Equivalent transformation of nonuniform lossless lines and distributed RC networks

The equivalence properties of nonuniform transmission lines with different parameter distributions are analysed in detail. Both LC(lossless) and RC lines are treated. The formulation adopted may be considered as an appilication of the method of spatial-variable transformation to differential equations that govern the transfer-matrix parameters of these lines. The principal result is an equivalence theorem which establishes a general method of equivalent transformation for nonuniform transmission lines. Emphasis is placed on the derivation of the transformation function which plays a key role in the equivalent transformation. The generality of the proposed method of equivalent transformation lies in the fact that there is a large freedom of choice of the form of the transformation function which is pertinent to the problem in hand. Details of the procedure of equivalent transformation are described, and the quantities which are invariable under equivalent transformation are discussed. Furthermore, as an application of the equivalent transformation, the relationship between two particular classess of nonuniform LC lines is elucidated, namely, semiuniform lines having uniform series inductance, and reciprocal lines having a constant propagation factor. On the basis of this relationship, it is possible to design various inhomogeneous-layer components by the direct use of the available data on corresponding nonuniform-line components.