Computationally Efficient Method of Calculations Involving Lumped-Parameter Transmission-Line Models

Computations involving ladder networks may be tedious if many elements are present. Lumped-circuit iterative models are traditional approximations of transmission lines and have been used well before [1]. The number of sections used to approximate the transmission line is limited by the computational expense involved in analyzing a high-order circuit. This paper develops a closed-form expression for the voltage transfer ratio for ladder networks as a function of the number of sections. Presently, lumped-circuit models [1]-[5] are analyzed using loop-current or node-voltage equations, both time-consuming and costly. The closed-form expression developed in this paper allows one to perform rapid circuit calculations for two-conductor lines, even if the number of sections is large (e.g., 50 sections or more) with very little computational effort.