Analysis of Four-Terminal Cascade Networks

This paper presents a new approach to the analysis of cascaded networks. A second-degree difference equation for the current along the cascade is obtained for the general cascaded structure. In general, difference equation techniques lead to solutions in the form of infinite series having unknown properties. This difficulty is overcome by attacking the problem in reverse. Starting with functions of known properties as solutions, groups of networks that satisfy these functions are found. This method leads to solutions to many groups of networks in terms of well known functions and polynomials including Chebyshev polynomials. Several illustrative examples are included.