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 don´t ask for any conditions/requirements for safely starting oscillations (loop gain AL >1). That´s 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 didn´t see any formulas or something like this in textbooks or papers.

buddypoor

Hi Eugene !
Thanks for your reply.
However, your answer doesn´t 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 that´s 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 don´t 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

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

loose-electron wrote on Jul 15^th, 2008, 5:38pm:

Of course, it is a "control system problem". Sorry, but I don´t understand the meaning of the next two sentences.