On the convergence of MoM and mode matching solutions for infinite array and waveguide problems

It is shown that the method of moment (MoM) fails to analyze an infinite array of strip discontinuities if the number of basis functions and the number of expansion modes are set equal, however large they individually may be. Using spectral analysis and linear vector space theory it is found that for a given number of basis functions,there exists a minimum number of expansion modes required for a reasonable accuracy. Subsequently, for a given number of expansion modes, there is an upper limit for the number of basis functions. The mode matching (MM) analysis is viewed as a special case of the MoM analysis and the accuracy of the analysis is discussed wit h respect to the number of modes in the waveguides.