The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> Right or wrong ?
https://designers-guide.org/forum/YaBB.pl?num=1211465502

Message started by buddypoor on May 22^nd, 2008, 7:11am

Title: Right or wrong ?
Post by buddypoor on May 22^nd, 2008, 7:11am

Title: Re: Right or wrong ?
Post by Eugene on May 22^nd, 2008, 8:22am

Good question.

I believe the answer to your question lies in the fact that your ideal inverting amplifier has no dynamics; it is a purely static device. You are asking the simulator to solve a simple linear algebraic problem that has a unique finite solution regardless of the sign of the feedback. I suspect a transient simulation of this circuit would also converge. My point is that the sign of the feedback is irrelevant when there are no energy storage element to introduce delays as a perturbation propagates around the loop. Also, since the DC analysis ignores energy storage elements, the simulator still finds an operating point even when the feedback in a dynamic system is positive. However, in that case if you were to run a transient simulation you would quickly see the problem, probably as a convergence error.

Title: Re: Right or wrong ?
Post by buddypoor on May 22^nd, 2008, 9:44am

Eugene, thank you !

Sorry, but I´ve made a typing error. The gain is in both cases negative (-R2/R1) .

More than that, I forgot to mention that I´ve used no ideal but a real 2-pol-opamp model (with delay terms).
During TRAN analysis the output voltage saturates immediately.

budypoor

Title: Re: Right or wrong ?
Post by sheldon on May 22^nd, 2008, 12:31pm

Buddy,

Maybe I am misunderstanding things but, the question you seem
to be asking the simulator in the ac analysis is,

If I can enforce this operating point, what would the small
signal characteristics of the circuit be?

This is a perfect good question to ask a simulator and it gives
a reasonable result.

The point that the transient analysis is making is that the
operating point only exists for an instant before the large signal
effects of positive feedback, mismatch, noise, etc. take effect and
force the output into the power supply.

An experiment to try would be to perform the ac analysis at small
time intervals as the circuit latches and watch the time progression
of the gain.

Another point would be that while you can calculate it and the results
are valid, practically, the circuit will not operate at that point. It will only
pass through the point on the way to railing, latching up.

In the end, it may not be a question of right or wrong, rather a
question of relevant or irrelevant. The transient analysis is telling you
that the circuit can not be used in this configuration even it is well
behaved in ac analysis.

Finally, in this case the results may be of limited utility. However,
if you were actually designing a latch, the results would be interesting
because latch time is related to the gain.

Some thoughts for what its worth.

Best Regards,

Sheldon

Title: Re: Right or wrong ?
Post by Eugene on May 22^nd, 2008, 9:51pm

Buddypoor,

You say the AC analysis gives the correct gain. I assume you mean low frequency gain. One does not assess stability only by DC gain. Does the Nyquist plot of the loop gain encircle the Nyquist point in the clockwise direction? If you have an unstable "open loop" system, does the Nyquist plot encircle the Nyquist point once for every open loop pole in the RHP?

When you make that assessment, be sure to start with a very low frequency so that you can see the effects of the positive feedback. Sometimes you need to know where the Nyquist plot starts to know whether you encircled the Nyquist point.

I would bet that if you carefully examined the Nyquist plot you would see that the AC analysis indeed predicts instability when you reverse the sign of the feedback.

Title: Re: Right or wrong ?
Post by vivkr on May 22^nd, 2008, 11:29pm

buddypoor wrote on May 22^nd, 2008, 7:11am:

Hi, everybody !

I have a more or less philosophical question regarding positiv analog feedback.

Imagine we have a simple opamp inverter circuit with a resistive voltage divider in the feedback path.
The gain is simply G=-R2/R1.

Now, the opamp terminals are interchanged and we have positive feedback.

A SPICE ac-simulation of this circuit gives a quite good operating point at 1/2 VSS and results in a voltage gain
of G=+R2/R1

Now my question: Is this result (a) correct (b) false or (c) something else ?

In addition to what all the others have already said before, I would like to add that you are computing your amp gain with a very simple model (ideal gain with no poles)
while your simulation model is more realistic and latches.

The above calculation as Sheldon pointed out is mathematically correct but irrelevant in practical terms. If you could indeed build a true pole-free amplifier and bias it at the correct operating point, you might get the behavior you calculate, but since the first is impossible (in any case due to the finite speed of light), the resulting expression for closed-loop gain is irrelevant.

Regards
Vivek
(Of course I know, that this can´t be measured and that a TRAN analysis would fail).

Expecting your opinion
Regards
buddypoor

Title: Re: Right or wrong ?
Post by buddypoor on May 23^rd, 2008, 8:17am

Thank you to all contributors. As I´ve mentioned at the beginning – it is a question of more or less philosophical nature. My point of interest was only how to characterize results of ac simulations for unstable systems. Of course, we all know that in reality an opamp circuit with only pos. feedback will not function as an linear amplifier.

Here are some further comments from my side:

Sheldon: In the end, it may not be a question of right or wrong, rather a question of relevant or irrelevant.

From your assessment I would conclude that the result of an ac simulation is correct, but irrelevant as it assumes conditions which are not realistic (noise free, ideal constant supply)

Eugene: You say the AC analysis gives the correct gain. I assume you mean low frequency gain. One does not assess stability only by DC gain.

No, the ac analysis indicates stable operation also for higher frequencies, but the phase goes up with rising frequencies. This, of course, together with the 180 deg phase shift at low frequencies - in spite of feeding the plus terminal – looks a bit contradictory.
By the way: Handmade calculations using classical formulas give the same result as AC analyses with simulation programs.

Eugene: I would bet that if you carefully examined the Nyquist plot you would see that the AC analysis indeed predicts instability when you reverse the sign of the feedback.

Yes, no surprise, the open loop response indicates instability !

Vivkr: I would like to add that you are computing your amp gain with a very simple model (ideal gain with no poles) while your simulation model is more realistic and latches.

No, as already mentioned, I have used a two-pole opamp model.

The above calculation as Sheldon pointed out is mathematically correct but irrelevant in practical terms.

Yes, agreed.
___________________________________________________

Finally, let me formulate something like a mechanical analogon:
Put a small ball upon another ball (which may be larger). Under ideal conditions (no air movement, both centres of mass exact perpendicular, no other disturbances) the system will not loose balance. I guess a similar effect happens in the opamp with positive feedback.

Perhaps it is surprising, but the results of ac simulations of unstable opamp circuits are not completely useless. Presently, I am investigating a method to calculate phase and gain margins of feedback systems via ac analyses without opening the loop. And in this context play unstable feedback loops and their ac behaviour a certain role.

Thank you again.