On Definition of Operator o for Weakly Nonlinear Circuits
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2016 International Journal of Electronics and Telecommunications
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. License
The non-commercial use of the article will be governed by the Creative Commons Attribution license as currently displayed on https://creativecommons.org/licenses/by/4.0/.
2. Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. The undersigned also warrants that the manuscript (or its essential substance) has not been published other than as an abstract or doctorate thesis and has not been submitted for consideration elsewhere, for print, electronic or digital publication.
3. User Rights
Under the Creative Commons Attribution license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may alter, transform, or build upon this work, 3. they may use this contribution for commercial purposes.
4. Rights of Authors
Authors retain the following rights:
- copyright, and other proprietary rights relating to the article, such as patent rights,
- the right to use the substance of the article in own future works, including lectures and books,
- the right to reproduce the article for own purposes, provided the copies are not offered for sale,
- the right to self-archive the article
- the right to supervision over the integrity of the content of the work and its fair use.
5. Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
6. Termination
This agreement can be terminated by the author or the Journal Owner upon two months’ notice where the other party has materially breached this agreement and failed to remedy such breach within a month of being given the terminating party’s notice requesting such breach to be remedied. No breach or violation of this agreement will cause this agreement or any license granted in it to terminate automatically or affect the definition of the Journal Owner. The author and the Journal Owner may agree to terminate this agreement at any time. This agreement or any license granted in it cannot be terminated otherwise than in accordance with this section 6. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
7. Royalties
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by the Journal Owner or its sublicensee.
8. Miscellaneous
The Journal Owner will publish the article (or have it published) in the Journal if the article’s editorial process is successfully completed and the Journal Owner or its sublicensee has become obligated to have the article published. Where such obligation depends on the payment of a fee, it shall not be deemed to exist until such time as that fee is paid. The Journal Owner may conform the article to a style of punctuation, spelling, capitalization and usage that it deems appropriate. The Journal Owner will be allowed to sublicense the rights that are licensed to it under this agreement. This agreement will be governed by the laws of Poland.
By signing this License, Author(s) warrant(s) that they have the full power to enter into this agreement. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
