Circuit Theory Based on New Concepts and Its Application to Quantum Theory

6. Transmission Circuit Theory Based on Eigen-Values of Cascade Matrix

Abstract

First, we demonstrate that the eigen-values and corresponding eigen-vectors of the cascade matrix of a lossless reciprocal circuit are the iterative parameters known in classical circuit theory. When these iterative parameters are used, conjugate impedance matching is demonstrated to be a valid matching method of circuit theory. In addition, the iterative impedances at the left and right of an asymmetric circuit are complex conjugates; hence, an impedance-matched network can be obtained by iteratively connecting the same circuits. In other words, the roles of the regularly spaced knots, which were proposed by O. Heaviside and are the bases of the lumped loading coils, are shown to be valid from the theory of iterative parameters. Networks with a periodic structure obtained by iteratively connecting the same circuits are effective for obtaining resonances and eigen-oscillations.