Extracting the Dispersion of Periodic Lossless LC Circuits Using the White Noise

The spectral energy density (SED) method is used to obtain the phonon dispersion of solids in molecular dynamics tools, e.g., LAMMPS. We show how the electric analog of the SED method is used to find the dispersion of periodic lossless LC circuits. The application of this idea is three-fold: (1) demonstrating how SED proves useful, should the analytic methods of calculating dispersion of a circuit render difficult (due to nonlinearity or having many elements), (2) teaching the concepts like Brillouin Zone, dispersion (or band structure), zone folding, gap formation and avoided crossing to students of physics and electrical engineering by highlighting the similarities of phonon and periodic circuits, and (3) studying the thermal devices, e.g., heat rectifiers using commercial circuit simulators.