A novel nonlinear macromodeling using time piecewise volterra series representation

Accurate and effective nonlinear system-level macromodeling has played a very important role in solving electromagnetic compatibility problems in modern circuit and system design. The technique based on Volterra series expansions provides the possibility to approximate complex nonlinear circuit models. However, the traditional Volterra series macromodel has limited ability to illustrate strong nonlinearities, resulting from the inconsistency between the complex nature and the required computing cost. In this paper, a novel nonlinear macromodeling scheme using time piecewise Volterra series representations is proposed. In this method, the whole training time series is first divided into several piecewise time series according to the nonlinear characteristics and the model fidelity required. We then process each piecewise time series by the lower order Volterra series, and collect the piecewise Volterra kernels by the Volterra kernel set. Finally, we obtain the output result by combining the Volterra kernel set and the weight function. This approach, which combines the piecewise idea with Volterra series methods, strives to deliver a macromodel that can describe strong and weak nonlinearities simultaneously. Computational results and performance data are presented for the examples of a memristor and selected nonlinear circuits. These examples demonstrate that the proposed method is efficient and precise.