Characterization and modeling of multiple coupled lines in an inhomogeneous medium from time-domain reflection measurements

A synthesis technique of an equivalent lossless (nondispersive) uniform multiconductor n-coupled lines (UMCLs) 2n-port system from the measured discrete time-domain reflection response is presented. This procedure is based on the decomposition of characteristic immittance matrix of UMCL in terms of partial mode immittance matrices. The decomposition scheme leads to the discrete transition matrix function of a UMCL an-port system. This, in turn, establishes a relationship between the normal-mode parameters of the UMCL and the measured impulse reflection and transmission response. Equivalence between the synthesis procedure presented in this paper and the solution of a special form of algebraic Riccati matrix equation whose solution can lead to the normal-mode parameters and including real termination network is illustrated. In order to exemplify the procedure, a typical microstrip structure with three lines is synthesized from the time-domain reflection (TDR) data.