Generalization of Linear Rosenstark Method of Feedback Amplifier Analysis to Nonlinear One
Abstract
This paper deals with an extension of the Rosenstark’s linear model of an amplifier to a nonlinear one for the purpose of performing nonlinear distortion analysis. Contrary to an approach using phasors, our method uses the Volterra series. Relying upon the linear model mentioned above, we define first a set of the so-called amplifier’s constitutive equations in an operator form. Then, we expand operators using the Volterra series truncated to the first three components. This leads to getting two representations in the time domain, called in-network and inputoutput type descriptions of an amplifier. Afterwards, both of these representations are transferred into the multi-frequency domains. Their usefulness in calculations of any nonlinear distortion measure as, for example, harmonic, intermodulation, and/or cross-modulation distortion is demonstrated. Moreover, we show that they allow a simple calculation of the so-called nonlinear transfer functions in any topology as, for example, of cascade and feedback structures and their combinations occurring in single-, two-, and three-stage amplifiers. Examples of such calculations are given. Finally in this paper, we comment on usage of such notions as nonlinear signals, intermodulation nonlinearity, and on identification of transfer function poles and zeros lying on the frequency axis with related real-valued frequencies.References
S. Rosenstark, “A simplified method of feedback amplifier analysis,” IEEE Transactions on Education, vol. E-17, pp. 192–198, November 1974.
S. Rosenstark, Feedback Amplifier Principles. New York: Macmillan Publishing Company, 1986.
G. Palumbo and S. Pennisi, “High-frequency harmonic distortion in feedback amplifiers: analysis and applications,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 50, pp. 328–340, March 2003.
G. Palumbo and S. Pennisi, Feedback Amplifiers: Theory and Design. Norwell, MA: Kluwer, 2002.
Y. Miao and Y. Zhang, “Distortion modeling of feedback two-stage amplifier compensated with Miller capacitor and nulling resistor,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 59, pp. 93–105, January 2012.
L. O. Chua, “Device modeling via basic nonlinear circuit elements,” IEEE Transactions on Circuits Systems, vol. CAS-27, pp. 1014–1044, November 1980.
A. Borys, “On in-network and other types of amplifier descriptions for nonlinear distortion analysis,” International Journal of Electronics and Telecommunications, vol. 56, no. 2, pp. 177–184, 2010.
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.
E. Bedrosian and S. O. Rice, “The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs,” Proceedings of the IEEE, vol. 59, pp. 1688–1707, December 1971.
L. O. Chua and C. Ng, “Frequency domain analysis of nonlinear systems: general theory,” IEE Journal of Electronic Circuits and Systems, vol. 3, pp. 165–185, 1979.
L. O. Chua and C. Ng, “Frequency domain analysis of nonlinear systems: formulation of transfer functions,” IEE Journal of Electronic Circuits and Systems, vol. 3, pp. 257–269, 1979.
A. Borys, “A simplified analysis of nonlinear distortion in analog electronic circuits using the Volterra-Wiener series,” Scientia Electrica, vol. 30, no. 3, pp. 78–103, 1984.
S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Effects of nonlinear feedback in the frequency domain,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 53, pp. 225–234, February 2006.
A. Borys, “On correctness of the basics of Palumbo and Pennisi’s means of harmonic distortion calculation in analog integrated circuits,” Zeszyty Naukowe Wyszej Szkoy Informatyki w Łodzi: Teoria i zastosowania informatyki, vol. 8, no. 2, pp. 5–16, 2009.
R. G. Meyer, M. J. Shensa, and R. Eschenbach, “Crossmodulation and intermodulation in amplifiers at high frequencies,” IEEE Journal of Solid-State Circuits, vol. SC-7, pp. 16–23, February 1972.
A. Borys, “Exploiting admittance formalism in the nonlinear analysis,” Zeszyty Naukowe Wyszej Szkoy Informatyki w Ł odzi: Teoria i zastosowa- nia informatyki, vol. 8, no. 2, pp. 17–39, 2009.
G. Palumbo, M. Pennisi, and S. Pennisi, “Miller theorem for weakly nonlinear feedback circuits and application to CE amplifier,” IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 55, pp. 991–995, October 2008.
S. Narayanan, “Application of Volterra series to intermodulation distortion analysis of transistor feedback amplifiers,” IEEE Transactions on Circuit Theory, vol. CT-17, pp. 518–527, November 1970.
P. Wambacq, G. Gielen, P. Kinget, and W. Sansen, “High-frequency distortion analysis of analog integrated circuits,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, no. 3, pp. 335–344, March 1999.
B. Hernes and W. Sansen, “Distortion in single-, two- and three-stage amplifiers,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 5, pp. 846–856, May 2005.
M. Fliess, M. Lamnabhi, and F. Lamnabhi-Lagarrigu, “An algebraic approach to nonlinear functional expansions,” IEEE Transactions on Circuits and Systems, vol. 30, no. 8, pp. 554–570, 1983.
S. Narayanan, “Intermodulation distortion of cascaded transistors,” IEEE Journal of Solid-State Circuits, vol. SC-4, no. 3, pp. 97–106, June 1969.
Y. L. Kuo, “Frequency-domain analysis of weakly nonlinear networks. “Canned” Volterra analysis, part 1,” IEEE Circuits and Systems Maga- zine, vol. 11, no. 4, pp. 2–8, August 1977.
S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Distortion analysis of Miller-compensated three-stage amplifiers,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 5, pp. 961–976, May 2006.
S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “An approach to model high-frequency distortion in negativefeedback amplifiers,” International Journal of Circuit Theory and Ap- plications, vol. 36, pp. 3–18, 2008.
A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design. New York: McGraw-Hill, 1968.
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