Interpolated Z‐transform of the S‐parameter in the transient analysis of electrical networks

Abstract Earlier, the author proposed a method for transient analysis of the RLC passive electrical network. In that method, fundamental circuit elements constituting the electrical network such as lumped RLC elements, a branching point and a voltage source are represented in terms of the S‐parameter by introducing a fictitious transmission line. The S‐parameter which is a function of complex frequency s is then operated by the interpolated z‐transform, through which the network is expressed by the recursive equation in the time domain. However, this method has a drawback in that a fictitious transmission line which causes a time delay equivalent to one calculation time step must be introduced to interconnect the fundamental circuit components. This leads to errors in the calculated response waveforms, degrading the effectiveness of the proposed method. This paper reveals that by applying the matrix operation to the proposed analyzing method, the undesired time delay introduced by the fictitious transmission line can be eliminated completely. The method for determining the value of characteristic impedance of the fictitious transmission line which affects significantly the calculation accuracy is presented also. The relations between the various interpolated z‐transforms and difference equations, as well as the stability of each, are discussed.