Synthesis of compatible impedances using semi-uniformly lossy two-port coupling networks

The authors present a theory for the synthesis of compatible impedances using coupling networks with resistive losses. This is achieved by introducing an impedance transformation that transforms a semiuniformly lossy network into a lossless counterpart, together with a complex normalized scattering matrix for describing a semiuniformly lossy two-port, terminated in two compatible non-Foster PRD_z impedances, one of which is 1 Ω. The resulting scattering matrix has paraunitary characteristics. A constructive synthesis procedure for the design of a semiuniformly lossy two-port is used to establish sufficiency with examples to illustrate the usage of the new generalized compatibility theorem