Cross-Polarization Components in Inter-Antenna Coupling Calculations

This paper examines the coand cross-polar char­ acteristics of antennas on the surface of a cylinder when the transmitting antenna and the observer are arbitrarily positioned. The theory is based on the analytical approach used by Pathak and Wang for the fields of a source radiating on a convex surface. It takes care of torsion. There is a different cross-polarization effect when both the transmitting and the receiving antennas are in the equatorial planes. The cross-polarized components E and E z f p p f z are not zeros even in the equatorial planes. The cross-polarized ratios have been computed and their variations with different parameters are presented. Introduction In EMC problems of antennas on complex structures, existing inter-antenna coupling programs such as IEMCAP [1] and AAPG [2] do not calculate the cross­ polarized components. In intra-system problems in­ volving high power levels for emitters and highly sensitive receivers, these components become important to consider. It has been found that not only is the actual coupling path of importance, but also its conse­ quence in the generation of cross-polarized field components along its trajectory. A close examination of the analytical approach of Pathak and Wang [3] is made for the case of antennas on cylindrical structures. Although this theory can predict the coand crosspolar components, some inconsistencies in the results are noted which deserve closer examination. Theory The surface electric and magnetic fields dfl̂ and dE due to a magnetic dipole moment dpm on a convex surface whose one radius of curvature is large compared to the other are given by [3], dHm (Q/Q') = ^ d p m (Q'){2Y0 (b'b[(l 4 ) V.CQ +D2 ( i ) 2(As U K ) + Ac V(?) + ^ T 02 (UK) VK))] + t’t[D2 + jL U K ) 2 (i-)2 (ASU K ) + Ac VK))] + (t'b + b't)[^-T0 (UK) VK))]} • D Gg(kt) and (1) dEJQ/Q’) = ^ d p m (Q'){2(b'n[(ljL) V(C) + v & ' ^ c? ))] + [T0 i t " V (C )D } • D G0 (kt) (2) Similarity, the surface fields dHg and dEe on an arbitrary convex surface are given by dEe (Q/Q!) = ^ d p e (Q,){2Z0n ,n [ V © jL V(?) + 4 ) 2 (As V K ) + AC -UK)) + T02 i (UK) VK)]}D Gg (kt) and (3) dHe (Q/Q’) = tie(.Q'){2(n'b[(l i ) V K ) + Tq2 4 (UK) VK))] + n't [T0 £ (UK) VK))]} • D GQ(kt) (4) where Yg is the intrinsic impedance of the medium in which the structure is immersed; t = /az (cf>2-(l>2.)2+ (z2_zl)2 ’ the torsion factor T„ = Cot 6, where 6 is the angle of entry with the 1/3 cylinder axis; m = (k pg/2) ; £ = mt/pg ; Pg = a/Sin2 5; Ac is a blending function equal to unity for a cylinder. Expression for the Case of a Cylinder For the case of the cylinder with arbitrary posi­ tions of transmitting and receiving antennas, let (a,' ,z') and (a,,z) be the coordinates of transmit­ ting and receiving points. Then t and £ are given by t =v42 (<)>2 "j ) 2 + Cz 2 "z l } 2 ? =>/a2 (2 _1 ) 2 + (z 2 "zl ^ 2 * the angle of entry 6 with cylinder axis is given by tan 6 = a(d>2_1)/(z2_zi^ and the torsion factor Tg = Cot o . With a little algebra, the different coand cross-polarized components as obtained from (1)-(4) are given by Hzi' " ’ [(1‘ VtE) * * V i m o v ( o ) i s E t i i s i Kt / t V ' < l v® * 2 CH2294-7/86/000-0184 $01.00©1986 IEEE 184 SESSION 3B Si V z dPm * 0 W Ez'p = # dPm w id v® + V k w n exp(-jkt) St and E , . = TOdPm ( U © V K ) j S 2 t M P P 4irt S i Due to Electric Dipole Moment V = # dpe {v® i t ' + 4 ^ 2 u® + T02 i i C U(0 V(?)> g g L i M /t Hp'z = # dPe {(1 ♦ T0 4 {U(0 V(C))} exp(-jkt) Si and HP> = T~0 i t dPe {u^ VCC)} ^ 2 ^ 1 By reciprocity, u , = u , , u ., = u , , and so on. ' * ' ’ pp' p’p ’ p' p ’ Discussions and Conclusions The coand cross-polar electric and magnetic components have been computed for several cases of transmitting and receiving antennas on a cylindrical structure with different parameters. The computations were repeated for transmitting and receiving positions in different z-constant planes and in the same plane. Some of the results showing the decay of coand crosspolarized components are presented in Figs. 2 and 3. The transmitting dipole moment is equal to unity and the receiving antenna is a point source in the compu­ tations. It is found that the cross-polar components Ep' *■311(1 Ep''z 3̂11(1 V are m°re weak than the co-polar components H . (and H . ) and H. ,, (and Z Z Z ( Dy H^,^) while Hz,p is not. In the equatorial plane case, the cross-polar components H^,z, E^)p and do not get excited but E , and H , are not predicted z'p p z r to assume zero values. This aspect requires further investigations. Tables 1(a) to (c) give the relative values of shading loss of coand cross-polar compon­ ents for the same path length for equatorial and arbitrary positions. It is found that the coand cross-polar components differ in intensity consider­ ably for the same path length in equatorial and non-equatorial cases particularly for smaller radii of curvature of the cylinder. This is because even though the path length is the same for the non-equatorial case the effective radius of curvature depends on the angle of entry. Also, the above analytical model is accurate for large values of radius of curvature of the surface. 1RS References [1] J.L. Bogdanor, R.A. Pearlman, and M.D. Siegel, Intrasystem Electromagnetic Compatibility Analy­ sis Program. Vol. I, User’s Manual, Usage Section, AD A-008-527, December 1974; User's Manual, Engineering Section, AD A009-52b, December 1974, NTIS, U.S. Dept, of Commerce, Springfield, VA. [2] Hans Peter Widmer, A Technical Description of the AAPG Program. Report ECAC-CR-83-048, November [3] P.H. Pathak and Nang Wang, "Ray Analysis of Mutual Coupling between Antennas on a Convex Surface", IEEE Trans. Vol. AP-29, No. 6, September 1981, pp. 911-922.