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Journal Article•DOI•

Application of Volterra series to intermodulation distortion analysis of transistor feedback amplifiers

S. Narayanan1•
01 Nov 1970-IEEE Transactions on Circuit Theory (IEEE)-Vol. 17, Iss: 4, pp 518-527
TL;DR: In this paper, the authors analyzed the intermodulation distortion of a solid-state feedback amplifier and showed that the feedback is fully effective in reducing the open-loop second-order distortion.
Abstract: This paper analyzes the intermodulation distortion of a solid-state feedback amplifier. Each transistor of the amplifier has been represented by a frequency-dependent model incorporating four nonlinearities. The Volterra series is used as the analysis tool. The primary motivation for this study is that intermodulation distortion is a critical problem in high-frequency long-haul solidstate systems. A computer program that calculates the amplifier intermodulation distortion has been developed. This program can be used to select the optimum bias point of each stage, optimum interstage and feedback networks, and optimum load and source impedances. Good correlation between calculated and measured results was obtained. The closed-form expressions derived show that the feedback is fully effective in reducing the open-loop second-order distortion and that the feedback may not significantly reduce the open-loop third-order distortion, if the "second-order interaction" phenomenon is dominant. The second-order interaction is explained in detail in this paper.
Citations
More filters
Journal Article•DOI•
V.J. Mathews1•
TL;DR: The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation.
Abstract: Adaptive nonlinear filters equipped with polynomial models of nonlinearity are explained. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in adaptive filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. Adaptive algorithms using system models involving recursive nonlinear difference equations are then treated. Such systems may be able to approximate many nonlinear systems with great parsimony in the use of coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is described. >

541 citations

DOI•
01 Nov 1980
TL;DR: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way as discussed by the authors, where the limitations, relationships and applicability of the methods are discussed throughout.
Abstract: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory and included. The limitations, relationships and applicability of the methods are discussed throughout.

491 citations

Journal Article•DOI•
E. Bedrosian1, S.O. Rice•
01 Dec 1971
TL;DR: Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented.
Abstract: Troublesome distortions often occur in communication systems. For a wide class of systems such distortions can be computed with the help of Volterra series. Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented. The n-fold Fourier transform G n of the nth Volterra kernel plays an important role in the analysis. Methods of computing G n from the system equations are described and several special systems are considered. When the G n are known, items of interest regarding the output can be obtained by substituting the G n in general formulas derived from the Volterra series representation. These items include expressions for the output harmonics, when the input is the sum of two or three sine waves, and the power spectrum and various moments, when the input is Gaussian. Special attention is paid to the case in which the Volterra series consists of only the linear and quadratic terms.

479 citations

Journal Article•DOI•
TL;DR: It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.

446 citations

Journal Article•DOI•
01 Aug 1974
TL;DR: Analytical modeling of communication receivers to account for their nonlinear response to multiple input signals is discussed, based on the application of the Wiener-Volterra analysis of nonlinear functionals.
Abstract: Analytical modeling of communication receivers to account for their nonlinear response to multiple input signals is discussed. The method is based on the application of the Wiener-Volterra analysis of nonlinear functionals. The derived analytical relations were embodied in a computer program which provides nonlinear transfer functions of large circuits specified by their parameters. This method was applied to the prediction of behavior of communication receivers in the presence of interference. Examples illustrate the method and demonstrate its validity in the small-signal region.

425 citations

References
More filters
24 Jul 1959
TL;DR: In this paper, a thesis submitted to M.I.T. Dept. of Electrical Engineering, July 24, 1959, is described, based on which the following paper is presented:
Abstract: "July 24, 1959." Based on thesis submitted to M.I.T. Dept. of Electrical Engineering, July 24, 1959.

238 citations

Journal Article•DOI•
TL;DR: In this article, the second and third harmonic distortion for a given set of input frequencies and transistor parameters is computed using the Volterra series representation, where the nonlinear nodal equations are solved by expressing nodal voltages in terms of the VOLTERRA series expansion of the input voltage.
Abstract: Intermodulation distortion due to nonlinear elements in transistors is analyzed using Volterra series representation. It is shown that this technique is well suited for the analysis of transistor distortion where the nonlinearities are small but frequency dependent. An ac transistor model incorporating four nonlinearities is briefly described. The nonlinear nodal equations of the model are successively solved by expressing nodal voltages in terms of the Volterra series expansion of the input voltage. Based on this analysis, a digital computer program has been developed which computes the second and the third harmonic distortion for a given set of input frequencies and transistor parameters. The results compare favorably with measured values. This method also enables the derivation of closed form ac expressions for a simplified model; these expressions show the dependence of distortion on frequency, load and source impedances, bias currents and voltages, and the parameters of the transistor. The technique is also extended to cascaded transistors, and simplified expressions for the overall distortion in terms of the distortion and gain of individual transistors are derived. Finally, a few pertinent practical applications are discussed.

192 citations

Journal Article•DOI•
J. F. Barrett1•
TL;DR: In this paper, the authors present a systematic development of this idea and present analogous expansions in a series of terms orthogonal with respect to input statistics, which is applicable equally to linear or non-linear systems.
Abstract: This report is an attempt to develop a method of analysis applicable equally to linear or non-linear systems. The main method discussed is the expansion of the input-output relation in a functional power series–an idea first due to Volterra for general functional relationships and to Wiener in its application to non-linear communication problems. The report attempts to present a systematic development of this idea. The last part of the report discusses analogous expansions in a series of terms orthogonal with respect to input statistics.

184 citations


"Application of Volterra series to i..." refers background in this paper

  • ...Barrett [ 7 ], Brilliant [S], George [9], and Zames [ 103 have analyzed a general nonlinear feedback...

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Report•DOI•
03 Mar 1958
TL;DR: This thesis is based on a thesis submitted to M.I.T. Dept. of Electrical Engineering, January 13, 1958 and aims to provide a history of electrical engineering in the United States.
Abstract: "March 3, 1958" Based on a thesis submitted to MIT Dept of Electrical Engineering, January 13, 1958

134 citations

Journal Article•DOI•
George Zames1•
TL;DR: An operator theory is outlined for the general, nonlinear, feedback loop and it is shown that feedback reduces distortion for band-limited inputs and an iteration whose rate of convergence is optimized is derived.
Abstract: An operator theory is outlined for the general, nonlinear, feedback loop. Methods for bounding system responses and investigating stability are introduced. An iterative expansion of the feedback loop, valid for large nonlinearities and unstable systems, is derived. The theory is applied to the study of nonlinear distortion in a class of amplifiers; it is shown that feedback reduces distortion for band-limited inputs. A model of the distortion is obtained, shown to be stable, and an iteration whose rate of convergence is optimized is derived.

129 citations


Additional excerpts

  • ...Desoer [3], Zames [ 4 ], Sandberg [.5], and Holtzman [6] have applied contraction mapping principle....

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