Analysis of nonlinear coupled circuits

The method of high-order phase planes1 or phase space is applied to the solution of nonlinear coupled circuits. Two simple examples are given to illustrate the application of this method. In the first example, a nonlinear resistance is introduced in the primary circuit. In the second example, a nonlinear inductance is used. It is possible to extend the application of the method to circuits with nonlinear capacitance and nonlinear mutual inductance. The method is applicable to any number of coupled circuits with nonlinear elements in any of the meshes or in the coupling between the meshes.