Use of Phasors in Nonlinear Analysis

Andrzej Borys, Zbigniew Zakrzewski

Abstract


In this paper, the well-known method of phasor analysis of linear ac circuits is extended in a rigorous mathematical way to nonlinear analysis. This fills the lack of such a theory in the literature. The results derived enable carrying out the needed corrections of some results published recently that regard harmonic distortion analysis of weakly nonlinear circuits.


Full Text:

PDF

References


G. Palumbo and S. Pennisi, “High-frequency harmonic distortion in feedback amplifiers: analysis and applications,” IEEE Transactions onCircuits 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 Transactions on Circuits andSystems-I: Regular Papers, vol. 53, pp. 225-234, February 2006.

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, pp. 961-976, May 2006.

S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Analysis and evaluation of harmonic distortion in the tunnel diode oscillator,” in Proceedings ofISCAS’06, Island of Kos, May 2006, pp. 5135-5138.

G. Palumbo, M. Pennisi, and S. Pennisi, “Analysis and evaluation of harmonic distortion in the Hartley oscillator,” in Proceedings of NOLTA 2006, Bologna, September 2006, pp. 643-646.

G. Palumbo, M. Pennisi, and S. Pennisi, “Analysis of harmonic distortion in the Colpitts oscillator,” in Proceedings of ICECS’06, Nice, December 2006, pp. 196-199.

G. Palumbo, M. Pennisi, and S. Pennisi, “Distortion analysis in the frequency domain of a Gm-C biquad filter,” in Proceedings of ECCTD’07, Seville, August 2007, pp. 212-215.

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

G. Palumbo, M. Pennisi, and S. Pennisi, “Wien-type oscillators: evaluation and optimization of harmonic distortion,” IEEE Transastions onCircuits and Systems-II: Express Briefs, vol. 55, pp. 628-632, July 2008. [Web of Science]

G. Palumbo, M. Pennisi, and S. Pennisi, “Miller theorem for weakly nonlinear feedback circuits and application to CE amplifier,” IEEE Transastions 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 onCircuit Theory, vol. CT-17, pp. 518-527, November 1970.

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.

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, August 1971.

C. P. Steinmetz, “Theory and calculation of a. c. phenomena,” 1897, New York.

B. Konorski, Podstawy Elektrotechniki. Warszawa: PWN, 1961, (in Polish).

S. Boyd and L. O. Chua, “Fading memory and the problem of approximating nonlinear operators with Volterra series,” IEEE Transactions onCircuits and Systems, vol. CAS-32, pp. 1150-1161, November 1985.

I. W. Sandberg, “Causality and the impulse response scandal,” IEEETransactions on Circuits and Systems - I: Fundamental Theory andApplications, vol. 50, pp. 810-811, 2003.

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.

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, “Exploiting admittance formalism in the nonlinear analysis,” Zesz. Nauk. WSInf: Teoria i Zastosowania Informatyki, vol. 8, no. 2, pp. 17-39, 2009.


Refbacks

  • There are currently no refbacks.


International Journal of Electronics and Telecommunications
is a periodical of Electronics and Telecommunications Committee
of Polish Academy of Sciences

eISSN: 2300-1933