Determining the steady state output of nonlinear periodic circuits

When determining the steady-state output of lightly damped nonlinear systems with a stable periodic response, simply integrating the system equations until the response is periodic can be computationally expensive. Previous proposed time-domain solutions for finding the steady-state output directly include an extrapolation method, a gradient method, and a Newton method. Many variations on the Newton method have been proposed which sacrifice quadratic convergence to achieve a larger region of convergence. We propose and discuss a modification to the Newton method which exhibits better convergence properties than that of the Newton method but is faster than previously proposed modified Newton methods. This modified method exhibits significantly better convergence properties, however, only when applied to nonautonomous circuits. Multiple shooting is then introduced and applied to the problem of determining the steady-state output of both nonautonomous and autonomous circuits. The results show significant improvement in convergence over that of the single shooting method without sacrificing speed, as is the case with most modified Newton methods. Finally, the convergence and speed properties of these methods are discussed and conclusions are made regarding when to use particular methods