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Periodic steady state analysis using shooting and wave‐form‐newton
Author(s) -
Kevenaar Tom A. M.
Publication year - 1994
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490220107
Subject(s) - shooting method , mathematics , iterated function , boundary value problem , relaxation (psychology) , newton's method , initial value problem , mathematical analysis , steady state (chemistry) , differential equation , interval (graph theory) , iterative method , mathematical optimization , nonlinear system , physics , chemistry , quantum mechanics , psychology , social psychology , combinatorics
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.