Multimode network approach for the solution of two-dimensional waveguide discontinuities

This paper presents the multimode network formulation for the solution of arbitrarily shaped 2-D metallic discontinuities which reside in a rectangular waveguide. Traditional integral equation solutions to waveguide problems involve the use of a Green's function which is frequency dependent. Therefore, the whole analysis must be repeated for each frequency of interest. However, the method presented below, reformulates the Green's function in such a manner that the solution of the problem can be found via the scattering from an N-port network. The elements of the admittance matrix which describes the N-port are determined from a related integral equation, and they are formed by frequency independent TE and TM parts. These frequency independent TE and TM interactions are first determined and represent the bulk of the numerical effort. The impedance matrix of the integral equation is then constructed from the frequency independent parts (i.e. jωTE + TM/jω). Once these frequency independent TE and TM interactions have been found and stored, solutions at any frequency can be determined by solving multiple matrix equations (the matrix elements themselves are constructed from the frequency independent TE and TM parts and thus the fill time is very short). A comparison between measurement and theory for two x-band discontinuities is given.