Volterra kernels extraction from frequency-domain data for weakly non-linear circuit time-domain simulation

Volterra series have been popular in non-linear system analysis and modeling for a long time. Volterra representation adapts the convolution concept from linear time-invariant (LTI) systems, generalizes it to “super convolutions” and, hence, are able to characterize the dynamical behavior of non-linear circuits using familiar LTI techniques. It is extensively used in white-box verification problems where small order distortion terms occur such as transistor circuits. This paper presents an experiment with finite order non-linear circuits and uses frequency-domain data obtained from Harmonic Balance (HB) simulation to extract Volterra kernels.

[1]  M. Steer,et al.  Nonlinear circuit analysis using the method of harmonic balance—A review of the art. Part I. Introductory concepts , 1991 .

[2]  David E. Root,et al.  X-Parameters: Characterization, Modeling, and Design of Nonlinear RF and Microwave Components , 2013 .

[3]  Michael B. Steer,et al.  Nonlinear circuit analysis using the method of harmonic balance—a review of the art. II. Advanced concepts , 1991 .

[4]  Stephen P. Boyd,et al.  Analytical Foundations of Volterra Series , 1984 .

[5]  S. Billings,et al.  Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems , 2011 .

[6]  S. Billings,et al.  Volterra series truncation and reduction in the frequency domain for weakly nonlinear system , 2006 .

[7]  David Root,et al.  X-Parameters: Multi-tone and multi-port cases , 2013 .

[8]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[9]  P. J. Lawrence.  Estimation of the Volterra functional series of a nonlinear system using frequency-response data , 1981 .

[10]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[11]  Chunyu Xin,et al.  Radio frequency circuits for wireless receiver front-ends , 2005 .

[12]  Weng Cho Chew,et al.  Volterra Series-Based Time-Domain Macromodeling of Nonlinear Circuits , 2016, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[13]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[14]  D.E. Root,et al.  Polyharmonic distortion modeling , 2006, IEEE Microwave Magazine.

[15]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .