During the study of the phase margin of linear systems, this criterion is often suggested by students grasping for an intuitive understanding of stability. Unfortunately, although counterexamples are easy to provide, I do not know of a satisfying disproof to the Barkhausen Stability Criterion that combats this intuition. Some textbooks even state the Barkhausen Stability Criterion although none refer to it by name. In their introduction of the Nyquist Stability Criterion, Chestnut and Meyer state If in a closed-loop control system with sinusoidal excitation the feedback signal from the controlled variable is in phase and is equal or greater in magnitude to the reference input at any one frequency, the system is unstable. The history of the Barkhausen Stability Criterion is an unfortunate one. This equation was originally intended for the determination of the oscillation frequency for use in radio transmitters.
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There are two types of approaches to generate sine waves Using resonance phenomena This can be implemented with a separate circuit or using the non linearity of the device itself By appropriately shaping a triangular waveform. Multivibrator is a circuit which generate non sinusoidal wave forms such as square, triangular, pulse e. Oscillators are circuits which generates sinusoidal wave forms.
Multi vibrators are basic building blocks in function generators and nonlinear oscillators whereas oscillators are basic building blocks in inverters. Often feedback network consists of only resistive elements and is independent of frequency but amplifier gain is a function of frequency.
At that frequency overall gain of system is very large theoretically infinite. Noise at the input of amplifier consists of all frequencies with negligible amplitudes.
For all frequencies other than the oscillator frequencies the amplifier gain will not be enough to elevate them to significant amplitudes. But at that frequency where oscillator oscillates it provides very large gain and the amplitude of corresponding sine wave will be limited by the nonlinearity of the active device. The frequency of oscillation depends mostly on few circuit parameters such as passive elements such as resistance, inductance, and capacitance e.
The principle cause of drift of these circuit parameters is temperature. Therefore compensation measures should be taken for balancing temperature induced variations. Leave a Reply Your email address will not be published.
Critère de stabilité de Barkhausen