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Proceedings Article•DOI•

Harmonic analysis of RC-active phase shift oscillators

John Taylor1•
University of Bath1
17 Nov 2008-pp 1131-1134
TL;DR: The proposed method introduces the truncated harmonic transfer function (THTF) which is related to the two-sinusoidal-input describing function (TSIDF) of non-linear control theory and allows accurate calculation of the distortion terms in oscillator systems containing higher signal levels and therefore higher levels of nonlinearity than is possible with conventional methods.
Abstract: This paper describes a significantly improved method for calculating the harmonic distortion content of active-RC phase shift oscillators. The proposed method introduces the truncated harmonic transfer function (THTF) which is related to the two-sinusoidal-input describing function (TSIDF) of non-linear control theory. This allows accurate calculation of the distortion terms in oscillator systems containing higher signal levels and therefore higher levels of nonlinearity than is possible with conventional methods. The method is quite general in its application and this paper considers both cubic and quadratic nonlinearities. The method is demonstrated using examples employing the Wien RC-bandpass oscillator with a quadratic nonlinearity.
Citations
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Journal Article•DOI•
Design and implementation of op-amp-rc sine wave oscillator

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Khalid Awaad Humood, Adham Hadi Saleh, Wurod Qasim Mohamed
01 Mar 2015
TL;DR: In this paper, a proposed design of sine wave oscillator type RC phase shift has been performed using three approaches: theoretically using the basic theorems used to generate oscillations, such as the condition of oscillation criteria, and simulation technique (multisim11).
Abstract: The oscillator is a form of frequency generators which can be generate a sinusoidal wave with constant frequency and amplitude. The frequency oscillator can be considered as a one of basic circuits, which must be existing in most electrical, electronic, communication circuits and systems. In this paper, a proposed design of sine wave oscillator type RC phase shift has been performed using three approaches. The first approach proposed design is done theoretically using the basic theorems used to generate oscillations, such as the condition of oscillation criteria. Secondly it is done using simulation technique (multisim11). Thirdly the simulated design is implemented practically using single operational amplifier with passive elements such as resistors & capacitors. All the obtained results from the above three approaches (3.800 kHz, 3.510 kHz & 3.600 kHz respectively) are seems to be equal approximately. These obtained results from the designed oscillator were very encouraging.
References
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Book•
Microelectronic circuits

[...]

Adel S. Sedra
01 Jan 1982

1,413 citations

Book•
Multiple-Input Describing Functions and Nonlinear System Design

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Arthur Gelb, Wallace Earl Vander Velde
01 Jan 1968
TL;DR: The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control, but these theories do not, however, lay to rest all questions of importance to the control engineer.
Abstract: ABRAMSON Information theory and coding BATTIN Astronautical guidance BLACHMAN Noise and its effect on communication BREMER Superconductive devices BROXMEYER Inertial navigation systems GELB AND VANDER VELDE Multiple-input describing functions and nonlinear system design GILL Introduction to the theory of finite-state machines HANCOCK AND WINTZ Signal detection theory HUELSMAN Circuits, matrices, and linear vector spaces KELSO Radio ray propagation in the ionosphere MERRIAM Optimization theory and the design of feedback control systems MUUM Biological control systems analysis NEWCOMB Linear multiport synthesis PAPOULIS The fourier integral and its applications R. N. BRACEWELL) STEINBERG AND LEQUEUX (TRANSLATOR Radio astronomy WEEKS Antenna engineering PREFACE The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, lay to rest all questions of importance to the control engineer. The designer of the attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less value to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way …

1,244 citations

"Harmonic analysis of RC-active phas..." refers background or methods in this paper

  • ...The oscillation frequency (fundamental) and amplitude can be calculated using the describing function (DF) approach [5]....

    [...]

  • ...The proposed method introduces the truncated harmonic transfer function (THTF) which is related to the two-sinusoidal-input describing function (TSIDF) of non-linear control theory....

    [...]

  • ...In this more complete formulation, which is related to the two-sinusoidalinput describing function (TSIDF), the harmonic components are permitted to have arbitrary amplitudes and phase relationships to the fundamental....

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  • ...The proposed method relates to the two-sinusoidal-input describing function (TSIDF) of non-linear control theory from which a truncated harmonic transfer function (THTF) is derived....

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  • ...This more complete formulation is related to the twosinusoidal-input describing function (TSIDF) [5] and is referred to as the truncated harmonic transfer function (THTF) of the network....

    [...]

Book•
Microelectronic circuits, 2nd ed.

[...]

Adel S. Sedra, Kenneth C. Smith
01 Jan 1987

392 citations

"Harmonic analysis of RC-active phas..." refers background in this paper

  • ...For oscillation to occur, the Barkhausen Criterion must be satisfied [7]....

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Journal Article•DOI•
On the design of voltage-controlled sinusoidal oscillators using OTAs

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Ángel Rodríguez-Vázquez1, Bernabe Linares-Barranco1, José L. Huertas1, Edgar Sanchez-Sinencio2•
University of Seville1, Texas A&M University2
01 Feb 1990-IEEE Transactions on Circuits and Systems
TL;DR: In this paper, a unified systematic approach to the design of voltage-controlled oscillators using only operational transconductance amplifiers (OTAs) and capacitors is discussed, and two classical oscillator models, i.e., quadrature and bandpass-based, are employed to generate several oscillator structures.
Abstract: A unified systematic approach to the design of voltage-controlled oscillators using only operational transconductance amplifiers (OTAs) and capacitors is discussed. Two classical oscillator models, i.e. quadrature and bandpass-based, are employed to generate several oscillator structures. They are very appropriate for silicon monolithic implementations. The resulting oscillation frequencies are proportional to the transconductance of the OTA, and this makes the structures well-suited for building voltage controlled oscillators (VCOs). Amplitude stabilization circuits using both automatic gain control (AGC) mechanisms and limitation schemes are presented. The circuits are compatible with the transconductance amplifier capacitor oscillator (TACO). Experimental results from bipolar breadboard and CMOS IC prototypes showing the potential of OTA-based oscillators for high-frequency VCO operation are included. >

133 citations

"Harmonic analysis of RC-active phas..." refers background or methods in this paper

  • ...The inherently wider bandwidth of OTAs makes them suitable for sinewave generation at higher frequencies and confers other advantages as well, for example frequency control by means of a single resistor [3], [4]....

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  • ...A more sophisticated approach considers the response of G when driven not only by a fundamental sinusoid, as assumed in [3], but also by the harmonics of the sinusoid, fed back and filtered by the action of the oscillator phase shift network....

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  • ...This is the approximate approach described in [3]....

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  • ...This method has been used in the literature for oscillator design and although it is accurate at the fundamental the results for the harmonics are very approximate, especially for signal amplitudes greater than about 50 mV [3]....

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Journal Article•DOI•
Operational amplifier circuits for the Wien-bridge oscillator

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A. Budak1, K. Nay1•
Colorado State University1
01 Sep 1981-IEEE Transactions on Circuits and Systems
TL;DR: In this paper, the magnitude and phase response of the Wien-bridge oscillator were adjusted to keep the poles on the imaginary axis at much higher frequencies than is normally expected, thus extending the range of operation of the oscillator.
Abstract: As the frequency of operation increases, the poles of the Wien-bridge oscillator depart from the imaginary axis because of the frequency dependence of the amplifier gain. By properly shaping the magnitude and phase response of the amplifier, it is possible to keep the poles on the imaginary axis at much higher frequencies than is normally expected, thus extending the range of operation of the oscillator. Experimental results verify the vast improvement that is predicted.

34 citations

"Harmonic analysis of RC-active phas..." refers background in this paper

  • ...A number of RC-active circuits exist for the purpose using operational amplifiers (op-amps) as the gain block [1], [2] and more recently employing operational transconductance amplifiers (OTAs)....

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