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. | 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 Spheroidal Antennas INTRODUCTION 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 to obtain the electric and magnetic fields. The Mathematica code written allows a user to model each of the three types of antenna radiation problem discussed in this chapter. The type of antenna used in this chapter is a prolate spheroid excited by a slot cut through the spheroid. Axial symmetry prevails regardless of the location of the slot. In aircraft applications the antenna used is generally mounted on the nose of the aircraft and the type of antenna used is often a slot antenna. Therefore it is possible to model this antenna configuration as a slot antenna mounted on a spheroid. The effects of a protecting coating layer or radome on such a configuration can also be investigated and considered in the optimized operation. 145 146 SPHEROIDAL ANTENNAS PROLATE SPHEROIDAL ANTENNA Antenna Geometry A perfectly conducting prolate spheroidal antenna excited by a specified field over an aperture on its surface and immersed in a homogeneous isotropic medium is a convenient introductory problem. It is also assumed that the surrounding medium is nonconducting and nonmagnetic. To simplify the situation it is assumed that .
