Cascade transmission-line networks with lossy junctions

This paper treats the synthesis problem of cascade transmission-line (TL) networks. The TL's in the network are assumed to be lossless and commensurate, but the TL junctions are allowed to be lossy. A new concept of image network was introduced, and the scattering parameters of the network were represented in terms of four sets of pseudoorthogonal polynomials. Through this concept, two alternative optimum synthesis procedures were developed that result in a TL network with a minimum number of resistors required in its realization. The synthesis procedure itself also constitutes the set of necessary and sufficient conditions for the realizability of the class of TL networks.