An efficient algorithm for transmission line matrix analysis of electromagnetic problems using the symmetrical condensed node

A study of the symmetrical condensed TLM (transmission line matrix) node is presented. The study reveals not only that the characteristic scattering matrix satisfies the law of conservation of energy but also that electromagnetic fields are conserved even for finite node spacing. Using the results of this study, the authors develop an efficient algorithm for TLM analysis using the symmetrical condensed node. This algorithm significantly reduces the number of floating point operations so that the speed of computation is comparable to that of other expanded node analysis schemes. The case of a lossy medium is also discussed. With a better understanding of this symmetrical node and equipped with a fast algorithm, TLM analysis of three-dimensional electromagnetic problems can improve the computer-aided design of microwave and millimeter-wave circuits