scholarly journals Circuit Distortion Analysis Based on the Simplified Newton's Method

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
M. M. Gourary ◽  
S. G. Rusakov ◽  
S. L. Ulyanov ◽  
M. M. Zharov ◽  
B. J. Mulvaney
Keyword(s):  
Harmonic Balance ◽  
Volterra Series ◽  
Nonlinear Circuits ◽  
New Technique ◽  
Computational Technique ◽  
Computationally Efficient ◽  
Weakly Nonlinear ◽  
Distortion Analysis ◽  
Circuit Components ◽  
Derivatives Of

A new computational technique for distortion analysis of nonlinear circuits is presented. The new technique is applicable to the same class of circuits, namely, weakly nonlinear and time-varying circuits, as the periodic Volterra series. However, unlike the Volterra series, it does not require the computation of the second and third derivatives of device models. The new method is computationally efficient compared with a complete multitone nonlinear steady-state analysis such as harmonic balance. Moreover, the new technique naturally allows computing and characterizing the contributions of individual circuit components to the overall circuit distortion. This paper presents the theory of the new technique, a discussion of the numerical aspects, and numerical results.

scholarly journals Use of Phasors in Nonlinear Analysis

2013 ◽  
Vol 59 (3) ◽  
pp. 219-228 ◽  
Author(s):  
Andrzej Borys ◽  
Zbigniew Zakrzewski
Keyword(s):  
Nonlinear Analysis ◽  
Harmonic Distortion ◽  
Nonlinear Circuits ◽  
Weakly Nonlinear ◽  
Distortion Analysis ◽  
Weakly Nonlinear Circuits ◽  
Phasor Analysis

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.

scholarly journals On Definition of Operator o for Weakly Nonlinear Circuits

2016 ◽  
Vol 62 (3) ◽  
pp. 253-259
Author(s):  
Andrzej Borys
Keyword(s):  
Nonlinear Distortion ◽  
Volterra Series ◽  
Linear Part ◽  
Harmonic Distortion ◽  
Nonlinear Circuits ◽  
Nonlinear Circuit ◽  
Weakly Nonlinear ◽  
Circuit Description ◽  
Definition Of ◽  
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. Its 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 communicated 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.

scholarly journals On In-Network and Other Types of Amplifier Descriptions for Nonlinear Distortion Analysis

2010 ◽  
Vol 56 (2) ◽  
pp. 177-184
Author(s):  
Andrzej Borys
Keyword(s):  
Time Domain ◽  
Nonlinear Distortion ◽  
Volterra Series ◽  
Harmonic Distortion ◽  
Weakly Nonlinear ◽  
Distortion Analysis ◽  
Frequency Domains ◽  
Distortion Measure ◽  
Nonlinear Amplifiers ◽  
The Time Domain

On In-Network and Other Types of Amplifier Descriptions for Nonlinear Distortion Analysis Basics of modelling analog weakly nonlinear amplifiers at higher frequencies for the purpose of nonlinear distortion analysis are addressed in this paper. First, the constitutive relation for this class of amplifiers, with the use of a Volterra series, is formulated. It is the basis for formulation and derivation of the so-called in-network and input-output type descriptions of an amplifier in the time domain, which are then transferred into the multi-frequency domains. Usefulness of the general models achieved, which were not published up to now in the literature, lies in the fact that they can be used for any topology in which the amplifier is incorporated and for any nonlinear distortion measure assumed. Some examples of calculations are given at the end of the paper for cascade and feedback topologies, and for harmonic distortion measure.

scholarly journals Understanding of Meyer and Stephens’s operator o as a multi-operational one

2016 ◽  
Vol 62 (3) ◽  
pp. 273-277
Author(s):  
Andrzej Borys
Keyword(s):  
Volterra Series ◽  
Nonlinear Circuits ◽  
Weakly Nonlinear ◽  
Extended Operator ◽  
Weakly Nonlinear Circuits

Abstract In this paper, the idea of an extended operator o introduced in the literature on modelling weakly nonlinear circuits by Meyer and Stephens is revisited. The mathematically precise definitions of this operator for the successive Volterra series terms are given. Furthermore, the exhaustive formal and illustrative descriptions of these definitions are also presented. Finally, the possibility of a reverse formulation for the convolution operations occurring in descriptions of weakly nonlinear circuits is reported.

AM-PM conversion introduced by weakly nonlinear circuits

2000 ◽  
Vol 87 (8) ◽  
pp. 931-940 ◽  
Author(s):  
H. Jardon-Aguilar ◽  
J. Aguilar-Torrentera ◽  
F. Iturbide-Sanchez
Keyword(s):  
Nonlinear Circuits ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Circuits

Using Transfer Matrices for Parametric System Forced Response

1987 ◽  
Vol 109 (4) ◽  
pp. 356-360 ◽  
Author(s):  
J. W. David ◽  
L. D. Mitchell ◽  
J. W. Daws
Keyword(s):  
Harmonic Balance ◽  
Forced Response ◽  
Computational Techniques ◽  
Computational Technique ◽  
Transfer Matrices ◽  
Frequency Branch ◽  
Balance Technique ◽  
Systems Analysts ◽  
The Many ◽  
Harmonic Balance Technique

For many years, engineers and scientists have sought to deal with the many phenomena exhibiting parametric characteristics. While many approximate techniques are available for the analysis of such systems, the harmonic balance technique can be used to accurately model the response of systems where the coefficient variation is large. Also, in analyzing complex physical systems, analysts have sought to develop efficient computational techniques that are sufficiently general for the analysis of arbitrary systems. In this paper, it is shown that combining the harmonic balance technique with transfer matrices produces an efficient computational technique for the analysis of parametric systems where the coefficient variations can be large. The technique is demonstrated by considering a single-degree-of-freedom system with time varying stiffness. The harmonic balance technique is used to frequency-branch the transfer matrices, thus allowing multifrequency response calculations to be done simultaneously. The results are compared with direct numerical integrations of the equations. Lastly, this technique is applied to a simple gear coupled rotor system to demonstrate the application of this technique to large order systems of more engineering relevance.

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