ON THE SYNTHESIS OF RESISTOR N-PORTS
POLYTECHNIC INST OF BROOKLYN NY MICROWAVE RESEARCH INST
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The problem of determining the necessary and sufficient conditions for a symmetric matrix to be the short-circuit admittance matrix of a transformerless resistor n-port is a classic problem in network theory. The problem is formulated topologically, and it is shown that it can be related to the well known solution for the realization of a nodal admittance matrix. In fact, the short-circuit admittance matrix and the nodal admittance matrix are shown to be related by a congruence transformation which is uniquely defined by the topology of the ports. In the special case of an n1 terminal realization, this transformation becomes the Kron transformation. The problem of realizing a given symmetric matrix is, therefore, reduced to the determination of the configuration of port voltages. It is shown that the n1 terminal case is identical to the problem of realizing a given matrix as a fundamental cut-set matrix, i.e., finding a graph which has a fundamental cut-set matrix such that it is equal to the given matrix. The n1 terminal case is studied in detail, and a simple procedure for determining the topology of the port voltages from a given matrix which contains no zero elements is derived. This synthesis procedure has th advantage of being direct, and it proceeds almost by inspection. A number of examples are given which illustrate the relative simplicity of this technique, and the synthesis of three ports is considered in detail.
- Electricity and Magnetism