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Analysis of harmonic distortion in analog circuits with the use of Volterra series and Kronecker products

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This paper was inspired by an article entitled “An approach to model high-frequency distortion in negativefeedback amplifiers” by S. O. Cannizzaro, G. Palumbo, and S. Pennisi. The objective of this presentation is to point out that some results presented therein are not so novel as argued. First, we point out here that an idea of partition of a nonlinear circuit into interconnected smaller basic blocks, used in the above paper under a name of an analytical approach, is not new. For the first time, it has been used in the literature by S. Narayanan, pioneer of the Volterra series usage in calculations of nonlinear distortion in electronic circuits, and afterwards by many others. Second, we show that descriptions of the basic blocks mentioned above follow from their more general representations by the Volterra series, specialized for harmonic inputs. Third, we recall references in which the joint and complementary elements as well as some invariants occurring in modelling of op amp inverting and noninverting configurations for the purpose of nonlinear distortion evaluation have been reported before publication of some similar results by S. O. Cannizzaro, G. Palumbo, and S. Pennisi. Finally, we show that an operator o that was introduced by the above authors in their paper can lead to calculation errors. Alternative approach to this point is presented.
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  • Department of Marine Telecommunications, Gdynia Maritime University, Gdynia, Poland
Bibliografia
  • [1] 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.
  • [2] S. Narayanan, “Transistor distortion analysis using Volterra series representation,” The Bell Syst. Tech. Journal, vol. 46, pp. 991-1024, May-June 1967.
  • [3] S. Narayanan, “Intermodulation distortion of cascaded transistors,” IEEE Journal of Solid-State Circuits, vol. SC-4, pp. 97-106, June 1969.
  • [4] S. Narayanan, “Application of Volterra series to intermodulation distortion analysis of a transistor feedback amplifier,” IEEE Trans. Circuit Theory, vol. CT-17, pp. 518-527, Nov. 1970.
  • [5] 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.
  • [6] A. Borys, “On intermodulation and harmonic distortion in singleamplifier active filters,” Journal of the Audio Engineering Society, vol. 28, Oct. 1980.
  • [7] A. Borys, “Harmonic and intermodulation distortion analysis in singleamplifier active filters using the Volterra-Wiener series approach,” Archiwum Elektrotechniki, z. 4, 1981.
  • [8] A. Borys, “Nonlinear distortion in active RC filters,” Proceedings of the Sixth Summer Symposium on Circuit Theory, Prague, Czechoslovakia, pp. 207-212, 1982.
  • [9] A. Borys, “An analysis of slew-induced distortion in single-amplifier active filters using the Volterra-Wiener series technique,” Int. J. Cir. Theor. Appl., vol. 10, pp. 81-94, 1982.
  • [10] L. O. Chua and C.-Y Ng, “Frequency domain analysis of nonlinear systems: formulation of transfer functions,” IEE J. Electron. Circuits and Systems, vol. 3, pp. 257-269, 1979.
  • [11] 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 .
  • [12] 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 .
  • [13] S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Accurate estimation of high-frequency harmonic distortion in two-stage Miller OTAs”, Proc. IEE, vol. 152, Oct. 2005, pp. 417-424.
  • [14] S. O. Cannizzaro, G. Palumbo, and S. Pennisi, “Distortion analysis of Miller-compensated three-stage amplifier”, IEEE Trans. Circuits and Systems-I: Regular Papers, vol. 53, pp. 961–976, May 2006.
  • [15] B. Hernes and W. Sansen, “Distortion in single-, two- and three-stage amplifiers,” IEEE Trans. Circuits and Systems-I: Regular Papers, vol. 52, pp. 846–856, May 2005.
  • [16] L. O. Chua and C.-Y. Ng, “Frequency domain analysis of nonlinear systems: general theory, IEE J. Electron. Circuits and Systems, vol. 3, pp. 165-185, 1979.
  • [17] A. Borys, “A simplified analysis of nonlinear distortion in analog electronic circuits using the Volterra-Wiener series,” Scientia Electrica, vol. 30, pp. 78-103, 1984.
  • [18] 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, Feb. 1972.
  • [19] S. Ganesan, E. Sánchez-Sinencio, and J. Silva-Martinez, “A highly linear low-noise amplifier,” IEEE Trans. Microwave Theory and Techniques, vol. 54, pp. 4079-4085, Dec. 2006.
  • [20] F. J. Casas, J. P. Pascual, M. L. de la Fuente, E. Artal, and J. Portilla, “Simple nonlinearity evaluation and modeling of low-noise amplifiers with application to radio astronomy receivers”, Review of Scientific Instruments, vol. 81, pp. 1-6, 2010.
  • [21] A. Borys, “On correctness of the basics of Palumbo and Pennisi’s means of harmonic distortion calculation in analog integrated circuits,” Zesz. Nauk. WSInf w Łodzi: Teoria i zastosowania informatyki, vol. 8, pp. 5- 16, 2009.
  • [22] A. Borys and N. Fliege, “Complementary transformation in mildly nonlinear feedback systems,” Proceedings of the ECCTD'89, Brighton, United Kingdom, pp. 445-447, 1989.
  • [23] A. Borys, “Effect of op amp output resistance on intermodulation distortion of single amplifier filters,” Proceedings of the ECCTD'81, The Hague, The Netherlands, pp. 988-992, 1981.
  • [24] A. Borys, „Exploiting admittance formalism in the nonlinear analysis,” Zeszyty Naukowe WyĪszej Szkoły Informatyki (WSInf) w Łodzi, Teoria i zastosowania informatyki, vol. 8, pp. 17-39, 2009.
  • [25] M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, New York: John Wiley & Sons, 1980.
  • [26] A. Borys, “On analysis of harmonic distortion in op amps based circuits via Volterra series,” Proceedings of the 23rd International Conference Mixed Design of Integrated Circuits and Systems, ŁódĨ, Poland, pp. 330-335, 2016.
  • [27] A. A. M. Saleh, “Matrix analysis of mildly nonlinear, multiple-input, multiple-output systems with memory,” The Bell System Technical Journal, vol. 61, pp. 2221-2243, Nov. 1982.
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Bibliografia
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