Variational integrators for electric circuits
作者： Sina Ober-Blöbaum , Molei Tao , Mulin Cheng , Houman Owhadi , Jerrold E. Marsden
DOI: 10.1016/J.JCP.2013.02.006
关键词: Resistor 、 Topology 、 Degeneracy (mathematics) 、 Mathematics 、 Control theory 、 Variational integrator 、 Equations of motion 、 Voltage 、 Electric potential 、 Electronic circuit 、 Discretization
摘要: In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering dynamics an circuit, one is faced with three special situations: 1. The system involves external (control) forcing through (controlled) voltage sources resistors. 2. constrained via Kirchhoff current (KCL) laws (KVL). 3. Lagrangian degenerate. Based on geometric setting, appropriate formulation presented to model circuit from which equations motion are derived. A time-discrete provides iteration scheme circuit. Dependent discretization, intrinsic degeneracy can be canceled discrete scheme. way, constructed that gains several advantages compared standard integration tools circuits; in particular, comparison BDF methods (which usually method choice circuits) shows even simple LCR circuits, better energy behavior frequency spectrum preservation observed using developed integrator.
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