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https://designers-guide.org/forum/YaBB.pl Design >> Analog Design >> Condition of oscillation https://designers-guide.org/forum/YaBB.pl?num=1211963589 Message started by buddypoor on May 28th, 2008, 1:33am |
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Title: Condition of oscillation Post by buddypoor on May 28th, 2008, 1:33am Hello to everybody, I wonder if there is a criterion for harmonic oscillation of a circuit with feedback which is sufficient. We all know that the Barkhausen formula is only a necessary condition for a circuit to oscillate. (Counter example: A notch filter connected with a positive amplifier in a loop can have a loop gain AL=1 and is not able to produce sustained oscillations). I donīt ask for any conditions/requirements for safely starting oscillations (loop gain AL >1). Thatīs another subject. My question is simply: Is there any mathematical formulation of a condition to be met in addition to the known requirement AL=1 which can be considered as a sufficient condition for sustained oscillation ? Up to now, I didnīt see any formulas or something like this in textbooks or papers. buddypoor |
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Title: Re: Condition of oscillation Post by Eugene on May 28th, 2008, 6:26pm For sustained oscillation, I think you also need a nonlinearity in the loop that reduces the gain as the signal amplitude increases. Otherwise, unless you place the closed loop poles EXACTLY on the imaginary axis (which is impossible in real circuits), the oscillations either die out or grow without bound. You might try reading up on describing functions. They do not cover all possible unstable nonlinear systems but they may give you some insight into the sufficient conditions you seek. |
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Title: Re: Condition of oscillation Post by buddypoor on May 29th, 2008, 1:22am Hi Eugene ! Thanks for your reply. However, your answer doesnīt meet exactly the subject of my question. Most probably I have missed to express myself clearly. Quote: For sustained oscillation, I think you also need a nonlinearity in the loop that reduces the gain as the signal amplitude increases. I am aware of this, and in my inquiry I have tried to exclude this additional requirement from the formulation of the problem. I know that such a nonlinearity always is necesssary ! Ohh no ! There is one exception: the double-integrator loop, I have discussed this specific problem in this forum some weeks ago. The topic (theory of harmonic oscillators) has startet on Jan 15th. I fight for the fact, that this circuit does not need any nonlinearity for producing sinusoidal signals. But thatīs another point. Quote: You might try reading up on describing functions. They do not cover all possible unstable nonlinear systems but they may give you some insight into the sufficient conditions you seek. No, I donīt think that describing functions can answer the question. The reason: (1) The DF rely on non-linearities and cannot give cause to start oscillation, (2) I think, the DF principle requires a lowpass behaviour of the frequency dependent part of the circuit. There are enough oscillator counter examples without lowpass characteristics (notch and allpass oscillators). Thanks again. Buddypoor |
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Title: Re: Condition of oscillation Post by buddypoor on May 29th, 2008, 5:27am Sorry, but I have to correct myself just for clarification - as far as the double-integrator loop is concerned. I did express myself in a misleading way: I know that such a nonlinearity always is necesssary ! Ohh no ! There is one exception: the double-integrator loop, I have discussed this specific problem in this forum some weeks ago. The topic (theory of harmonic oscillators) has startet on Jan 15th. I fight for the fact, that this circuit does not need any nonlinearity for producing sinusoidal signals. But thatīs another point. In fact, the double-integrate oscillator needs a non-linearity caused by the limited supply voltage. However, it comes not into saturation ! As soon as a very small amount of clipping occurs the created harmonics of the fundamental frequency cannot sustain. Therefore, the signal returns to the fundamental frequency only. However, my basic question remains as it was: Is there an oscillation condition which is sufficient ??? |
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Title: Re: Condition of oscillation Post by buddypoor on Jul 13th, 2008, 8:13am However, my basic question remains as it was: Is there an oscillation condition which is sufficient ??? I like to repeat my question to all analog oriented members: Does really nobody has heard about a book or another contribution containing a formula or something else which can serve as a sufficient condition for an electronic circuit to produce sustained sinusoidal oscillations ? This would be surprising for my opinion. Regards |
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Title: Re: Condition of oscillation Post by loose-electron on Jul 15th, 2008, 5:38pm This is essentially a control systems problem. Additive gain and phase around a loop eseentially. Not really sure what the big deal is??? |
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Title: Re: Condition of oscillation Post by buddypoor on Jul 16th, 2008, 12:26am loose-electron wrote on Jul 15th, 2008, 5:38pm:
Of course, it is a "control system problem". Sorry, but I donīt understand the meaning of the next two sentences. |
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