Iterative technique for computing soliton solutions to periodic nonlinear electrical networks

Abstract

Solitary waves (solitons) are fundamental modes supported by nonlinear guiding structures and propagate without any distortion due to dispersion. They can be used in the synthesis of waveforms with desired spectral or time-domain characteristics. However, the nonlinearity inherent to solitons complicates their analysis on general guiding structures. This paper proposes an iterative algorithm that can compute soliton solutions supported by general periodic electrical networks loaded by nonlinear capacitors. The proposed technique accounts for the exact dispersion of the structure and allows the capacitance to take on an arbitrary function of voltage. The algorithm computes the solution throughout the entire structure while only modeling a single unit cell, thus reducing the computational cost significantly. It is implemented within an in-house solver and verified against a commercially available circuit simulator. Different circuits which include lumped inductors, ideal transmission lines, and co-planar waveguides are simulated and shown to agree with commercial harmonic balance solvers. The presented technique will allow microwave and optical engineers to design and optimize a wide variety of nonlinear guiding structures efficiently.