Synthesis of a resistively terminated cascade of uniform lossless transmission lines and lumped passive lossless two-ports

This paper presents a general solution to the problem of synthesizing a passive two-port consisting of a cascade of uniform lossless transmission lines, commensurable or incommensurable, and lumped passive lossless two-ports in an arbitrary sequence with a resistive termination at the receiving end. After a basic discussion is given on the foundation of the multivariable synthesis of networks composed of uniform lossless transmission lines and lumped passive elements, the necessary and sufficient condition is given on the scattering function for it to be realizable as a cascade network. Based on this result, some special cases of the problem are discussed. Further, the equivalence of the multivariable and frequency-domain approaches to the above-mentioned problem is established.