Volterra Series Based Time-domain Macro-modeling of Nonlinear Circuits

TL;DR

This paper introduces a systematic method to extract Volterra kernels from X-parameters, enabling efficient time-domain modeling of nonlinear circuits and broadening the application of Volterra series in circuit analysis.

Contribution

It presents a novel approach to derive Volterra kernels from X-parameters, including frequency sweep and output indexing schemes, facilitating time-domain simulation of nonlinear circuits.

Findings

Effective extraction of Volterra kernels from X-parameters

Validation of the method through time-domain verification

Enhanced capability for nonlinear circuit macro-modeling

Abstract

Volterra series representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. In this work, a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters is presented. A concise and general representation of the output response due to arbitrary number of input tones is given. The relationship between Volterra kernels and X-parameters is explicitly formulated. An efficient frequency sweep scheme and an output frequency indexing scheme are provide. The least square linear regression method is employed to separate different orders of Volterra kernels at the same frequency, which leads to the obtained Volterra kernels complete. The proposed Volterra series representation based on X-parameters is further validated for time domain verification. The proposed method is systematic and general-purpose. It paves the way for time domain simulation with X-parameters and constitutes a powerful supplement to existing blackbox macro-modeling methods for nonlinear circuits.