Geometric Modeling of Nonlinear RLC Circuits
IEEE Transactions on Circuits and Systems I: Regular Papers, 52 (2):
396--404 (February 2005)DOI: 10.1109/tcsi.2004.840481
Abstract
In this paper, the dynamics of nonlinear RLC circuits including independent and controlled voltage or current sources is described using the Brayton-Moser equations. The underlying geometric structure is highlighted and it is shown that the Brayton-Moser equations can be written as a dynamical system with respect to a noncanonical Dirac structure. The state variables are inductor currents and capacitor voltages. The formalism can be extended to include circuits with elements in excess, as well as general noncomplete circuits. Relations with the Hamiltonian formulation of nonlinear electrical circuits are clearly pointed out.