A method for deriving the state space equations for degenerate linear time invariant circuits

Abstract

A procedure for writing the state space equations for linear time invariant circuits is proposed. With this method the state equations for both degenerate and nondegenerate circuits can be derived in a systematic and unified manner. Capacitors' voltages and inductors' currents are chosen as state variables. First all the capacitors and inductors are replaced with voltage and current sources, respectively, and the modified nodal analysis is applied to this new circuit. By inspecting the system of equations obtained in this way and identifying the dependent equations among them, it is possible to detect any degeneracy, that is, dependency among the capacitors' voltages and inductors' currents, and subsequently refine the list of state variables. No knowledge of the circuits' graph is required and only its netlist description is needed in order to derive the equations, which makes it suitable for implementation as a computer program. Several examples are presented in which application of the method is demonstrated.