On Definition of Operator o for Weakly Nonlinear Circuits

Authors

  • Andrzej Marek Borys Gdynia Maritime University

Abstract

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.

References

S. Narayanan, “Transistor distortion analysis using Volterra series representation,” The Bell Syst. Tech. Journal, vol. 46, pp. 991-1024, May-June 1967.

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

R. Meyer and M. Stephens, “Distortion in variable-capacitance diodes,” IEEE Journal of Solid-State Circuits, vol. 10, pp. 47-54, February 1975.

G. Palumbo and S. Pennisi, “High-frequency harmonic distortion in feedback amplifiers: analysis and applications,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 50, pp. 328-340, March 2003.

S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Effects of nonlinear feedback in the frequency domain,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 53, pp. 225-234, February 2006 .

G. Palumbo, M. Pennisi, and S. Pennisi, “Miller theorem for weakly nonlinear feedback circuits and application to CE amplifier,” IEEE Trans. Circuits and Systems-II: Express Briefs, vol. 55, pp. 991-995, October 2008 .

S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “An approach to model high-frequency distortion in negative-feedback amplifiers,” Journal of Circuit Theory and Applications, vol. 36, pp. 3-18, 2008.

H. Shrimali and S. Chatterjee, “Distortion analysis of a three-terminal MOS-based discrete-time parametric amplifier,” IEEE Trans. Circuits and Systems-II: Express Briefs, vol. 58, pp. 902-905, December 2011.

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.

A. Borys, “Strange History of an Operator o,” Proceedings of the 22nd International Conference Mixed Design of Integrated Circuits and Systems MIXDES’2015, pp. 504-507, June 2015.

A. Borys and Z. Zakrzewski, “Use of phasors in nonlinear analysis,” Int. Journal of Telecommunications and Electronics (JET), vol. 59, pp. 219-228, 2013.

J. J. D’Azzo and C. H. Houpis, Linear Control Systems Analysis and Design, New York: McGraw-Hill, 1988.

J. J. Bussgang, L. Ehrman, and J. W.

Graham, “Analysis of nonlinear systems with multiple inputs”, Proceedings of the IEEE, vol. 62, pp. 1088-1119, 1974.

R. Meyer, private communication, April 2016.

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Published

2016-09-08

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Section

Signals, Circuits, Systems