The forward transmission matrix (FTM) method for S-parameter analysis of microwave circuits and their metamaterial counterparts

In classical Electromagnetics textbooks, microwave circuits such as circulators, couplers, and filters are solved by non-systematic approaches such as even-odd mode analysis. Hence an electrical engineering student coming from the conventional circuit theory background encounters difficulties in understanding and solving microwave circuits. In this paper, we propose a modified node voltage analysis method in which the circuit branches are represented by their forward transmission matrices so that the electromagnetic wave propagation is taken care of. The Kirchhoff's current rule, tailored for high frequencies, is applied to formulate the simultaneous node voltage equations which are subsequently solved by matrix inversion. The proposed forward transmission matrix (FTM) method is applied to evaluate the S-parameters of some well-known microwave devices including the recently-developed metamaterial-based circuits. The FTM node analysis is a natural extension of the classical node analysis which is taught in the early stages of an Electrical Engineering program. Hence we anticipate that the proposed method will ease up the conceptual transition of electrical engineering students and academicians from the low-frequency alternating current circuits to high frequency RF and microwave circuits.