Analysis of cascade of four-terminal networks

"The object of this thesis is to find analytic expressions for the voltage and current variations along a structure composed of a cascade of identical dissymmetrical four-terminal networks driven harmonically at the sending end and working into an impedance at the receiving end and an impedance that can be placed at any of the junctions along the cascade. The method of analysis that is applied is analogous to that used in solving the long-line problem. A transmission system usually consists of the line or cable itself plus numerous other links whose purpose it is to correct defects in the line performance or to supply selective or other characteristics to the system that may be required by the class of service that is expected of the structure as a whole. Each of these single links can be considered to be a four-terminal network. Then the complete line is composed of a number of these four-terminal networks connected in cascade. The transmission lines or cables are known as distributed-constant networks while the remaining portions of the line are known as lumped-constant networks. Since the performance of the distributed-constant four-terminal networks can be reduced to the same basis as that of the lumped-constant networks, the system as a whole becomes homogeneous and a consistent method of analysis for the determination of the overall performance can be developed. A solution for the voltages and currents along the line has been obtained for a communication line of this type loaded with an impedance at the end of the line, but so far no solution has been published for the case considered in this paper. Since it is sometimes of advantage to place an additional load at different junctions along a communication line, it seems appropriate to determine the equations for the voltages and currents at the various junctions along the line so that these can be calculated if desired. It is the purpose of this paper to develop these equations"--Introduction, page 1-2.