Synthesis of lumped-distributed cascades with lossy transmission lines

In the analysis of large systems such as high-speed digital computing networks and circuits on an LSI or VLSI silicon chip, lossy lumped-distributed networks have been used to model their interconnections. A solution of the synthesis problem for these networks will aid in the design of these circuits. This paper establishes single-variable realizability conditions and synthesis procedures for the class of lossy lumped-distributed cascade networks which contain lossy transmission lines and are desctribed by a driving point impedance expession of the form where are two-variable, real polynomials in and , with the characteristic impedance, the progagation constant, and To the total "electrical length" characterizing each of the lossy lines. The cascade networks consist of commensurate, uniform and/or tapered, lossy (except distortionless [3], [4]) transmission lines interconnected by passive, lumped (lossless and/or lossy) two-ports and terminated in a passive load. This class includes general lines, leakage-free lines, -lines and acoustic filters. The results also apply to cascades with noncommensurate lines and to cascades of mixed transmission-line types.