General-purpose analysis of nonlinear circuits containing saturating/hysteretic inductors by the harmonic-balance technique

The systematic application of the harmonic-balance (HB) technique to nonlinear circuits containing saturating/hysteretic inductors subjected to high driving levels is discussed. Ferromagnetic hysteresis is described by the Jiles-Atherton (JA) model. The traditional HB approach is extended to accept a generalized parametric formulation of the nonlinearities allowing the JA model to be dealt with in a straightforward way. The nonlinear HB system is solved by Newton iteration coupled with the exact calculation of the Jacobian matrix and an advanced norm-reduction scheme. This results in excellent robustness and fast convergence of the analysis algorithm even at very large signal levels, in spite of the high nonlinearity of the JA differential equation. Two techniques for finding the initial magnetization curve are also discussed. The proposed approach is validated by comparing the hysteresis cycles of several materials obtained from HB calculations with time-domain and experimental results. An example of a general nonlinear circuit analysis problem is also provided. The analysis technique is complemented by a systematic algorithm for the local and global stability analysis of the large-signal steady state