Finite difference method for steady state analysis of nonlinear circuit with distributed elements

In this paper the technique of finite difference is applied to solve for periodic steady state waveforms of the nonlinear circuit containing linear distributed elements driven by one tone periodic input signal. First, the linear distributed elements are transformed into an asymptotically equivalent system with respect to the input signal. The system equation of the transformed circuit is formulated. The differential operator is then approximated by finite difference and the convolution operator is evaluated by piecewise linear approximation. Finally, the system of nonlinear algebraic equations is obtained. Newton method with an iterative solver called GMRES is used to solve for the periodic waveform from these nonlinear equations. A numerical example is illustrated.