Modelling of 2-D Real Rational Reactance Functions. A Parameter-Based Approach

Abstract

Summary Lossless (reactive) one-ports are of great importance in the field of linear network theory. This statement also applies for the two-dimensional (2-D) case, where the design of corresponding impedance or admittance functions is a much more challenging task. In this paper a model for 2-D real rational reactance functions is introduced which is a rational function in p 1 and p 2 where the coefficients are functions of parameters. The following features make it best suited for the computer based design of lossless one-ports, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D real rational reactance functions, and the coefficients are polynomials in the parameters. The synthesis of 2-D lossless networks and skew symmetric matrices form the basis of our considerations.