Volterra Series-Based Time-Domain Macromodeling of Nonlinear Circuits

Volterra series (VS) representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher order Volterra kernels limited its broader applications. In this paper, 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 provided. 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 VS 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 the existing blackbox macromodeling methods for nonlinear circuits.