Equivalent Distributed ParameterZ-Y-G∞Networks

Abstract

The principle of electrical equivalence for distributed parameter (d.p.) networks is generalized and proved using the concept of ‘matrix parameter functions (m.p.f.)’ in terms of which all the voltage-current matrix parameters of any two-port three-terminal d.p. network may suitably be expressed. Exact mathematical expression for the equivalent length corresponding to each of the three different patterns of variation of per unit length (p.u.l.) parameters associated with any class of d.p. networks is presented. All specific member of d.p. networks, obtainable from the three patterns of variation of the p.u.l. parameters of a class of d.p. structures, may be shown to be electrically equivalent to one another, if their physical lengths are so chosen as to conform to the conditions of electrical equivalence. The equivalence principle may find applications in many other fields, such as acoustics, microwaves, design of mechanical delay lines and filters, etc., in which various devices are adequately represente...