مرکز منطقه ای اطلاع رساني علوم و فناوري - Synthesis of lumped-distributed cascades with lossy transmission lines

Abstract :

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 $Z_{0}=frac{\\sum _{i=0}^{n} a_{i}(s,z_{0})e^{(2i-n)}T_{0}\\gamma (s)} {\\sum _{i=0}^{n} b_{i}(s, z_{0})e^{(2i-n)}T_{0}\\gamma (s)}$ where $a_{i}(s, z_{0}), b_{i}(s, z_{0})$ are two-variable, real polynomials in $s$ and $z_{0}$ , with $z_{0}$ the characteristic impedance, $\\gamma (s)$ 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, $RC$ -lines and acoustic filters. The results also apply to cascades with noncommensurate lines and to cascades of mixed transmission-line types.

Keywords :

Cascade circuits; General analysis and synthesis methods; Lossy circuits; Circuit analysis computing; Circuit synthesis; Computer networks; Distributed parameter circuits; Impedance; Integrated circuit interconnections; Large scale integration; Network synthesis; Propagation losses; Transmission lines;