A Neural Network-Based Harmonic Balance Technique for Analysis of Periodic Responses of Nonlinear Circuits

A neural network-based harmonic balance technique for the analysis of periodic responses of nonlinear circuits has been developed, which takes advantage of a special back propagation neural network to train the steady-state solutions to satisfy the governing equations of nonlinear circuits. The neural network consists of three layers, where the inputs are the discrete time points in one complete period, and the hidden layer is composed of trigonometric functions that represent different frequency components of the harmonics or the mixing products, and the output layer is made up of neurons representing the steady-state solutions of the circuit. The proposed method can avoid the time- and frequency-domain transformation during the iterations and converge from random generated starting values. Both single-tone and multi-tone excitations can be solved directly by using this method. Numerical simulations are preformed, and the accuracy is good according to the comparison of the simulated results with the commercial simulation software.