# Is there a rigorous oscillation criterion?

Discussion in 'General Electronics Chat' started by Winterstone, Jun 19, 2013.

1. ### MrAlWell-Known MemberMost Helpful Member

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Hello Steve,

Looks like Winterstone left us. So i guess it depends on how much you'd like to come up with a list of your own and we can compare lists i guess?

2. ### steveBWell-Known MemberMost Helpful Member

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I'm still interested to think about this, but my approach right now is to study some simulations to understand the nonlinear part, and do that Nyquist type of analysis to understand the linear part.

For example, I just did a simulation last night using your recommended simple opamp model with that problem-ridden circuit. This turned out to oscillate without latching on the rail. So now I'm trying to understand the actual constraints for latching. This is just an academic curiosity for me because we will all agree that the issue can be avoided in practice with the design approach already mentioned.

3. ### MrAlWell-Known MemberMost Helpful Member

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Hi Steve,

Yes that sounds like a good idea. It seems to me that the DC gain less than 1 criterion you had been mentioning kicks in once we go to the practical, because any op amp is bound to have some output DC offset either positive or negative. The theoretical circuit i had been looking at will not have this problem because there is just plain and simple no DC on the output, it's a theoretical zero DC just like the pole pair is a theoretical exactly on the jw axis. In the presents of the tiniest DC though, i think we have to consider your specification that the DC gain has to be lower than 1 because if not it would just ramp the output up (or down) indefinitely until it hit one of the rails.
So for the theoretical model it probably wouldnt matter if the DC gain was 10, as long as there was no DC it cant ever feed back and become a problem.
That's the way i see it so far.

But you know i cant help but think, we've had various opinions come up in this thread now, and they usually turn out to be just different ways of looking at it, and that varies with the person and what they are expecting based partly on what they know already. So i cant help but wonder just who was Barkhausen's audience? If they were beginners in the field or intermediates they might have had little knowledge about these issues and so 1000 questions were bound to come up. But what if they were highly educated and experienced in the field. Maybe he took it for granted that they would surely know that there has to be a little more to it than that (his two conditions for oscillation) such as start up conditions and DC feedback and such. Maybe that's the way he was thinking when he wrote his formulas. He assumed the target audience knew enough about this so he did not have to spell every little thing out in black and white. On the other hand, i can also see that questions come up for almost everyone at one time or another regarding his criterion, and it's often talked about as if he was "wrong". Was he really wrong or was it just that he assumed a minimum level of proficiency, which would then mean he considered everything else obvious.

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5. ### ericgibbsWell-Known MemberMost Helpful Member

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hi Al, Steve,

This lecture pdf has some interesting points covering Barkhausen.

I find this comment from the pdf amusing.

Know Barkhausen Criteria to satisfy interviewers questions but use CECO to design sinusoidal oscillators.

Eric

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6. ### MrAlWell-Known MemberMost Helpful Member

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Hello Eric,

Yes that's an interesting paper too. He talks about using non linearity to force the circuit to oscillate. That's what we were thinking about for the practical circuit.

But the more i read this stuff now the more i cant help but think Barkhausen must have known that every circuit cant be exactly as he stated because he must have built oscillators before he wrote his papers. And as everyone here knows, all it takes is to build ONE oscillator and they will quickly see that it's impossible to build an oscillator with a pole pair on the jw axis that STAYS on the jw axis, and also maintain a gain of 1 (or -1 depending on the viewpoint) that also stays like that forever. So he must have been after the bare minimum theoretical specification for an oscillator. To that end, i think he succeeded. So rather than call him outright "wrong" i think he deserves much more respect than that. It appears that maybe he just did not want to have to dig down into the grim details because there are so many possibilities once we leave the purely theoretical.

7. ### ericgibbsWell-Known MemberMost Helpful Member

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hi Al,

I think your post sums it up quite clearly.

I was called 'names' for thinking in terms of practical oscillator design in considering the effect of the temperature parameter.

As you say if we designed an oscillator that had the poles on the jw axis, the smallest change in component temperature could move the poles into the LHP and the oscillation would cease.

I guess it might be interesting to 'know' the so called system design for 'rigorous criteria'.

But would a practical engineer use that system design criteria to create an oscillator design, I think it would be very unlikely.

I suspect Barkhausen came to the same conclusion.

Eric

Last edited: Jul 4, 2013