Extracting the Dispersion of Periodic Lossless LC Circuits Using White Noise

TL;DR

This paper demonstrates how the spectral energy density method can be adapted using commercial circuit simulators to analyze the dispersion relations of periodic lossless LC circuits, providing educational insights and potential applications in thermal device simulation.

Contribution

It introduces a novel approach to analyze circuit dispersion using SED with circuit simulators, bridging phonon concepts and electrical engineering education.

Findings

SED method effectively reveals dispersion in LC circuits

Analogies between phonons and circuits enhance teaching methods

Circuit simulators can simulate thermal device behaviors

Abstract

The spectral energy density (SED) method is used to obtain the phonon dispersion of materials in molecular dynamics codes, e.g., LAMMPS. We show how the electric analog of the SED method can be done using commercial circuit simulators to find the dispersion of periodic lossless LC circuits. The purpose of this article is (a) to demonstrate how SED proves useful, should the analytic methods of calculating dispersion of a circuit render difficult e.g., due to nonlinearity or having large number of elements in each unit-cell, and (b) to show how the concepts like Brillouin zone (BZ), dispersion (or band structure), zone folding, gap formation, and avoided crossing can be taught to students of electrical engineering by highlighting the analogies between phonons and periodic circuits. This analogy also suggests that thermal devices, e.g., heat rectifiers can be simulated and understood using commercial circuit simulators.