Calculation of steady-state oscillations in non-linear circuits

Abstract

An analytical approach for calculations of stationary (steady-state) oscillations in non-linear circuits is considered. The circuit block-diagram is simplified so that the variable at the input of the element with non-linear characteristic is considered. The obtained higher-order non-linear differential equation is expanded using a combination of the harmonic balance method and perturbation techniques into a system of differential equations. Then the forced solutions of all equations in the system are calculated and the solution of the initial equation is obtained as the sum of these forced solutions. Consideration is concentrated on techniques that permit fast and efficient solution of the first three equations of the system. The approach is especially suitable for circuits where steady-state oscillations have a dominant first harmonic.