Cấu trúc sóng chức năng trong điện lý thuyết P6

In this chapter, a solution of EM radiation from a prolate spheroidal antenna, excited by a voltage across an infinitesimally narrow gap somewhere around the antenna center, is obtained. Three specific cases are considered: an uncoated antenna, a dielectric-coated antenna, and an antenna enclosed in a confocal radome. The method used is that of separating the scalar wave equation in prolate spheroidal coordinates and then representing the solution in terms of prolate spheroidal wave functions. A simplified version of the solution, after taking account of the fact that the antenna is symmetrical in the &direction, can then be used...
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Cấu trúc sóng chức năng trong điện lý thuyết P6 Spheroidal Wave Functions in Electromagnetic Theory Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong Copyright  2002 John Wiley & Sons, Inc. ISBNs: 0-471-03170-4 (Hardback); 0-471-22157-0 (Electronic) 6 Spheroidal Antennas6.1 INTRODUCTIONIn this chapter, a solution of EM radiation from a prolate spheroidal an-tenna, excited by a voltage across an infinitesimally narrow gap somewherearound the antenna center, is obtained. Three specific cases are considered:an uncoated antenna, a dielectric-coated antenna, and an antenna enclosedin a confocal radome. The method used is that of separating the scalar waveequation in prolate spheroidal coordinates and then representing the solutionin terms of prolate spheroidal wave functions. A simplified version of the so-lution, after taking account of the fact that the antenna is symmetrical in the&direction, can then be used to obtain the electric and magnetic fields. TheMathematics code written allows a user to model each of the three types ofantenna radiation problem discussed in this chapter. The type of antenna used in this chapter is a prolate spheroid excited bya slot cut through the spheroid. Axial symmetry prevails regardless of thelocation of the slot. In aircraft applications, the antenna used is generallymounted on the nose of the aircraft, and the type of antenna used is often aslot antenna. Therefore, it is possible to model this antenna configuration as aslot antenna mounted on a spheroid. The effects of a protecting coating layeror radome on such a configuration can also be investigated and considered inthe optimized operation. 145146 SPHEROIDAL ANTENNAS6.2 PROLATE SPHEROIDAL ANTENNA6.2.1 Antenna GeometryA perfectly conducting prolate spheroidal antenna excited by a specified fieldover an aperture on its surface and immersed in a homogeneous, isotropicmedium is a convenient introductory problem. It is also assumed that thesurrounding medium is nonconducting and nonmagnetic. To simplify thesituation, it is assumedthat symmetry about the axial direction prevails. The geometry of the prolate antenna is shown in Fig. 6.1. The semimajorand semiminor axes of the spheroid are designated a and b, respectively, andthe interfocal distance d, as indicated in previous chapters. In general, thesurface of the spheroid is < = 51, and the excitation gap can be locatedanywhere, say at 7 = ~0.6.2.2 Maxwell’s Equations for the Spheroidal AntennaFor the symmetrical situation (i.e., a/&$ = 0), Maxwell’s equations in freespace, relating E and H, take the form (6.la) 1 a(P%J (6.lb) hrE77 = -GT’ (6.1~) (6.ld) 1 a(Pw (6.le) hrH,, = -jClowpdSy achvH,) w-QH< -icowhth,E4, - > (6.lf) at drl =where p = dJ(1 - q2)(S2 - 1)/2, ht and h, have been defined in Chapter 2.Also, ~0 and ~0 are the permittivity and permeability of free space, respec-t ively. From Eqs. (6.la) to (6.lf) it is observed that the problem may be split intotwo parts. If the applied field on the aperture has only an Eq component, theexcited magnetic field has only the H$ component and E+ = 0. On the otherhand, if the applied field has only an E4 component, the excited electric fieldhas only an E+ component and H& = 0. PROLATE SPHEROlDAL ANTENNA 147 iv=+1 I : b I : I i T -- 1Fig. 6.1 Prolate spheroid model of an antenna.148 SPHEROIDAL ANTENNAS Here we consider only the former case; that is, the applied field has only anI$, component and is considered in the subsequent analysis. Then, followingSchelkunoff [35], we set A ...