Periodic steady state analysis using shooting and wave-form-newton

This paper describes a method of determining the forced periodic steady state response of non-linear circuits. the method is closely related to the work of Aprille and Trick Proc. IEEE, 60, 108-114 (1972) and also to the finite difference method for solving a boundary value problem. The new approach is a shooting method in the sense that in every iteration an initial value problem is solved. It is, however, also a relaxation method, because in every iteration a periodic wave-form is obtained. This is achieved by solving in each step a linear time-dependent differential equation whose solution can be easily transformed into a periodic solution satisfying this linear equation. Because the iteration takes place on wave-forms rather than initial values and every solution satisfies the boundary conditions, the method is robust. It will be shown that for a causal approximation of the time derivatives the iterated wave-forms are equal to those found using the finite difference methods.