Application of generalized phasors to eigenvector and natural response computation of LTI circuits

Abstract

This paper focuses on the natural response computation of linear time-invariant (LTI) circuits, in those cases in which a closed-form solution, rather than numerical integration of the state-variable equations, is preferable. A computationally efficient procedure is presented to individually obtain the eigenvectors of matrix A, both for distinct and repeated eigenvalues. Instead of performing orthogonal matrix transformations, the proposed method relies on the solution of the nodal equations corresponding to a zero-input circuit in the generalized phasor domain. This allows propagation of natural modes to be computed by means of a simple procedure that closely resembles conventional ac analysis.