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Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


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Journal ArticleDOI
TL;DR: In this article, a nonlinear theory of noise in synchronized oscillators is outlined, thus extending Kurokawa's work from small to arbitrary injection levels, and simple expressions for the various output noise and noise conversion factors in the case when the nonlinear characteristic of the active device can be described by a third-order (van-der-Pol) polynomial.
Abstract: A nonlinear theory of noise in synchronized oscillators is outlined, thus extending Kurokawa's work from small to arbitrary injection levels. The description is of phenomenological nature: it uses the describing function method of control theory for calculating the carrier waves, and the circuit theory of periodically driven nonlinear systems for an analysis of the noise sidebands. Simple expressions are derived for the various output noise and noise conversion factors in the case when the nonlinear characteristic of the active device can be described by a third-order (van-der-Pol) polynomial.

26 citations

Journal ArticleDOI
TL;DR: In this article, two measuring techniques are presented for measuring the higher order sinusoidal input describing functions (HOSIDF) of a non-linear plant operating in feedback.

26 citations

Journal ArticleDOI
Chin Chang1, G.W. Bruning
TL;DR: In this article, the authors analyzed the self-oscillating LC parallel resonant inverter for electronic ballast applications from a control system point of view and found that the accuracy of the frequency prediction via the Hamel locus approach is high, while the accuracy via the describing function approach is circuit Q-value dependent.
Abstract: In this paper, the authors analyze the self-oscillating LC parallel resonant inverter for electronic ballast applications from a control system point of view. It is observed that the self-oscillating parallel resonant inverter with lamp loads can be naturally modeled as a relay system with negative hysteresis. Based on this formulation, the self-oscillating frequencies of the circuit are found via the time-domain-based Hamel locus. Also, the predicted self-oscillating frequencies via the describing function approach and the Hamel locus approach are compared with the prototype measurement results. It turns out that the accuracy of the frequency prediction via the Hamel locus approach is high, while the accuracy via the describing function approach is circuit Q-value dependent.

26 citations

Journal ArticleDOI
TL;DR: In this article, the dependence of periodic orbits on the parameters of autonomous systems with piecewise linear character-istic functions has been analyzed for two and three dimensions, and a first harmonic bifurcation diagram associated with the periodic orbits of such systems is obtained for two-and three-dimensional systems.
Abstract: The describing function method (used normally as a first approximation to study the existence and the stability of periodic orbits) is used here to analyze the dependence of periodic orbits on the parameters of autonomous systems. The method can be applied to a large class of nonlinear systems but, for simplicity, attention here is paid to a class of single-input, single-output control systems with a piecewise linear character- istic function. A first approach to the bifurcation diagram associated with the periodic orbits of such systems, called a first harmonic bifurcation diagram' is obtained for two and three dimensions. This diagram in two dimensions describes all the qualitative behaviour of such systems. Although this is not the case in three dimensions, the information contained in the corresponding first harmonic bifurcation diagram is of great value. It shows much of the complexity of the periodic structure that can be found in such three-dimensional systems; in fact, part of the first harmonic b...

26 citations

Journal ArticleDOI
TL;DR: A survey of methods for localization of hidden oscillations in dynamical systems can be found in this paper, where Hilbert's sixteenth problem for quadratic systems, Aizerman's problem, and Kalman's problem on absolute stability of control systems, and chaotic hidden attractors are considered.
Abstract: The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described

25 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847