Application of Mathieu functions to the analysis of radiators conformal to elliptic cylindrical surfaces

摘要

In this paper the problem of the derivation of a proper set of eigenfunctions to be used in the analysis of radiators conformal to elliptic cylindrical surfaces is addressed. In particular the case of a circumferential slot cut on a conducting elliptic cylinder is considered. It will be shown that the field distribution on the slot obeys to a Mathieu equation and that it can be expressed in terms of Mathieu functions of integer, read and complex order. In what follows, a short account of the theory of the Mathieu equation and of the Mathieu functions will be given and an algorithm for their computation will be described. The electric characteristics of slots, such as radiation fields and resonant frequencies, will be analysed as functions of the eccentricity of the elliptic cylinders. [References: 21]