The Transmission Line Theory to Solve Electromagnetic Coupling within Cavities. Part II - Coupling to TE (or TM) modes

This second part of the article, dedicated to the extension of line theory applied to electromagnetic cavities, addresses the issue of coupling energy to TE (or TM) modes.

Unlike the transverse electromagnetic modes (TEM) studied in the first section [D 1 327] , TE or TM modes generated in cavities formed by waveguides short-circuited at both ends can only be described by phenomena involving wave propagation in the transverse direction of the guide. Despite this theoretical difficulty, and subject to simplifying assumptions, it is still possible to assimilate a TE or TM mode to a virtual transmission line. This is demonstrated in a paper published in 2001 by Tadeusz Konefal et al. from which this second part, subdivided into two paragraphs, will draw in part .

The first section deals exclusively with the coupling of an electrical monopole located on one of the metal walls of a waveguide of rectangular cross-section and infinite longitudinal dimension.

Since coupling analysis cannot ignore the properties of TE (or TM) mode propagation, the first step in our reflection will be to solve the wave equation leading to the formulation of cutoff frequencies, propagation constants, modal impedances and transverse field distribution. We'll see that the choice of a guide with a rectangular cross-section provides access to analytical solutions expressed in the very simple form of circular functions. We will restrict ourselves to solutions relating to transverse electric modes only, designated under the symbol TE _mn where the positive integers m and n specify, depending on the vocabulary adopted, the order or rank of the mode. The restriction to TE modes alone is explained by the physical nature of the coupling exerted by the electric monopole. Knowing that TM _mn modes represent the dual form of TE _mn , the extension to this class of phenomena of the properties examined subsequently should not pose any theoretical...