An Improved State Equations Extraction Method for Linear Circuits

State variable method is a powerful tool for analyzing dynamic circuits, and the key to its application lies in the extraction of state equations. In this paper, an improved modified nodal approach (MNA) has been proposed to extract the state equations. Based on the basic principle of linear circuits, the hybrid equations which can deal with all kinds of linear elements have been established. The non-state variables in the hybrid equations are eliminated by elementary row transformation method, and the state equations with capacitance voltage and inductance current as state variables is obtained. Aiming at the problem that the order of the hybrid equations is too large, a reduced order method has been put forward, which can eliminate the voltage source current and some node voltage variables in the hybrid equations. Matrix dimension calculation and case analysis results showed that the reduced order method can reduce the amount of computations in the extraction of state equations and the new method is more efficient.