Synthesis of lumped-distributed networks: Lossless cascades

This paper establishes single-variable realizability conditions and simple synthesis procedures for the driving-point impedance of lossless lumped-distributed cascades. The cascades considered consist of commensurate, uniform, lossless transmission lines interconnected by lossless lumped two-ports and terminated by either lumped passive or resistive loads. The reaizability conditions are stated and the analysis is carried out entirely in terms of a single variable, which allows the extension of the results to cascades with lossy lumped networks In addition, a detailed comparison between the realizability conditions in this paper and those in the literature using a two-variable formulation is given with the two sets shown equivalent. However, the computational effort required to check for realizability and to carry out the synthesis procedures is simpler and less obscure for the methods of this paper.