T-MATRIX VERSUS ABCD-MATRIX IN-CIRCUIT ANALYSIS

Analogue lossless ladder networks have long been used in communication engineering because of their low element-value sensitivity and reduce d network complexity. In low-frequency applications, in order to avoid the use of bulky and often lossy inductors, active RC devices are the preferable form of realization. However, component tolerances and par ameter sensitivities associated with an active device usually border o n or exceed the practical limits of realizability at high frequencies. As a result, one has to resort to the passive LC design. Moreover, ac tive filters with the best performance are usually those which are bas ed on direct simulation of the resistively terminated LC ladder networ ks.(1,2) For these reasons, the study of LC ladder circuits should sti ll deserve some attention. An analogue ladder circuit which may be rep resented as a general two-port network composed of a cascade of two-po rt subnetworks, has traditionally been analysed by the ABCD-matrix (or transmission matrix) approach.(3-6) The T-matrix (or wave-chain matri x) approach,(4,5) while popular with some people, has tended to be avo ided by others because the use of voltage-wave parameters can be mathe matically more unwieldy. In this paper, both approaches to the derivat ion of recursive algorithms for computing the transfer-function coeffi cients of an analogue ladder circuit are described and compared.