Properties and synthesis of distributed‐parameter circuits composed of resistors and unit elements

Abstract

AbstractThe circuit composed of alternatively cascaded resistors and unit elements is the most fundamental among distributed‐parameter circuits containing resistors. The necessary and sufficient conditions for realization of the driving point immittance in which element parameters satisfy given relations have been reported. As for R (resistor)‐terminated circuits composed of alternatively cascaded n resistors Rj's and characteristic impedances Zj's, there are three types of circuit configurations: 1) R1 > Z1, Rν+1 > Zν + Zν+1, R > Zn, 2) R1 = Z1, R̄ν+1 = Zν + Zν+1, R = Zn; 3) R1 < Z1, Rν+1 < Zν + Zν+1, R < Zn (ν = 1, 2, …, n‐1). For 1) the realization condition was reported. For 2) and 3), the circuit properties and synthesis methods have not yet been investigated. In this paper the driving point immittance for 2) is derived in case that the element parameters satisfy given relations. This immittance function is that for the RL or RC circuit which is degenerated with respect to Richard's variable p. A new synthesis method which differs from 1) is proposed.