values of ka. Figures 4(a)-(c) show the x-y plane patterns for three values of ka which correspond to the normalized radius ka of a cylinder of diameter 2m at 30 MHz, 60 MHz and 200 MHz respectively. It should be noted from Figure 4 that towards the lower end of the frequency band, the pattern is approximately isotropic over most of the range of 0. More importantly, it has been found from our numerical results, the phase of the radiation stays almost constant for small values of ka, and over an appreciable range of 0 on either side of = 0. This appears to justify the assumption of using isotropic sources for the calculation of the excitation coefficients for an array of such slots, as discussed in section 2.2. 2.5 Patterns of an Array of Two Slots Figure 5 shows the pattern produced by a pair of axial slots located at = 00 and 02 = r/4. The two slots are excited equally, i.e., V =V2 = 1 and 1 = /2 0. Observe that the beam maximum occurs at 0 = Tr/4 which is in agreement with Equation (7). Observe, also that the pattern maximum in the 9

s —0 O 0= 0 Figure 4(a): Theoretical pattern of an axial slot on the surface of a conducting cylinder, ka = 0.27r. 10

TT't 0'O = mi'jaPUTnIAo 2alonpuoo e Jo aojajns aq uo:ols IeTXe u-e jo una:ed voio:oaoaqj,lL:(q), aojn2ij W-5._-5 IC'fy 1 20t 2 30 35 -f-~ 35 3 5 20 7 1 0 15 1o=0 _e~~~~~~~~~~~~~~

'Ir 0~ = 00 Figure 4(c): Theoretical pattern of an axial slot on the surface of a conducting cylinder, ka = 4/3ir. 12

~=o Figure 5: Theoretical pattern of a pair of equally excited axial slots located on the surface of a c~onducting cylinder, ka=0.4r, V1 =V =1.0, 12=0 1 29 13

direction 0T = r/4 is about 15dB larger than that in the direction 0 = 34/2. It appears from the results that by using third slot located at 03 = 37/2, the beam direction may be changed from 0 = 7/4 to 0 = -7/4 by exciting slots 1 and 3 only. 2.6 Patterns of an Array of Three Slots Figure 6 (a) - (c) show the patterns produced by an array of three axial slots located at 01 = 0~ 02 = r/4 and 03 = r/2 with uniform amplitude excitation, i.e., V1 = V2 = V = 1.0. The phase of the excitation is chosen such that 1 = P3 = ka/ 2, L2 = ka obtained from Equation (7) for a beam maximum in the direction 0o = 7r/4. Figure 6 indicates that appreciable amount of directivity may be obtained in the upper half of the frequency band of interest. Figure 7 (a)-(b) show the patterns produced by the same 3-slot array, but with non-uniform amplitude of excitation such that V1 = V3 = 0.5 and V2 = 1.0. Comparing Figures 7 (a) and 6 (a), it is found that the patterns are quite similar. The pattern shown in Figure 7 (b) is for ka = 0. 7077r and is found to be clean in the shadow side of the antenna. This may be found interesting for some applications. 2.7 Patterns of 4-Slot Array The results discussed in the previous sections indicate that it is possible to obtain appreciable directivity in the upper end of the frequency band with a 3-slot antenna configuration. In general, it has been found that for such an array with ka' 0. 87 the pattern has a principal maximum in the direction 4 = 450. In directions + 90~ away from the main beam, the field is about 13dB down from the maximum (Figure 6 (b)). To reduce the field in the direction 90 away from the main beam, we have used a fourth slot with proper exciation. 14

o 0= 0 Figure 6(a): Theoretical pattern of three axial slots located on the surface of a conducting cylinder, ka = 0. 4ir, V1 2 = V = 1.0, 2 ka, =ka//. 15

- D; 0 - eg oI 91 0 I f-00 Figure 6(b): Theoretical pattern of three axial slots located on the surface of a conducting cylinder, ka = 0. 8r, V1 = V3 =V =1.0, b2 =ka, 1 =p3 =ka/ 2. 16

- p=oo Figure 6(c): Theoretical pattern of three axial slots located on the surface of a conducting cylinder, ka = 1. 0r, Vi=V=V3=1. 0 2 = ka,' I = 3 = ka//4. 17

8T C* ~/vs[ /' =g' O'T1= A'S'O= A= A'a O = v'Iap pAo Pu^onpuoo e jo aoj;jns eaq uo paeooI sois Ieixe aaeiq jo njaed Itooe[ajoeaq:(B)L a9mn2Ij oO = 0 30a 5

0 0 Figure 7(b): Theoretical patterns of three axial slots located on the surface of a conducting cylinder, ka = r/2, v, = V3 = 0.5, V1 = 1., = ka, = 3 = ka//. 19

Figures 8 (a)-(c) show the patterns produced by the 4-slot array located on a cylinder for various values of ka. Observe that for ka = 0. 87 (Figure 8(b)) the field in ~ = - 45~ region is about 30dB down from that at the maximum. For ka = 1. 0r (Figure 8(c)) the field in the 0 - 45~ region is about 17dB down while for ka = 0.47 the pattern is not much different from that of a single slot on a cylinder discussed earlier. 20

=0 0= 0 Figure 8(a): Theoretical pattern of four axial slots located on the surface of a conducting cylinder, ka = 0.4, V1 = V = V = 1.0 V = 0.25, 1 =3 ka/2 = ka, g4 = 0. 21

~=0O Figure 8(b): Theoretical pattern of four axial slots located on the surface of a conducting cylinder, ka = 0. 8r, V =V2 = V3 = 1. V v4 = 0.25, 1 = ~3 = ka//, / = ka, 4 = 0. 22

0~=o Figure 8(c): Theoretical pattern of four axial slots located on the surface of a conducting cylinder, ka = 1. 0r, V1 = V = V = 1.0, V = 0.25, V1 =V3 = ka/' 2 = ka, 4 = 0. 23

II EXPERIMENTAL RESULTS AND COMPARISON WITH THEORY 3.1 Elementary Slot As mentioned earlier, the elementary radiator used is a magnetic dipole or a slot. The experimental model may be fabricated out of stripline. The slot has the advantage that it requires minimum protrusions when mounted on the cylinder surface. Figures 9a and 9b show the photographs of the front and back sides of the stripline slot radiator. The measured x-y plane pattern of the slot on a cylinder with ka' 1.3877r is shown in Figure 10. The corresponding theoretical pattern is also shown in Figure 10. The agreement between theory and experiment may be considered to be satisfactory. It has been found that for a slot of length approximately equal to a wavelength, the input VSWR stays within 1:3 in the frequency range of 2. 8 - 3.4 GHz. 3.2 3-Slot Array A photograph of the 3-slot array mounted on the cylinder is shown in Figure 11(a). An array of 3 axial slots mounted on a cylinder with ka -1.47r has been fabricated. For mechanical simplicity the individual slots in Figure 11(a) are made of reduced height waveguide sections. Figure 11(b) shows a sketch of a slot on the broad wall of a cavity made of reduced height waveguide. The system is fed by a coaxial probe as shown. The impedance characteristics of the slot depends critically on the locations of the slot and the height of the waveguide. The measured x-y plane pattern of the antenna is shown in Figure 12. The results shown in Figure 12 agree fairly well with the theoretical pattern discussed in section 2.6. During the experiment the three slots were fed by a 3-way power divider and phasing of the slots were done with the help of appropriate length of transmissinn line. The measured input VSWR as a function of frequency for the 3-slot antenna is shown in Table I. 24

l > 0 -;i~i~-:~ —---- - l~~~~~~~~~~~~ Al Figure 9(a)- iPhotograph of: the font side of the stripline slot radiator Figure 9(b): Photograph of the back side of the stripline slot radiator. 25

25 =0~ 0 = 0 0 Figure 10: Patterns of an axial slot on the surface of a conducting cylinder, ka = 1. 397r. - theoretical - - experimental. 26

+.: ~ ~ ~ ~ ~ ~ ~ ~ ~.................................................................................................................................................................... a ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~................................................................... n-3i....1 ~ ~ ~ ~................. ~~~~~~~~~~~~~~~~~~~~~~~~...................... ~ ~ ~~~~~~~~~~~~~~~s ~ ~......................... s~ ~ ~ ~ ~ ~ ~ ~~~~~ ~~~~~~~~~~~~...............................

Coaxial | - - Short Probe Short 3" 2-1/8" — _ -I-__ —- _ _1/32_" /4 2 9i/ Figure ll(b): Sketch of a slot on the broad face of a reduced height waveguide cavity. 28

Figure 12: Experimental pattern of three axial slots located on the surface of a conducting cylinder, ka = 1.4r, V1 = V2 = V3 = 1.05 1 = -3 ka/2, 2 5 ka, f= 3.5 GHz. 29 29

Table I. Input VSWR for the 3-slot array. Frequency (GHz) VSWR 2.9 1.06 3.0 1.06 3.1 1.06 3.2 1.08 3.3 1.14 3.4 1.18 3.5 1.31 3.6 1.36 3.7 1.43 It may be of some interest to know the VSWR at the input of each slot and this data are shown in Table I below. Table II. VSWR at the input of each slot. Frequency Slot 1 Slot 2 Slot 3 (GHz) 3.0 3.9 3.8 3.6 3.2 1.95 2.4 1.95 3.3 1.39 1.56 1.34 3.4 1.65 1.60 1.57 3.5 2.4 2.39 2.4 The results given in Tables I and I indicate that the input end of the power divider is well matched. This was achieved by designing the power divider such that the impedance of each slot is properly matched to the power divider. 3.3 The 4-Slot Array The individual slots of the 4-slot array are made of reduced height waveguide as in Figure 11(a). Figures 13(a)-(e) show the experimental and theoretical x-y plane patterns of the antenna at different frequencies. The 30

slots were fed by 4-way power dividers to provide the appropriate amplitude of excitation. The phasing was done by appropriate amount of line length. The agreement between theoretical and experimental patterns shown in Figure 13 may be considered to be satisfactory. The measured cross-polarization patterns of the antenna over the same frequency range are shown in Figure 14 (a)-(e). Typically at f = 3.1 GHz the cross-polarization component is about 25dB down in the direction of the beam maximum. In other directions the cross-polarization response is lower than 25dB. The input VSWR as a function of frequency is shown in Table II. Table III. Input VSWR for the 4-slot array. Frequency (GHz) VSWR 3.1 1.38 3.2 1.05 3.3 1.26 3.4 1.60 3.5 1.68 31

0= Figure 13(a): Patterns of an array of 4 axial slots on the surface of a conducting cylinder, ka = 1.312w, f = 3.1 GHz, V1 = V2 = V3 = 1.0, V4 =0.4,1 =3 ka/, = ka, 0. --- - theoretical experimental. 32

Z 0= 0=0 Figure 13(b): Patterns of an array of 4 axial slots on the surface of a conducting cylinder, ka = 1.3547r, f = 3.2 GHz, V1 =10 V: = V = 10.4, 1=3 = ka//2 2 = ka, 4 = 0. -- theoretical ------ experimental. 33

,,r4r ~ ~ ~ 3 00 Figure 13(c): Patterns of an array of 4 axial slots on the surface of a conducting cylinder, ka = 1.396Or, f = 3.3 GHz, V V =V =V =1.0, V4=0.4, P: = =ka/f2, b2= ka, b4 =0. theoretical -.- experimental. 34

0= 0=0~ Figure 13(d): Patterns of an array of 4 axial slots on the surface of a conducting cylinder, ka = 1.4397r, f = 3.4 GHz, V =VV 3 =V =1.0, V4 =0.4, 1 b3 =ka /2,'2 = ka, q4 = 0. - theoretical ----- experimental. 35

=0 ~0 Figure 13(e): Patterns of an array of 4 axial slots on the surface of a conducting cylinder, ka = 1.4817r, f = 3.5 GHz, V1 =V2 =V3 =1.0, V4 0.4, =1:: =ka/ 2 = ka, 04 = 0. -- theoret ical --- experimental. 36

01 = 00 Figure 14(a): Measured cross-polarization pattern of an array of 4 axial slots on the surface of a conducting cylinder. ka= 1.312r, f =3.1GHz, V=V =V = 1.0, V4 = 0.4, /1 = = ka//2, 2 ka, 4 =" 0. Maximum cross-polarization ~ -25dB down. 37

'0 =0~ Figure 14(b): Measured cross-polarization pattern of an array of 4 axial slots on the surface of a conducting cylinder. ka = 1.354r, f =3.2GHz, V =V2 -V = 1.0, V4 = 0.4, = 3 = ka/2 a'2 = kao P4 0. Maximum cross-polarization ~ -26.5dB down. 38

-0O ~ 0I r I I O ~g1 91 001 9 0 9 g 0 9Z O 9 0 9 = 00 Figure 14(c): Measured cross-polarization pattern of an array of 4 axial slots on the surface of a conducting cylinder. ka = 1.396r f = 3.3 GHz, V = V =V = 1.0, V4 =0.4, i = q3 =ka/, q'2 = ka, q4 =0~Maximum cross-polarization - -27.5dB. 39

OC S 01T -i O 9 C OS ~ - O S S __ OZ V 1=0 Figure 14(d): Measured cross-polarization pattern of an array of 4 axial slots on the surface of a conducting cylinder. ka = 1.439r, f = 3.4 GHz, V = V = V = 1.0, V4 =0.4, 1 = 3 = ka//2, 2 ka, 4 0. Maximum cross-polarization r -26. O0dB. 40

91 -I 9 01 f I I I 0~ 9' 9, O U I ~ 0~ = 00 Figure 14(e): Measured cross-polarization pattern of an array of 4 axial slots on the surface of a conducting cylinder. ka = 1.4817r, f = 3.5 GHz, V = V V3 = 1.0, V4 = 0.4, 41 = == ka/2, 4=0. Maximum cross-polarization -'-30. O0dB. 41

IV CONCLUSIONS The results of the theoretical and experimental investigation discussed in the previous sections indicate that it is possible to obtain a single beam pattern with the help of an array of axial slots on a circular cylinder. However, it appears from the results that the pattern will not be optimum at the lower end of the frequency band for the given size of the cylinder. The VSWR results indicate that it would be possible to achieve the design goal of 1:3 VSWR over the band of frequencies of interest. In an extension of this work it is recommended that the following studies should be performed: (i) Re-design the array so as to illuminate a region, perhaps 30~ to 75~, as measured from the nadir. (ii) Establish a lower frequency limit in terms of cylinder diameter/A., for which it is possible to obtain a 10dB difference in the illumination over the 300 to 75 angle spread. The discrimination is to be between the illuminated side and the corresponding same angle on the shadowed side. (iii) Slot spacings other than ir/4 investigated. (iv) Determine the effects of the waveguide height on the impedance characteristics of the individual slot. (v) Experimental studies to verify some of the findings of the theory for the re-designed array. 42

REFERENCES [ 1] J. R. Wait (1959), Electromagnetic Radiation from Cylindrical Structures, Pergamon Press, N.Y. [2] R.F. Collin and F.J. Zucker (1969), Antenna Theory, Part I, McGrawHill Book Co., New York. [3] J.J.Bowman, T.B.A.Senior and P.L.E.Uslenghi (1969), ElectroMagnetic and Acoustic Scattering by Simple Shapes, North Holland Publishing Co., Amsterdam. [4] D.L. Sengupta (1974), "VHF Antenna for Electrically Small Vehicles", Quarterly Status Report No. 1, Contract F19628-74-C-0020, The University of Michigan Radiation Laboratory, Ann Arbor, MI. 48105. 43

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