A novel linear algebra method for the determination of periodic steady states of nonlinear oscillators

Periodic steady-state (PSS) analysis of nonlinear oscillators has always been a challenging task in circuit simulation. We present a new way that uses numerical linear algebra to identify the PSS(s) of nonlinear circuits. The method works for both autonomous and excited systems. Using the harmonic balancing method, the solution of a nonlinear circuit can be represented by a system of multivariate polynomials. Then, a Macaulay matrix based root-finder is used to compute the Fourier series coefficients. The method avoids the difficult initial guess problem of existing numerical approaches. Numerical examples show the accuracy and feasibility over existing methods.