On Definition of Operator o for Weakly Nonlinear Circuits

Andrzej Marek Borys


For the first time, operator o appeared in the literature on weakly nonlinear circuits in a Narayanan’s paper on modelling transistor nonlinear distortion with the use of Volterra series. His definition was restricted only to the linear part of a nonlinear circuit description. Obviously, as we show here, Narayanan’s operator o had meaning of a linear convolution integral. The extended version of this operator, which was applied to the whole nonlinear circuit representation by the Volterra series, was introduced by Meyer and Stephens in their paper on modelling nonlinear distortion in variable-capacitance diodes. We show here that its definition as well as another definition communication to the author of this paper are faulty.  We draw here attention to these facts because the faults made by Meyer and Stephens were afterwards replicated in publications of Palumbo and his coworkers on harmonic distortion calculation in integrated CMOS amplifiers, and recently in a paper about distortion analysis of parametric amplifier by H. Shrimali and S. Chatterjee. These faults are also present in some class notes for students, which are available on WWW-pages.

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M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, New York: John Wiley & Sons, 1980.

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A. M. Niknejad, Class Notes EECS 242 on: Volterra/Wiener Representation of Non-Linear Systems; MOS High Frequency Distortion; BJT High Frequency Distortion, University of California, Berkeley, available on the WWW-page of prof. A. M. Niknejad.

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R. Meyer, private communication, April 2016.


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