Comments on "Two-Port Four-Terminal Matrix Parameter Functions of Solvable Distributed Parameter Z-Y-KZ Networks

Abstract

In the above correspondence,’ the matrix parameters of a fourterminal nonuniform transmission line have been derived by voltage and current gradient considerations. This approach has been suggested [l] as being more convenient than the previous integration method which, while practicable for uniform [2] and exponentionally tapered lines [3], [4], leads to superfluous subsidiary variables for the general nonuniformity [ 51. However, in the exposition of this procedure, Ahmed appears to have overlooked the fact that his equation (9) for the linear secondorder voltage differential equation (L,DE) may be derived directly from (l)-(3). Furthermore, the fictitious current i = i(x) introduced in (6a) has no obvious physical meaning in terms of the transmission line model in Fig. 1. A more direct method is to introduce a voltage variable v such that the voltage gradient along the upper line is given by du/dx = -Z(x)i1. Integration followed by substitution of the appropriate boundary conditions (e.g., u = V, - V1 between x = d and x = 4) to this and to the voltage solution (10) leads to a set of equations for the terminal variables of the network. Together with the corresponding current equations at the boundaries, these allow determination of the admittance parameters in terms of the solution determinant. By considering ports rather than terminals, the impedance parameters may also be derived [5], [6]. Unfortunately, Ahmed has also departed from the conventional notation [ 2]-[ 81. The renaming of characteristic functions as matrix parameter functions is justifiable in view of other connotations [9] of the former in electrical network theory, but their promulgation is of doubtful value. They have been adopted by only a single textbook [lo], and while allowing network representation in terms of only six functions, these must occur in ratios. They do not afford any significant advantage in network characterization or analysis and it is more troublesome to remember their relations with the standard matrix parameters ([z], [y] , [a], [h] , etc.) than to apply the widely available parameter conversion tables. Furthermore, comparison of the directly derived admittance and impedance parameters, in particular, permits ready study of duality conditions [2] -[ 81