.- -THE UNIVERSITY OF MICHIGAN 7300-1-T Radant Analysis Studies Interim Report No. 1 30 April through 31 July 1965 August 1965 Contract No. AF 33(615)-2811 Project 4161, Task 416103 Air Force Avionics Laboratory, AVWC Research and Technology Division, AFSC Wright-Patterson Air Force Base, Ohio 45433 0

THE UNIVERSITY OF 7300-1-T MICHIGAN FOREWORD This report was prepared by The University of Michigan under USAF Contract No. AF 33(615)-2811, Task 416103, Project 4161. The work was administered under the direction of the Air Force Avionics Laboratory, Research and Technology Division, Air Force Systems Command, E.M. Turner, Technical Manager; G. Tarrants, Project Engineer. This report covers work conducted from May through July 1965. I - iii --

. THE UNIVERSITY OF MICHIGAN - 7300-1-T TABLE OF CONTENTS I INTRODUCTION 1 II TRANSMISSION OF PLANE ELECTROMAGNETIC WAVE THROUGH AN ARTIFICIAL ANISOTROPIC PANEL 8 Introduction 8 The Tensor Permittivity and Permeability of 9 Arrays of Discs Transmission of a Plane Wave Through an 12 Anisotropic Panel Numerical Computation and Conclusion 19 III TRANSMISSION PATTERNS OF AN ANISOTROPIC PANEL EXCITED BY A SPHERICAL SOURCE 33 Introduction and Formulation 33 Transmission Through the Panel 42 Conclusion 54 IV EXPERIMENTAL MEASUREMENTS 58 REFERENCES 68! I - - -- - v _ _

, THE UNIVERSITY OF MICHIGAN 7300-1-T ABSTRACT The transmission characteristics of an anisotropic panel formed by conducting discs are investigated theoretically in this work. The result is intended to interpret the characteristics of the loop loaded radant (radome-antenna) panel originally studied at the Air Force Avionics Laboratory. Experimental work on the impedance variation of a ferrite-loaded horn antenna in the presence of the panel and the radiation pattern of the antenna structure are also reported in this interim report. vii

THE UNIVERSITY OF MICHIGAN 7300-1-T I INTRODUCTION In this report we will consider a particular radant structure. It consists of a panel which contains a square array of rectangular loops. This array is illuminated by a ferrite loaded slot antenna. The characteristics of the transmission pattern are then desired. It was reported, at the initiation of the contract work, that a significant improvement in gain and directivity as compared to a uniformly illuminated aperture was obtained with this radant structure. These initial experiments were performed at the Wright-Patterson Air Force Base Avionics Laboratory. The more significant gain improvements were obtained with the ferrite loaded slot antenna as a primary source at the low frequencies between 200-700 Me. In this frequency range the array panel dimensions in terms of wavelength were - - X. In view 2 of this, we will confine our analysis in this report to this frequency range. It should be pointed out that although the array panel can be termed broadband, since at these frequencies its characteristics remain fairly uniform, the radant structure, i.e. the combination of array panel and ferrite slot antenna is not. The slot antenna by itself is very frequency sensitive and its output drops sharply for frequencies not at the 350 Me resonance. The bandwidth between half power points is 80/0 for the solid ferrite slot antenna alone (Adams, 1964).! 1

THE UNIVERSITY OF MICHIGAN 7300-1-T It was reported that the single characteristic which makes this radant structure unusual was the critical spacing that had to be maintained between the slot antenna and the array panel. This spacing was around 1"-2". In terms of wavelength it was. 1I or less. For spacings other than these the unexpected gain improvement was not observed. This adds an additional complication to an already difficult theoretical problem. Therefore in the contract work this additional complication must be resolved. Is this gain improvement primarily due to a better match to free space which the array panel provides for a low efficiency (300/o) ferrite antenna or is the array panel the contributer in the gain improvement? An a priori speculation is that it is a matching phenomena, since (i) the spacing is critical, (ii) this effect was not observed at the higher frequencies when ordinary dipoles and horn antennas were used. This question can be resolved easily experimentally by using a small dipole antenna at these frequencies and observing the transmission pattern. Some experiments along those lines are planned. At present, the experimental phase of this work is concentrated on obtaining a variety of H and E plane patterns for different slot antenna-array panel spacing. The theoretical work is concentrated on obtaining an explanation for the behavior of the radant structure at these frequencies. This problem is approached as follows: the array panel is treated as an artificial anisotropic dielectric medium. The plane wave transmission coefficient is calculated and used to obtain the transmitted field when the anisotropic panel is illuminated by a spherical source. To I_______________ __2 12

THE UNIVERSITY OF MICHIGAN 7300-1-T expedite solutions to the theoretical problem various approximations are made, which,it is hoped, will be accurate enough so as not to introduce errors appreciably larger than are normally obtained in the experiments. The array elements which are rectangular loops are approximated by discs. The e and p of the artificial dielectric is then readily calculated. The approximation by discs should give accurate results since at the frequencies under considerations the array elements are in the Rayleigh region and as is well known, in this region differences between various scatterers are only second order effects. The primary effects are obtained from the induced dipole moments in the scatterer. However, as the frequency is increased the derived e and /a for the panel will become less accurate but will give useable results as long as kd < 1, where d is the length of an array element. For the array panel d=1. 63", and kd will be less than one for frequencies under 1200 Mc; hence, below this frequency the artificial dielectric approach is accurate. The field of the primary source (Adams, 1964) can be obtained from the far field beam pattern of a loaded rectangular waveguide opening out into an infinite ground plane, assuming dominant mode fields. Fig. 1.1 shows the coordinate system. 3

[ THE UNIVERSITY OF MICHIGAN 7300-1-T FIG. 1.1: COORDINATE SYSTEM FOR RECTANGULAR SLOT BEAM PATTERNS The E-plane pattern (= ) is k bsinO 0 = iok b sine o (1.1) and the H-plane pattern (0=0) is E =1 E -Y y o 2 k asinO 7T COS( ) cos0 2 iT -(k asinO)2 O (1.2) As the size of the aperture becomes electrically small, the pattern approaches that of a magnetic dipole oriented parallel to the broadwall of the waveguide (i ). x Figure 1.2 compares experimental beam patterns of a solid ferrite loaded rectangular cavity slot antenna mounted in a 3 ft. x 3 ft. ground plane with the I m 4

THE UNIVERSITY OF MICHIGAN 7300-1-T corresponding theoretical patterns. Beam patterns are also shown for the same antenna without flange. It is noted that the H-plane patterns (with flange) show good agreement with the theoretical data, whereas the E-plane patterns do not. The antenna aperture was 2" by 5" (b by a). It was filled with a solid ferrite of,=6.63, e=12.6, Q=30 at 300 Mc. The resonance frequency was 350 Me with a bandwidth of 19 Me and efficiency of 30~/o. It is seen that little agreeement between (1.1) and the experimental pattern exists. Hence in the calculations three different primary sources were used to approximate the ferrite slot antenna. The first is a tapered electric dipole oriente along the y-direction with electric field given by Aj"kR A o (1.3) E=E cosOe xi)xk (1.3) ~- o y R where k is the direction of observation. The second is a magnetic dipole oriented along the x-axis with electric field given by e-kR E=E (i xi R (1.4) The third is a direct approximation to the experimental pattern of Fig. 1. 2 with electric field in the E-plane given as, -jkR E E cos 0 -i (1.5) - o OR 5

_-. THE UNIVERSITY OF 7300-1-T MICHIGAN 1.0 2 6 E I.5.6 IE 2.5.4.3 -180 - 90 0 90 180 0 ( DEGREES ) FIG. 1.2: COMPARISON OF EXPERIMENTAL AND THEORETICAL BEAM PATTERN FOR A FERRITE LOADED SLOT ANTENNA [After Adams (1964), Fig. 27] 6

THE UNIVERSITY OF MICHIGAN 7300-1-T and the H-plane as -jkR A e E = E cos 0 i - o y R (1.6) 7

I THE UNIVERSITY OF MICHIGAN -- 7300-1-T II TRANSMISSION OF PLANE ELECTROMAGNETIC WAVE THROUGH AN ARTIFICIAL ANISOTROPIC PANEL Introduction To give a theoretical interpretation of the transmission properties of radome structures loaded with metallic wires or loops certain models are needed. One model which may offer some useful information concerning radome structures loaded with loops is an artificial anisotropic medium made of arrays of conducting disks as shown in Fig. 2. 1. z z 2r 0 0 0 a IX y x 00 FIG. 2.1: A THREE-DIMENSIONAL ARRAY OF DISKS AS AN ARTIFICIAL ANISOTROPIC MEDIUM 8

THE UNIVERSITY OF MICHIGAN 7300-1-T Physically, the electric and the magnetic polarizability of a disk should not differ too much from that of a wire loop. Analytically, the characteristics of an artificial anisotropic medium made of disks are well known as compared with that of a loop. In this report, we shall present a theoretical analysis of the transmissio property of a panel characterized by such an anisotropy. The Tensor Permittivity and Permeability of Arrays of Disks The tensor permittivity and permeability of a dielectric medium embedded with small conducting disks as shown in Fig. 2. 1 can be determined from Rayleigh's theory of scattering by small bodies. For bodies of the shape of an oblate spheroid, the theory was reviewed in great detail by this author using the method of spheroidal harmonics (C.T. Tai, 1952). The interaction between the neighboring bodies was discussed very thoroughly by Collin (1960) who also tabulated the pertinent data for prolate spheroids, ellipsoids as well as for the oblate spheroids. According to Rayleigh's theory, the induced electric dipole moment of an isolated disk due to an incident E-field polarized in the y or z direction can be written in the form Py =P= acE (2.1) where 9

THE UNIVERSITY OF MICHIGAN 7300-1-T E = amplitude of the incident E-field o e = dielectric constant of the ambient medium a = electric polarizability of an 16 3 isolated disk = - r 3 r = radius of the disk The induced magnetic dipole moment due to an incident H-field polarized in the x-direction is given by m =3 H (2.2) x o where H = amplitude of the incident H-field 3 = magnetic polarizability of an isolated disc 8 3 =- r 3 For a three-dimensional array of disks as shown in Fig. 2.1, one must take into consideration the interaction between the disks. The resultant effective permittivity and permeability can be written in the tensor form: e 0 0 e | 0 e1 0 (2.3) -~ ~ E1 1 10

THE UNIVERSITY OF MICHIGAN 7300-1-T 1 0 0 P- 0 0 (2.4) K 2o where =K = (1+ a (2.5) 1 e 1-aC e (l=Km o+ i- C )Po (2.6) m N = number of disks per unit volume / 2 )-1 = (a2c)-1 The values of the interaction constants C and C contained in (2.5) and (2. 6) e m depend on the actual dimensionality of the lattice. There are several alternative methods of evaluating these constants as described by Collin (1960). For a cubic lattice, corresponding to a=c, the values of C and C is given quite accurately by Lorentz's formula, namely, C= 1 (2.7) 3a3 Therefore, K and K are given, respectively, by' e m 16 r3 32 r 3 7 (-> 1+) 3 a 9 a K = 1+ (2.8) e 16 r 16 r 1- (a) - ( ) (9 a 9 a 11

THE UNIVERSITY OF MICHIGAN 7300-1-T and 8 r3 16 r3 3(a 9a Km l- 3 r3 9+ 9a r) T+~a 9(a (2.9) Transmission of a Plane Electromagnetic Wave Through an Anisotropic Panel Case A Incident E-field perpendicular to the plane of incidence. We consider now the problem illustrated in Fig. 2.2 z T d i R FIG. 2.2: A PLANE ELECTROMAGNETIC WAVE INCIDENT ON AN ANISOTROPIC PANEL The tensor permittivity and permeability of the panel are the same as the ones defined by (2.3) and (2.4). The E-field of the incident plane wave is assumed to be polarized in the y-direction. The general expressions for the fields in the three regions are given by: 12

THE UNIVERSITY OF 7300-1-T MICHIGAN Region I, z < 0 -i E = E ye O -j(k x + k z) x z (2.10) E -j(k x+ k z) -i o,i \ x z H = (-k x+k z) e WIA Z X (2.11) k = k sinO., X O 1 = R E e E =RE ye k =k cosO., k = z o 1 0 27.-. — j(k x-k z) x z (2.12) RE -j(k x-k z) -r o H =- (k x+k z) e 0J/ z x 0 (2.13) RegionII, 0< z< d -j(k' x + k' z) - E Tde x z -j(kt x-k' z) +Rle x 1 J (2.14) d E E - -i L-j(k'x-k'z) H d L0 i A LI A X Z H -= o T (-k' x+k'z)e x z COW L-1 z x + R (k' +k' ) e 1 z x -j(k x - k' z)1 x z (2.15) where [=]- denotes the inverse of /, and k' = k = k sin0. x x o 1 (2.16) 13

THE UNIVERSITY OF MICHIGAN 7300-1-T k'2 2 / e 2 k: = -(-)k't Z 1 1 /P X O =k2 K (K' -sin 0.) (2.17) o m e 1 K' =-K (2.18) e e e o Equation (2.16) results from the boundary condition that the field inside the panel should have the same phase as the incident field at the interface in order to satisfy the boundary condition. Equation (2.17) is a consequence of the fact that any plane wave solution inside the anisotropic panel must be a solution of the wave equation: V x / * VxE - e * E=0. Region III, d < z -j(k x+k z) (2.19) E=TE e x z 0 TE -j(k x+k z) H = (-k x+k)e x z (2.20) W~- P z xI By matching the tangential components of the E and H fields at the two interfaces, corresponding to z=0 and z=d, one can determine the unknown coefficients T1, R1, T, and R. The results are summarized below: 14

THE UNIVERSITY OF MICHIGAN 7300-1-T T = (l+) (2.21) 1 2 r j2kd (2.21) -2jk' d 1-r e R -j~k' d (2.22) 2 j(k -k')d l -r e T -j 2k d (2.23) -j2k' d R r(-e ) (2.24) 2-j2k'd 1-r e where JA k (,k )-1 r k Z- Z (2.25) it1k Z'+Z (1 z T+ ( rk' /okz Muo _ Z _- ~ (2.26) k cos0. z 1 Z't = m (2.27) kl 2 z K' - sin i e i or! 15

THE UNIVERSITY OF MICHIGAN 7300-1-T K cos0.-\ K -sin2.( It n -- 1 | e 1.. _(2.28) \K cos.+\ K' sin20. Y m 1 e i It can easily be verified that IT1i~2= 1 =2 (2.29) 2rsin k' d 1+ i- 2 ) 1-r and 1- R 2 = T 2=1r r)( IT1 -R1 ) (2.30) The power transmission coefficient I T2 becomes unity when k' d is equal to an z integral multiple of ir. It is seen that for an isotropic dielectric panel the coefficient r as defined by (2. 28) reduces 2 2 cosO.\- n -sin 0. r =.. (2.31) 2 2 cos 0. + \n -sin 0 1 X i and the phase constant k' defined by (2.17) reduces to z k'2 = k2 (n -sin2 0.) (2.32) Z 0 1 where 2 c n = (2.33) O These results are well known. I 16

i THE UNIVERSITY OF MICHIGAN 7300-1-T Case B Incident E-field parallel to the plane of incidence The orientation of the incident wave with respect to the panel for this case is shown in Fig. 2.3. z H'E'R G 2R.8i FIG. 2.3: The tensor permittivity and permeability of the panel are the same as the ones defined by (2. 3) and (2.4). It is convenient to define the reflection and the transmission coefficients with reference to the incident magnetic field. Thus, the expressions for the electromagnetic field in the different regions are given by Region I, z <0 - i A -j(3yY + 0ZZ) H=H Hxe o (2.34), H -j y +/ zz) E W E (- 0 zy + ) e 0 (2.35) where 17

- THE UNIVERSITY ( 7300-1-T )F MICHIGAN 3 =k sin0. y o 1 3 = k cos0. z o 1 2k k = o X Region II, 0 < z < d d T H =H x Tle do 1 -d H - w -0 +01 Z)M -j(l +R' e L * (-1y+Rz1 T3(-'z y +~ z)e 1 z y 3'; I'~ y z y z (2.36) + R' (3' y+ 3' z) e y 1 z y j (2.37) where [ denotes the inverse of E, and /3' = k sin0. y y o i Sz 1 1 y 2 2 = k2(K K' - sin 0.) o m e 1 K' = -K e c e o Region III, d<z - t A -j(3yy + z) H = T'H xe o (2.38) T'H - t o WE -j(/3y+1 z) (-Yz+/ 3 z)e Y z (2.39) (-zY py~) 18

I - THE UNIVERSITY OF MICHIGAN 7300-1-T By matching the tangential components of the E and H fields at the two interfaces, corresponding to z=0 and z=d, one can determine the unknown coefficients T, R', T' and R'. The results have the same algebraic forms 1' 1' as those given by (21) to (24) except that the coefficients k, k' and r are z z replaced, respectively, by j3, /3' and r' which are defined by z z 3 =k cos0. (2.40) Z 0 1 3' = k K K' - sin 20 (2.41) z o m e 1 K' cosO.-\ K K' -sin 0. r'=.1 m e (2.42) K' cos0. +K K'-sin2. e 1 m e Thus, the expression for I T'2 is given by l12 1~1 I -T- I- -- - = (2.43) /r' sin3' d 2 1+ Numerical Computation and Conclusion Before we discuss the effect of loading it is of some interest to point out the special characteristics of transparent panels at oblique incidence. Referring to Eqs. (2. 29) and (2.43) we see that IT| becomes unity when! 19

THE UNIVERSITY OF MICHIGAN 7300-1 -T k d K (K'-sin.) = NT (2.44) o m e 1 and T' becomes unity when 2 k d K K' -sin 0. = N' (2.45) o m e 1 where N and N' denote two integers. If we use the notations "I" and "//" to distinguish the two cases then the respective angle of incidences at which the power transmission coefficient becomes unity are given by 2 NX 2 sin2(0i =K (2 (2.46) e - K-2d - and 2 (wX) sin (Oi)/l =K K' - ( (2.47) m e 2d For convenience, these angles will be designated as "angle of transparency". For a panel with given values of K' and K it is possible to find the values for d e m d 1 such that the angle of transparency may occur at any desirable angle of incidence. For examnple, when d = 2 K =1, K'=2, (0i)l or (0i)// occurs at 1r/2. The dl curve labeled = in Fig. 1 shows such a case. In general, the transmission coefficient approaches zero when 0. approaches 90, corresponding to the 1 grazing incidence, unless the thickness of the panel is such that the angle of transparency occurs at the grazing incidence.! 20

THE UNIVERSITY OF MICHIGAN 7300-1-T When the incident E-field is perpendicular to the plane of incidence, it is seen from Fig. 2. 1 and Fig. 2.4 that for a panel with relative permittivity equal to two, the effect of disc loading, in general, does not change much the transmission characteristics except when the panel is transparent at certain incident angle, corresponding to d/X=0. 379 in Fig. 2. 4. For a denser panel, the loading may change considerably the angular dependence as shown by Figs. 2. 5 and 2. 8. In fact, for a panel with a thickness between a quarter-wavelength and a half-wavelength, the loading tends to provide a more uniform transmission except near the grazing incidence. When the incident E-field is parallel to the plane of incidence a dielectric panel becomes transparent when the angle of incidence is equal to the Brewster angle given by -1 (Oe)=tan - (2.48) 0 For = 2 and 4, the Brewster angle occurs, respectively, at 540-44' and E o 630-26" as shown in Figs. 2.9 and 2.10. For a panel made of discs only, the power transmission coefficient, as shown in Fig. 2. 11, is not too sensitive with respect to the thickness of the panel. The effect of disc loading in a dielectric panel is similar to the previous case. However, because of the phenomenon of transparency at the Brewster angle, the transmission coefficient tends to be more uniform with respect to the incident I —-------- -21

THE UNIVERSITY OF MICHIGAN 7300-1-T angle, unless the dielectric constant of the panel is high to start with, as shown by Fig. 2.13. By choosing the lattice spacing properly such that K KT =1, it is m e theoretically possible to move the Brewster angle to the grazing direction, hence to provide a quite uniform transmission through the panel. It is hoped that the study presented here may be used later to interpret the radiation pattern of a loop-radome structure which is presently being investigated experimentally. 22

THE UNIVERSITY OF 7300-1-T MICHIGAN d i X 16.7-.4.3.1 0 10 20 30 ei (in degrees) FIG. 2.4: THE TRANSMISSION COEFFICIENT T|2 FOR K =1, K =1, -=2 I m e c o 23

THE UNIVERSITY OF MICHIGAN 7300-1-T 1. d - T 4.8.7.5.4.3.2.1 10 20 30 40 2 ~ FIG.2.5: THE TRANSMISSION COEFFICIENT TI2 FOR K =1, K =1, - 4 m e E2 24

THE UNIVERS ITY OF MICHIGAN 7300-1-T d - T7 "2.9 4 2.5.4.3-.1 lo 70 80 90 W -1 ~~ 9 20 ov'0 20io el (in degrees) FIG.2.6 THE TORANSMISSION COEFFICIENT |TR2 FOR K =0.755, K =1.65, e 1 FIG. 2.6' THE TRANSMISSION COEFFICIENT 1T12 e'm' e' eo 25

THE UNIVERSITY OF 7300-1 -T MICHIGAN.7..6.4.3.1 0O 0 5( FIG. 2. 7: T IHE TRAI (in degrees) 70 8 SCOEFFICIENT T/ FOR K =0 755 26 e' I'-=2 0

THE UNIVERSITY OF 7300-1-T MICHIGAN 1.0 d I X 4.8.7..6 2 2 I 0 10 20 30 40 50 60 70 80 90 FIG. 2.8: THE 8; (in degrees) TRANSMISSION COEFFICIENT jTJ2 FOR K =0.755, K =1.65, e = 4 m e' o 27

THE UNIVERSITY OF MICHIGAN 7300-1-T d - 1.0- 1 2 16 2 2 4 4~~~~~~~~~~~~~~~~t I i\\ \ 0 0.810 20 304050 ~ 60 70 8 \196 O 10 20 30 4 50 60 70 80, So eS (in degrees) FIG. 2.9: THE TRANSMISSION COEFFICIENT IT 2 FOR K.1, K =1, =2 1 1 m Ve c o ILU

THE UNIVERSITY OF 7300-1-T MICHIGAN d _ X 4 1.0.9-.8.7-.6 8.5..3.2.1 0 10 60 70 80 90 j. (in degrees) FIG. 2.10: THE TRANSMISSION COEFFICIENT | T'2 FOR K =1 K =1 - = 4 Iim' e' 29 29

THE UNIVERSITY 7300-1 — OF MICHIGAN 1. d I X -"2 _ - -. _fft 4.7..6 IT'12.5 I I I I I I I I I I I I I I I I1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I.4.1 0 10 20 30 40 50 70 80 6; (in degrees) 90 FIG. 2.11: THE TRANSMISSION COEFFICIENT T1 OR K =0 7 K =1.65, FO3.MR0 K O 75, Ke - — 65 E = 1 30 0

THE UNIVERSITY OF 7300-1-T MICHIGAN 1.0 d -_ X ~16 / 16 / / 1 4 m m m ~ 2 IT'12.5.4.2-.1 10 2< 30 60 oi(in rdegrees) FIG. 2.12: THE TRANSMISSION COEFFICIENT |T'12 FOR K =0.755, K =1.65, = 2 *31 m e e 31

THE UNIVERSITY OF MICHIGAN 7300-1-T d - X -.8.7.4.3 i 0 0 10 20 30 40 50 60 90 8. (in degrees) FIG.2.13: THE TRANSMISSION COEFFICIENT |T'2 FOR K =0.755, K =1.65 = 4 l l m e'E 0 32

THE UNIVERSITY OF MICHIGAN 7300-1-T III TRANSMISSION PATTERNS OF AN ANISOTROPIC PANEL EXCITED BY A SPHERICAL SOURCE Introduction and Formulation We would like to obtain the field pattern which an anisotropic dielectric panel transmitts when excited by a small electromagnetic horn. The panel is an array of loops or discs which can be treated as an artificial anisotropic medium for which the tensor permittivity and permeability is found elsewhere. The plane wave transmis sion coefficient T for a panel of thickness d can then be obtained by the usual method of matching the tangential fields at the two surfaces of the panel. The excitation will be a horn or dipole antenna placed in the near or far field of the panel. To use the plane wave transmission coefficient when the source emmits spherical waves is very difficult. However, by assuming a cylindrical wavefront, the plane wave transmission coefficient can be readily used. Assuming a cylindrical wave, corresponds to a one-dimens ional analysis for our panel. This should give negligible error if we confine ourselves to E-plane and H-plane transmitted fields. Looking at a continuous one-dimensional radiating source, as shown in Fig. 3.1, the far field can be expressed as -jk R -jkr rt sin a o J o a jk x' sin0 1 a E ) = e E(r,0) = F f(x) R x') r a f(x')e dx' (3.1) a -a m I 33

THE UNIVERSITY OF MICHIGAN 7300-1-T Z E r 14/ 1 -a f(x') a FIG. 3.1: A RADIATING CONTINUOUS SOURCE However, when the panel is not a radiator itself, but is excited by a remote source, it should be treated as a secondary source. The reason for this is that the source will not only excite the panel but also the extension of the panel area which is free space. This extension will contribute to the observation point E(r, 0) in a Huygens source sense, i.e. the free space extension can be considered as a secondary source made of Huygens wavelets. Let us consider the special case of a plane boundary surface S1. For a plane infinite surface it can be inicshown, either by Babinet's principle or symmetry considerations that the equivalent electric and magnetic sources nxH and n x E contribute equally. Hence, the scattered field can be obtained from one of these terms alone, simply by doubling it. Applying the vector Huygens-Kirchhoff formula to this case we obtain the field E(r) in terms of an integral over the plane surface S j 34

I. THE UNIVERSITY OF MICHIGAN - 7300-1-T E(r) = 2Vx Jf 1 n x E(p') G(r,')da' (3.2) 1 e-jkR where G = 4- R; the radiation condition was applied to make the surface 47w R integral vanish at infinity. This is an exact form and is particularly suitable when apertures in a perfectly conducting screen are considered. Equation (3.2) is exact if the correct tangential component of E over the apertures are inserted. To apply (3.2) when the surface S1 is a combination of free space and a dielectric panel, we can let the aperture in a perfectly conducting plane sheet become very large and consider this large aperture to be the combination of freespace and the dielectric panel. Hence (3.2) is also valid for a plane dielectric surface of infinite extent. The geometry is shown in Fig. 3.2. z rE ( r, 0, )......-. x Dielectric Panel S - a FIG. 3.2: GEOMETRY OF THE DIELECTRIC PANEL mm 35

THE UNIVERSITY OF MICHIGAN 7300-1-T The primary source will be a small electromagnetic horn or a small dipole which will be placed in the near field or the far field of the plate. Let us approximate the primary source by a dipole source oriented along the y-direction with an additional cos 0' tapering as -jk R' E =E cos0'( xi ) xk' (3.3) -horn o y R' As we pointed out before we would like to use a plane wave transmission coefficient when a portion of S1 is a plane dielectric panel. The particular form (3) assumed for the primary source will make this difficult unless we use a matrix representation for T. Since the plane wave transmission coefficients, one for perpendicular and one for parallel polarization, are relatively easily derived for a dielectric panel, we will facilitate their use by assuming a cylindrical wave front. Hence, for perpendicular polarization (as defined with respect to a plane wave incident on the panel) let us assume that the primary source (3. 3) has only a variation in the z'x' plane, i.e. let 0'=0. Substituting 0'=0 in (3.3) we obtain -jk R' 0 E E i cos0' e3a) h o y (3.3a) z=0 which is similar to the field of an electric line source. For parallel polarization on the other hand, let us modify the primary source (3. 3) by assuming only a 36

THE UNIVERSITY OF MICHIGAN 7300-1-T variation in the zy' plane, i.e.'=. Substituting 0'= - in (3) we obtain 2 2 -jkR' ^ A 20 ^A_ e E = (-cos0'sin0'i +cos O'i )E cos0' (3.3b) -h ZO z y o R' -ikR' e = (cos0'40)E cose't Go R which is similar to the field of a magnetic line source. The above two results were obtained by using the expression k=r=sin0' cos0'i + sin s in'i + cos' i x y z and where R' h2,2 R= h +p P' = x,2+y,2 cos 0' = h/R' Expressions (3. 3) are approximations valid for the far field of a low gain small horn antenna; they show an additional cosine tapering in both the E and H plane over that of a pure dipole. As far as the - variation in amplitude is concerned, this is r not a good approximation in the near field; there, a faster drop-off with respect to -2 -3 r, such as r or r, would be more correct. However, since the excitation of our panel will depend largely on the pattern and phase of the horn antenna and since these are similar in the near and far field we will use (3. 3) as the field of our 37 ---

I THE UNIVERSITY ( 7300-1-T DF MICHIGAN primary source at the panel. Hence on S1, the nxE(p') term becomes A i xE z -h z z=0 -jk R' = E = E cos0e'i ix ('xT )Rx 0o z L yI R' (3.4) and the corresponding expressions using (3.3a) and (3.3b) are -jk R' 0 1 xEh z -h Z= and e = -E i cos0' e ox R' =0 -jk R' = -E i cos 0' 3 e ox R' (3.4a) (3.4b) 4A 1 xE z h z=C Substituting the above expressions in (3.2) and performing the V operation we obtain -jk R - 1 II) e 1 E(r) = X (I x Eh ) x (jk~)- )R da' b1 Z=U (3.5) Substituting (3.4a) we obtain E E(r) = 2 -O ffs —1 1 - jk R h -jk R' -ojkR - e (jko+ i )Rxi da' R 2 R oR x (3.5a) and substituting (3.4b) we obtain E E(r) 2= 2?r 3 -jko(R'+R) i'h e 1 A A I~ ~O,, (jk+-) R xi da' 1 (3.5b) 38

- THE UNIVERSITY OF MICHIGAN 7300-1-T Since we are interested in the far-field transmission pattern of the panel, we can simplify the above expression by substituting the far-field approximation for R, the distance between the source and observation point. Before we do this, we should note that this might lead to a non-existing integral. For example, when we examine the above integral of (3.5a) for large values of p' we observe that the integrand varies as dp'/p' which will give a convergent result upon integration. However, if the far field approximation is substituted, we see that the integrand varies as dp'/p' for large p', giving a lnp' dependence for the integral, clearly a nonconvergent result. One usually avoids these unpleasantries by restricting the integration to a finite surface. This approximation can usually be justified when the radiation pattern of the primary source is very sharp, such that only the central portion, primarily where the panel is located, receives appreciable excitation. If the entire S1 plane had a source distribution whose magnitude did not vary greatly over the plane, the far field approximation would not be valid in (3.5). We are interested in integrating over the area of the panel for obvious reasons. If we know the material composition of various panels, we can compute their transmission coefficients and substitute it in (3. 5) and restricting the area of integration will allow us to make the far field approximation in (3. 5) regardless of the excitation of the panel by the primary source. However, we must evaluate the contribution of the rest of the surface since it also receives excitation by the I 39

THE UNIVERSITY OF MICHIGAN 7300-1-T primary source and hence acts as a Huygens secondary source and it will give us the error if we want to approximate the transmis sion field by the finite area integral. Hence, let us divide S1 into S + S, the area of the panel plus the 1L a 00 rest of the surface. In the integration over S we can make the far field approxia mation since R will be assumed to be always large in terms of the diffracting system dimensions, i.e. R=| r-p'| = r-k ~ +... (3.6) Substituting this in (3.5) we obtain 1 ft A jk f Pl g E(r) j k I ( xEh e -da + (3.7) z=O a oo as the correct far field formulation. If we now use the electric line source approximation (3.4a) as our primary field is (3.7) we obtain -jk r jE e 0 f -ik (R'-. p') E — r-) k xie da'+...(3.5).., a oo (3.7a) If we use the finite magnetic line source approximation (3.4b) we obtain -jk r jE e ~ 3 -jk (R'-k p') E(r) o -- k xT xT -'e da'+fI (3.7b) -- 2rr -0 X R4 J a oo 40

THE UNIVERSITY OF MICHIGAN 7300-1-T In an effort to evaluate the integral over S we can examine various forms. For 00 example, in polar coordinates (3.7a) can be written as -jk r -jko(R'-k. p') jhE e -rjk P' d' E(r) kx Idtdo -e 2- r — ^0 xj, 2 p' dp'd - a R, a hE oo -2 Vxi 27r XJa at -jk R' e e' dp' R' 2 -jk\r+p' -2rp' sin 0 cos (0)'- ) Je 0 2..2 +. p do 0 1 2,,2,. _, _,.2 A. r +p' -zrp' sinU cos (p'-p) (3.8) Since V= -V, we can also write (3.2) with the primary source (3.3a) as hE -jkoR' -jkoR hE i 0 0 E(r)=- 2 x R 2 V R da' Then in rectangular coordinates (3.9) E(r)I... S -i hE oo o x o 2a a -jk R' -jk R -jk R e a__ e ^ 3 e, (- i + - -- )dx' dy' 2 ayI R y azi R Z -00 (3.10) -a -00 -a The differentiation with respect to z' is a limit process, where a finite z' is assumed in R and then the limit as z' —> 0 taken after the integration is 41

THE UNIVERSITY OF MICHIGAN 7300-1-T performed. The corresponding equations for the primary source (3.3b) are 3 2 identical to (3.8), (3.9), and (3.10), except that h is replaced by h and R' by 4 R'4. Transmission Through the Panel Let us formulate the integral over S in a form most suitable for calculation. a A dielectric will occupy the area S in our later formulation. If the surface a variables are expressed in spherical coordinates as x=h tanO' cos' y' =h tane' sin' (3.11) and this substitution made in the distance R', we obtain h2+ x2 +y'2 = hsecO' p = h tan 0' (3.12) Similarly the *~ p' term in (3.7) or (3. 8) can be written as' p' = sin (x' cos 0+ y' sin 0)=h sin tan' cos ('-0) The electric field of (3.7a) or (3.8) can then be expressed as -jk r -jk h [secO'-sinO tan0' cos(0'-j - jE 27rr - x e — _ 2,'r -k 2 x.~ { 2 da EJJr) 2nr lioxilS h sec 0' a (3.13)'Iff (3.14) 42

THE UNIVERSITY OF MICHIGAN7300-1-T Combining this with the expression for surface area element p'dp' d0' = h2 tan0' sec20' dO'dO' we obtain for the integral over the area S a -ik r j E e r -jk h [sec0 -sin 0 tan0' cos ( -)] E(r) =.-. k xi e htan0d'dO'. --- 27rr -o xJJ a (3.15) The corresponding result for (3.7b) can be obtained from (3. 14) or (3.15) by dividing the integrand of (3.14) or (3.15) by sin 0' a) One-dimensional approximation In order to make the integrations more tractable, let us confine ourselves to the transmission patterns in the E-plane (zy plane or 0= 7r/2 plane) and the H-plane (zx plane or 0=0 plane). Furthermore, when considering the H-plane (E-plane) pattern, let us also assume that the entire structure is infinite in the y-dimension (x dimension), i.e. let us make a one-dimensional approximation. Instead of a spherical source, we should now consider a line source. However, we pointed out before that we are primarily interested in changes of phase across the panel and that variations in amplitude should be of secondary importance. Since the phase dependence of a Hankel function is the same as that of a point source, we need not make any changes in the primary source. 43

I THE UNIVERSITY OF MICHIGAN 7300-1-T The H-plane pattern of a one-dimensional source can be obtained from (3.14) ^A~~ ^~~2 by substituting (0'-0)=0, kixi =i cos0, x'=htanO', dx'=h sec O'd0. We obtain x y -jk r jE e r a -jk h sec0'-sin0 tan O 1 E(r,O,0)== 2r i1 cosO J e dO'+ + -0 S a oo (3. 16a) The E-plane pattern can be obtained similarly from (3. 7b) and (3.11) - (3.13), with I e sti A 2 the substitutions ('-j=0, kxi = i, y'=htan0', dy'=hsec O'dO' as -ik r jE e, i a -jk h [sec -sin tan 03 E(rO,'- 2 ) 2 0 f cos O' e dO' a (3.16b) The integral over S (of (3.16a) can be written from (3. 8) as 00 hE oo -r VXi 27r XJ a a -jko h2+xT 2 e h +2x h +t x' -jk or2+x2 -,2rx'sinO e r --— 2x sdx' r +x' -2rx' sinO 00 (3. 17a) or from (3.10) as 1i 00 hEo ro 27 x az a a 2 2 2+2 -jk h +x'2 -jk (x-x') ~z e e (x-x') + z dx' (3. 18a) 44

THE UNIVERSITY OF MICHIGAN. 7300-1-T The corresponding integrals over S for (3.16b) can be written as 2 12 2 2 _2 3E 0 -jko h +y2 -ik0 r+y2-2ry'sin f1 h Eo, rC e e _ oc,,.~ p e I 2 J, 2 V x a 00 (h2+ y2)2 r +x'2 _ 2rx' sinO (3. 17b) and as 1 f Sh3E~A 3 r~ 2 JS 27r lx az Ja E 00 0k h e -jk (Y-Y) z2 e Ay, (h2+y2)2,)2 2 (y-y')+ z (3. 18b) or as h3E 2 10 27T 00 o00 -jk (R'+R) Ja e 4R -,-j a R,4 R (Jko+ -)dyt b) Transmission from a dielectric medium into free space If in Fig. 3. 2 the half space z < 0 is occupied by a dielectric medium with e r and /ur the relative permittivity and permeability, the transmission coefficient for an incident wave traveling from the dielectric (incident at angle 0') into free space (emerging at angle 0) is Vsin 20' sin 20 T= (3.19) I sin(0'+0) for E normal to the plane of incidence and 45

THE UNIVERSITY OF MICHIGAN 7300-1-T \ sin 20' sin 20 T// sin(0O'+0) cos(0'- 0) with E parrellel to the plane of incidence. If the primary source is again a small horn antennas with radiation properties as given by (3. 3) the electric field in the one-dimensional formulation can be expressed from (3.16) as -jh(kd sec 0-k sin 0 tan 0') co E~ ([6)e dO' + T(')... (3.21) 00oo The integral over SOD is the same as given by (3.17) or (3.18) except that the integrand is multiplied by the transmission coefficient T. Substituting T, the H-plane (zx plane) transmission field pattern can be determined from -jk h(\r sec'-sin0 tan0') e ~ Vr d s+ Tl (0. (3. 22) -jk r | x, 1 oT r E 0 A a -sin('+)-sin(-0) 2 E// (rO, - r) = i cos0 in (0'0 ) os 0 a -jk h(\Ir E sec0' - sin0 tanG') e r +dO' + T1 (0)... (3.23) S D00 and the E-plane (zy plane) transmitted field is -jk r o 0 jEe a sin(0'+0)- sin (0'-0) 2 E/ = 271r sin(0'~+) cos(0'-0) cos aa -jk h( \FVT secBt - sinG tanG') e dO'+ S T//(0')... (3.23) 00 I 46

THE UNIVERSITY OF MICHIGAN 7300-1-T c) Transmission through a non-magnetic, dielectric panel We will continue our physical optics type of analysis by considering radiation from a dielectric panel with =p / which is excited from the other side by the primary source (3.3). The length of the panel is 2a, thickness is d. The panel geometry is shown in Fig. 3. 3. z E(r,8) e z =d'///~ — 40. x A., - - - - I a \ a`u DIELECTRIC PANEL EXCITED BY A PRIMARY SOURCE The transmission coefficient for such a panel when a plane wave is incident from the region z< 0 at an angle 0' is given by 2jd(k cos' - k' ) T (-r )e (3.24) 2 e-j2k1Z d I r -- 47

THE UNIVERSITY OF MICHIGAN 7300-1-T where k =k \k -sin 0' and the reflection coefficient at a dielectric interface z o0 r for parallel polarization with respect to the plane of incidence is e cos' -\ -sin 0' r r -r='r o. = io oC\ cos0' +\ e -sin20' r r \o. GJU/ and for perpendicular polarization r = i cos 0' -\e -sin 0' r (3.26) cos O + E - sin20 r Substituting these in (3.16) the H-plane transmitted field becomes -jk r o 0 jE e a -jk h(sec 0'-sin0 tan 0') E.(r,,0)-= 0 cos0E T(r, d,0')e I 27rr y a d'+ 1s 10 S 00 (3.27) and the E-plane transmitted field is -jk r jE e a E//(r, 0, ) i T(r//,d,0')e a aa -jk h(sec0'-sin0 tan0') 2 cos O'd0' 1/ S 00 (3.28) the integrals over S are again given by (3.17) or (3.18). d) Transmission through an anisotropic dielectric panel The next case that we would like to consider is an anisotropic dielectric panel with tensor permittivity c and permeability A. The panel geometry is the same as that in Fig. 3.3. It is assumed that the material can be electrically 48

THE UNIVERSITY OF MICHIGAN 7300-1-T polarized in the z and y directions and magnetically in the x direction, such that E 0 011 0 0 0 e = 0 e 0 = 0 J - 0O O ~ ~ 0 /io The0 tra 0 The transmission coefficient can then be determined as (3.29) T j(k -k')d (-re z z (1-r )e 2 -j2k' d 1-r e (3.30) where k = k cos' z 0 k' = k K (K' -sin2') z o m e (3. 31) K' = (E/E )K, K E / K,/ e 0 e e 1o' mn 1 o The interface reflection coefficient r for the perpendicular polarization is f 2 \K cosO' -\ K' -sin 0' r = mn e 2 K cosO' + K' -sin 0' \m I e (3.32) Hence, the H-plane (xz plane) transmitted field is given from (3.16) as 49

THE UNIVERSITY OF MICHIGAN 7300-1-T -jkr 0 jE e a -jk h(sec0'-sin0tan0') Ej_(r, e,0)= i co's Trd,0')e d'+ — L 27r y Jo 1 dj a o0 (3.33) The S integration is given by (3.17a) or (3.18a). 00 For the other polarization, with E vector parallel to the plane of incidence the transmission coefficient is that of (3. 30). The interface reflection coefficient is given by K' cos0' - K K' -sin2 0 r =e \m e (3.34) 2 K' cosO' + K K' -sin 2e e m e and k' should be replaced by 13' where z z 3' =k \K K' -sin2' (3.35) z m e Hence for this polarization the transmission coefficient is 2 j(k -')d (1 -r,, ) e T// 1_2 -j2j 2d (3.36) The transmitted electric field in the E-plane (zy plane) is then from (3.16b) -jk r jEe r a 2 -jk hsec0'-sin tan 0 E// (r, -)= ---— i C e 22 ~ ~~~- 2/'( r/2' ('e' a oo (3.37) I I m 50

THE UNIVERSITY OF MICHIGAN —. 7300-1-T The integral over S is given by (3.17b) or (3.18b). 00 e) Transmission through an anisotropic dielectric panel excited by a Magnetic dipole source If a small slot antenna, with dimensions much smaller than a wavelength is used as a primary radiator, a good approximation to its radiation pattern is the field of a magnetic dipole oriented such that its axis is parallel to the long dimension of the slot. Hence, let us use the far field of a magnetic dipole, oriented parellel to the x-axis as primary source. -jkR' E'(r,O,) = E (t' x x)e R (3.38) o x RI To use the plane wave transmission coefficient we will again make use of the onedimensional approximation. This we hope will give good results if we confine our interest to the H-plane and E-plane transmission patterns of the dielectric panel. As before, we will use the H-plane (zx plane) pattern of the primary source as the excitation field for the dielectric panel when we desire the H-plane (zx) transmitted far field of the panel. The H-plane excitation pattern of a magnetic dipole can be obtained from (3. 38) by substituting 0'=0. Thus, -ikR' E'(r', 0,0) = E cosO' (3.39) E t e e te tr (1 and the corresponding n x E' to be used in the integrand of (3.16a) is 51

- THE UNIVERSITY OF MICHIGAN 7300-1-T -jkR' i xE' -E cosO' i (3.40) z - o x R' z=0 Hence, the transmitted far field of the anisotropic dielectric panel, using T1 (or (3.30)) is -jk r 0 0 jE e o a -jk h(sec 0'-sin0 tane') E (r, ~0)= = 1- 2 cos T1 e de' + ~1 27rr y 0 S a oo (3.41) which is identical to (3. 37). The E-plane (zy plane) transmitted far field pattern from the panel can be obtained similarly by using the E' plane pattern of the primary source. Hence the E' plane pattern of the magnetic dipole can be obtained from (3. 38) by substituting 7r 0'=2 2' Ajk R-jkRI iT e E'(r', O 2) = E (cosO' i -sin'i''2 o y z R' -~~~~~~jkRI~ ~(3.42) Ae o 0 R' The n x E' term becomes AxE' - F-jkR' i xE =-E cos0'i (3.43) z -o x R' z=0 The transmitted field in the E-plane is then 52

THE UNIVERSITY OF MICHIGAN 7300-1-T -jk r 7r jE e 0 -jk EjE (e ) a -jk h(sec0'-sin0tan0') E O., 7 ) = - i J T ~ eidit+ 3 JE44)'/ 2 2/r 10 -0 1/ a oo f) Transmission through an anisotropic dielectric panel excited by a Ferrite Slot Antenna In Fig. 1.1 of the Introduction the radiation patterns of a ferrite antenna are shown. When the experimental radiation patterns from a ferrite loaded slot antenna are examined it is seen that neither an electric nor a magnetic dipole source approximates these patterns well, at least not in both H and E planes. The agreement between the theoretical and experimental patterns is better for the H-plane patterns but no agreement exists for the E-plane patterns. In view of this disagreement let us choose a simple function which shows the characteristic behavior of the E and H plane patterns for a ferrite slot antenna with a flange (3 ft. x 3 ft. ground plane). From an examination of the experimental patterns, we see that in the Hplane the pattern is predicted well by E' =t cos0' (3.45) -y y This approximation can also be obtained by substituting k a < 1 in the EO expression of (1.2) in the Introduction. The E-plane pattern can be approximated by E~ = i cos0' (3.46) -o 0 53

THE UNIVERSITY OF MICHIGAN 7300-1 -T It should be noted that (3. 46) cannot be obtained by substituting k b < 1 in (1. 1) 0 of the Introduction. Hence this approximaton is not as good as (3. 45). The transmitted H-plane far field from the anisotropic dielectric panel, using (3.45) is then identical to the expressions given by (3.33) or (3.41). The transmitted E-plane far field from the anisotropic dielectric panel, using (3. 46) is then given by -jk r EjE e' i 0 -jk h(secO'-sinO tan0') E(r 2 ) 27r 0 J0 T//cos0'e d+ J a OD (3.47) Conclusion At present, the integrals for the transmitted electric field, both for the E-plane and H-plane are being computed. These will be compared to the experimental data, and since this data will be presented as power patterns, the final computations are for I E2. The error integrals, i.e. the integrals over S 00 will be determined approximately, either by using the first term in a power series expansion or by applying a stationary phase technique. Since the panel dimension is a, and since the evaluated integrals over SO will behave as 1/a raised to some power, the S integrals will give us the error committed when the trans00 mitted field is obtained from the integration over the area of the panel (instead of all space) only. I w 54

-THE UNIVERSITY OF MICHIGAN. 7300-1-T A preliminary analysis of the computed data for the integral (3.41) which represents the transmitted electric field in the H-plane can be given in the following table. It is a tabulation of the half power beamwidth for five dielectric panels h 1" 2" 160" J =1 E=2 88~ 82~ 64~ - =1 E=4 87~ 84~ 68~ K =.755 K =1.65 86~ 84~ 64~ m e K =.755 K =3.3 90~ 84~ 68~ m e K =.755 K =6.6 88~ 87~ 64~ m e Table 3-1: Tabulation of Half Power Beamwidth in the H-plane for Five Dielectric Panel for a Frequency of 370 Mc The distance of the primary source to the panel is given by h. The last column for h=160", is when the primary source is in the far field; hence it should be comparable to a plane wave source. Plane wave solutions for ordinary dielectric panels are known and can be compared to our case. Richmond (1965) calculated the transmitted field for a 2. 50 X dielectric slab of A = 1, e = 4, by a physical optics method and by an exact integration method. His results and our calculations agree excellently at the corresponding frequency. It should be pointed out that the rows in the above table correspond to an ordinary dielectric panel of e=2 and = 4 in the first and second row respectively. The third row corresponds to an 55

-- THE UNIVERSITY OF MICHIGAN 7300-1-T anisotropic artificial dielectric which consist of discs in free space, the fourth row corresponds to discs in a dielectric of e=2, and the fifth row to discs in a dielectric of E=4. If we plot beamwidth angle 0 versus distance h using the three points given in the table, it is suggested that we obtain a graph as follows: FIG. 3.4: BEAMWIDTH 0 VERSUS DISTANCE h OF A PRIMARY SOURCE o FROM A DIELECTRIC PANEL It is seen that optimum directivity is obtained when the illumination of the panel has a uniform phase along the panel which corresponds to a plane wave incident normally on the panel. Apparently, the different dielectric properties of the panels do not have significant effects upon the directivity. The spacing h of the primary souce determines the phase along the panel. Hence, for small values of h, when the phase is non-uniform, the directivity is poorer than for a more uniform phase front. The experimental data for h between 3/4" to 2" agree, 56

I THE UNIVERSITY OF MICHIGAN 7300-1-T with the calculated data except that the beamwidth is sharper by about 7 for all values of h. This constant difference could be due to the error in the one-dimensional approximation and the failure to include the integral over all space outside the dielectric panel surface, i.e., the integral over SO. However, the important characteristic, namely the behavior of the beamwidth versus primary source spacing h agree when the calculated data is compared to the experimental data. 57

I THE UNIVERSITY OF MICHIGAN 7300-1-T IV EXPERIMENTAL MEASUREMENTS The experimental phase of the research is concentrated at present on two aspects. The first concerns itself with VSWR measurements of the Radant structure whereas the second part has for its main objective the determination of the half power beam width 0 in the E and H planes. The VSWR measurements are completed. The results can best be summarized in Fig. 4. 1 and 4. 2. For these measurements the radant loops were oriented parallel to the E field. In this position the frequency at which minimum VSWR occured, changed from 300 Me to 346 Me as a function of the spacing between the array panel and the ferrite slot. With the loops normal to the E field no change in the VSWR was observed. At the higher frequencies (450-780 Mc) with the radant loops either parallel or normal to the E field, no change in the VSWR was observed. The VSWR was always less than 2:1 and it appeared that most of the power was absorbed by the ferrite material at the higher frequencies. The above measurements were performed with the ferrite loaded slot mounted flush in an 18 inch square ground plane. The radant structure was mounted so that the spacing between it and the ground plane could be changed in increments from 3/8" to 2". All of the patterns were made with a 48" square ground plane. 58

6+ 0 0 ~ Without radant Spacing 3/8" Spacing 3/4" Spacing 2" cD VSWR H z d Cf) HC 07l 5+ I -3 4+ 3+ C) 0 z 2+ Il ai i l l _ I 310 320 330 340 350 360 Frequency (MHz) FIG. 4.1: STANDING WAVE RATIO VS FREQUENCY: PRIMARY SOURCE FERRITE-LOADED ANTENNA (Loops in Parallel with E Field)

(A Without Radant Structure O Spacing 3/8", 1" and 2" 7.0 <TA VSWR IND 4t, ^ HP 415 B 6.0- VSWR HP HP 805 /Antenno 4.0- \ 612 3.0- Slotted Line 03 - \\ 20. \ I.0 450 500 550 600 650 700 750 800 Frequency (MHz) FIG. 4.2: STANDING WAVE RATIO VS FREQUENCY: PRIMARY SOURCE FERRITE LOADED ANTENNA (Loops in Parallel with the E Field) H z 0 d CO I F-Al 1

THE UNIVERSITY OF MICHIGAN 7300-1-T To perform the pattern measurements the radant structure was used as a receiver. A corner reflector antenna was used as a transmitter. Table 4.1 lists the beamwidth variation as a function of spacing between the primary source and the array panel. This variation is also shown in Fig. 4.3. We can make the following general observation (i) The H-plane is more directive than the E-plane (ii) The directivity improvement versus radant spacing is higher in E-plane ('20~/o) then in the H-plane ( 10%) (iii) In both planes the directivity improves with a larger radant spacing (iv) For a 3/8" spacing no remarkable change in pattern shape was observed (375 Me) (v) For a 2" spacing the E and H plane patterns are given in Fig. 4. 6 and 4.7 (375 Me) (vi) The E and H plane pattern of the primary source above are given in Fig. 4. 4 and 4.5 (375 Me) 61

THE UNIVERSITY OF MICHIGAN 7300-1-T 1 Table 4-1: Half-power Beam Width Expressed in Degrees as Function of Spacing, h, and Frequency 62

H ir 150~ r 140'- NR E-Plane t0" c..N I a 120o. (0 10 0~ N H-Plane 290~h - C) 1" 2" 2 NR = No Radant Structure > ~() Half Power Beamwidth E plane Z O) Half Power Beamwidth H Plane I I I I I I I I I I I I I I I I I I I I I k I I I I I I FIG. 4.3: HALF POWER BEAM AS FUNCTION OF SPACING (348 Mc)

t9,NVTId C1noflOI,,8 V HULIM VNNaIjNV LO IS aLI3[aad aHL JO N3aLVcd aNVId-a: a' a-DIj JI-T-00L NVI9 1HOIN I ] 10~~ AtIS AINfn aHJL

THE UNIVERSITY OF MICHIGAN 7300-1-T FIG. 4.5: H-PLANE PATTERN OF THE FERRITE SLOT ANTENNA WITH A 48" GROUND PLANE 65

THE UNIVERSITY OF MICHIGAN 7300-1-T FIG. 4.6: E-PLANE PATTERN OF THE RADANT (h, the slot antenna to array panel spacing is 2") 66

THE UNIVERSITY OF MICHIGAN 7300-1-T FIG. 4.7: H-PLANE PATTERN OF THE RADANT (h=2") 67

THE UNIVERSITY OF MICHIGAN 7300-1-T REFERENCES Adams, A.T. (1964), "The Rectangular Cavity Slot Antenna with Homogeneous Isotropic Loading, " University of Michigan Cooley Electronics Laboratory, Technical Report 147, AD 603657. Collin, R. E. (1960), Field Theory of Guided Waves, McGraw-Hill Book Company, New York, Chapter 12. Collin, R. E. (1960), Field Theory of Guided Waves, McGraw-Hill Book Company, New York, pp 520-525. Jackson, J.D. (1962), "Classical Electrodynamics, " John Wiley, New York, p.287. Stratton, J.A. (1941), Electromagnetic Theory, McGraw-Hill Book Company, New York, p. 512. Tai, C.T. (1952), "Quasi-Static Solution for Diffraction of a Plane Electromagnetic Wave by a Small Oblate Spheroid, " Trans. PGAP, Vol.1, pp 13-36. Richmond, J.H.(1965), "Scattering by a Dielectric Cylinder of Arbitrary Cross Section Shape, " Trans. PTGAP, Vol. AP-13, pp 334-341. 68

Unclassified Security Classification DOCUMENT CONTROL DATA - R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1. ORIGINATIN G ACTIVITY (Corporate author) 2a. REPORT SECURITY C LASSIFICATION The University of Michigan Radiation Laboratory Unclassified Department of Electrical Engineering 2b. GROUP Ann Arbor, Michigan 3. REPORT TITLE Radant Analysis Studies 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Interim Report No. 1 5. AUTHOR(S) (Last name, first name, initial) Tai, C-T and Plonus, M.A. and Andrade, E.S. 6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS August 1965 68 6 8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) AF 33(615)-2811 7300-1-T b. PROJECT NO. 4161 c. 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned Task 416103 thI report) d. 10. A VA IL ABILITY/LMITA TIoN NOTICES May obtain copies from DDC, Cameron Station, Alexandria, Virginia 22314 1 1. SUPPLEMENTARY NOTES 12. SPONSORING MIL ITARY ACTIVITY Air Force Avionics Laboratory, AVWC Research and Technology Division, AFSC Wright-Patterson Air Force Base, Ohio 45433 13. ABSTRACT The transmission characteristics of an anisotropic panel formed by conducting discs are investigated theoretically in this work. The result is intended to interpret the characteristics of the loop loaded radant (radome-antenna) panel originally studied at the Air Force Avionics Laboratory. Experimental work on the impedance variation of a ferrite-loaded horn antenna in the presence of the panel and the radiation pattern of the antenna structure are also reported in this interim report. IM -l_ _II UU l1JAN64 147/ 3 Unclassified Security Classification

Unclassified Security Classification l.14. LINK A LINK B LINK C KEY WORDS ROLE WT ROLE WT ROLE WT Antennas Radomes INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address of the contractor, subcontractor, grantee, Department of Defense activity or other organization (corporate author) issuing the report. 2a. REPORT SECURITY CLASSIFICATION: Enter the overall security classification of the report. Indicate whether "Restricted Data" is included. Marking is to be in accordance with appropriate security regulations. 2b. GROUP: Automatic downgrading is specified in DoD Directive 5200. 10 and Armed Forces Industrial Manual. Enter the group number. Also, when applicable, show that optional markings have been used for Group 3 and Group 4 as authorized. 3. REPORT TITLE: Enter the complete report title in all capital letters. Titles in all cases should be unclassified. If a meaningful title ca'nnot be selected without classification, show title classification in all capitals in parenthesis immediately following the title. 4. DESCRIPTIVE NOTES: If appropriate, enter the type of report, e.g., interim, progress, summary, annual, or final. Give the inclusive dates when a specific reporting period is covered. 5. AUTHOR(S): Enter the name(s) of author(s) as shown on or in the report. Enter last name, first name, middle initial. If military, show rank and branch of service. The name of the principal author is an absolute minimum requirement. 6. REPORT DAT7: Enter the date of the report as day, month, year; or month, year. If more than one date appears on the report, use date of publication. 7a. TOTAL NUMBER OF PAGES: The total page count should follow normal pagination procedures, i.e., enter the number of pages containing information. 7b. NUMBER OF REFERENCES: Enter the total number of references cited in the report. 8a. CONTRACT OR GRANT NUMBER: If appropriate, enter the applicable number of the contract or grant under which the report was written. 8b, 8c, & 8d. PROJECT NUMBER: Enter the appropriate military department identification, such as project number, subproject number, system numbers, task number, etc. 9a. ORIGINATOR'S REPORT NUMBER(S): Enter the official report number by which the document will be identified and controlled by the originating activity, This number must be unique to this report. 9b. OTHER REPORT NUMBER(S): If the report has been assigned any other repcrt numbers (either by the originator or by the sponsor), also enter this number(s), 10. AVAILABILITY/LIMITATION NOTICES: Enter any limitations on further dissemination of the report, other than those imposed by security classification, using standard statements such as: (1) "Qualified requesters may obtain copies of this report from DDC." (2) "Foreign announcement and dissemination of this report by DDC is not authorized." (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC users shall request through *, (4) "U. S. military agencies may obtain copies of this report directly from DDC. Other qualified users shall request through > s I (5) "All distribution of this report is controlled. Qualified DDC users shall request through _ If the report has been furnished to the Office of Technical Services, Department of Commerce, for sale to the public, indicate this fact and enter the price, if known. 11. SUPPLEMENTARY NOTES: Use for additional explanatory notes. 12, SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (paying for) the research and development. Include address. 13. ABSTRACT: Enter an abstract giving a brief and factual summary of the document indicative of the'report, even though it may also appear elsewhere in the body of the technical report. If additional space is required, a continuation sheet shall be attached. It is highly desirable that the abstract of classified reports be unclassified. Each paragraph of the abstract shall end with an indication of the military security classification of the information in the paragraph, represented as (TS), (S), (C), or (U). There is no limitation on the length of the abstract. However, the suggested length is from 150 to 225 words. 14. KEY WORDS: Key words are technically meaningful terms or short phrases that characterize a report and may be used as index entries for cataloging the report. Key words must be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location, may be used as key words but will be followed by an indication of technical context. The assignment of links, rules, and weights is optional. m TTncrl asfsifie Security Classification

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