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

9. Symmetric Lossless Circuit Constituted with Image Connection of Asymmetric Circuits

Abstract

As described in Session 5, the vibration of a one-dimensional crystal can be explained using an LC ladder circuit. LC ladder circuits are asymmetric, lossless, and reciprocal. There are two methods of connecting two identical asymmetric circuits, image connection and iterative connection. The image connection of two identical asymmetric circuits forms a symmetric circuit. The functions of circuits depend on the connection method (which port of the circuit comes first). The passband of iterative circuits is wider than that of image-connected circuits, increasing the ranges and numbers of resonance and eigen-oscillation frequencies (energies). In circuits with image or iterative parameters, a stopband appears in the high-frequency (high-energy) region, suggesting the possibility that renormalization theory can be avoided by using circuit theory.