Cascade synthesis of distributed networks by lumped ladder RC equivalents

This paper suggests a new presentation for the transmission-line networks. In the same way as Richards' presentation, in which the frequency transformation t = tanh sT was used to convert a class of transmission-line networks into lumped networks consisting of L, C, and unit elements, the frequency transformation q = sinh' sT is now used for converting the cascade transmissionline networks into a lumped ladder network consisting of R, C, and possibly an ideal transformer at one end. The new equivalent network maintains a one-to-one relationship with the components of the transmission-line network without doubling the number of components. It has the advantage that the final network presentation is a lumped two-element-kind network. Classical network theories can therefore be applied directly. For purpose of illustration, the cascade unit-element network and cascade unit-loop network are considered in detail. It is shown that the cascade unit-element network can be presented by a ladder RC network, and the cascade unit-loop network by a mid-series low-pass RC network. The continued-fraction expansion technique and the zero-shifting technique can therefore be used, respectively, for the synthesis of the two networks.