Analysis of Linear Networks

A method of analysing linear networks is developed, that is applicable to networks whose elements may have any number of terminals. Each multi-terminal element is handled as a complete entity, without having to represent it as an equivalent network of branches. The theory is based on an unconventional treatment of voltage, which seems to be suitable for the general case, in that voltages are handled without having to specify the terminal to which they are referred. A considerable part of the analysis can proceed without defining the voltage reference. The point in the analysis where reference has to be specified is studied, and what the required reference conditions are, and as a result it appears that the conventional method of fixing one terminal for voltage and current references is just one very special case out of a multitude of possibilities. N In the course of the analysis, admittance and impedance emerge as two concepts which are not exactly equivalent or dual to each other. It is shown that the admittance-impedance duality is a characteristic of 2-terminal and 3-terminal elements only, and breaks down in the general case. Admittance is a twoindexed magnitude, referring to 2 terminals, whereas impedance is four-indexed, referring to 2 terminal-pairs. The analysis of a given network can proceed on an admittance basis without a specified voltage reference, but impedance can be defined only after reference conditions have been imposed, and it depends on the reference conditions. The theory presented in this thesis is built up to the point where, given the characteristics of the nultiterminal elements composing a network, the network equations can be set up and then solved to give any required network characteristic. Thesis Supervisor: Ernst A. Guillemin Professor of Electrical Engineering U ~ -. =----______________