Title :
Minimization of the error in the calculation of the steady state by shooting methods
Author :
Welsch, G. ; Brachtendorf, H.G. ; Sabelhaus, C. ; Laur, R.
Author_Institution :
Inst. of Electromagn. Theory & Microelectron., Bremen Univ., Germany
fDate :
10/1/2001 12:00:00 AM
Abstract :
The periodic steady state of a circuit can be calculated with a variety of algorithms. One of them is the (multiple-) shooting method. For good performance, the shooting analysis uses a higher order multistep backward-integration method for the computation. Normally, in the very first step, the Gear 1 integration formula is used because no information of previous discretization points are available. The next step can be calculated with the second-order formula. After the calculation of (k-1) successive time-steps, it is possible to switch to the desired (kth-order) integration formula. The switching introduces an error to the solution of the steady state, which can be observed by a subsequent Fourier transformation. This paper presents a straightforward method to suppress the problem by generating additional starting values. The novel formulation is compared with the conventional shooting method on two example circuits
Keywords :
Fourier transforms; harmonic analysis; network analysis; Fourier transformation; Gear 1 integration formula; discretization points; higher order multistep backward-integration method; periodic steady state; shooting methods; starting values; steady state calculation; successive time-steps; Buck converters; Circuit simulation; Inductors; Minimization methods; Power electronics; SPICE; Steady-state; Switching circuits; Time domain analysis; Voltage;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on