Harmonic Oscillator with ideal Opamp models

Hello, I have a question to all who are involved in electronic circuits.


However, the question is not techical but more or less linguistic and concerns the
general speech comprehension.


Problem description: There are some configurations (I avoid the term „electronic circuits“) that exhibit oscillatory properties during transient simulations (in fact: they show self-sustained sinusoidal oscillations). However, only if IDEAL opamps are used. Therefore, only simulations can reveal threse properties.
As soon as real opamp models are used (at least one pole in the open-loop frequency response) there are no oscillations.
Instead, the amplifier output saturates immediately, because the mentioned amplifier pole is shifted to the right half of the s- plane (RHP).


The problem touches the validity of the well-known oscillation condition (Barkhausen) - and the question is simply:

Based on the general speech comprehension - should such a special configuration be called „circuit that is able to oscillate"? Even, if this is the case for ideal (artificial) models only?
Thank you
LvW

I believe you can make an oscillator with non-ideal opamps. I'm not really sure what your question is.

barry said:

I believe you can make an oscillator with non-ideal opamps. I'm not really sure what your question is.

Click to expand...

Thank you for answering.
You don't know what the question is?
I repeat my last semtence:
Based on the general speech comprehension - should such a special configuration be called „circuit that is able to oscillate"? Even, if this is the case for ideal (artificial) models only?

LvW

Hello,
I am afraid that I have expressed myself not clear enough.
Therefore, I will reformulate my question:

1.) Assume that there is an electronic circuit (hardware) that is not able to oscillate - in spite of unity loop gain at one frequency f=fo only. This is neither a surprise nor a failure of Barkhausen’s criterion because this rule is only a necessary one.
2.) Surprisingly, if this circuit is transferred to a simulation program and if an ideal opamp model (gain not frequency dependent) is used, the output shows a sinusoidal signal having a frequency fo. (By the way, I can explain this fact - but that is not my question).

Now the question:
Can that circuit be regarded as an oscillator in accordance with Barkhausen’s criterion: Yes or no?

Thank you
LvW

No!, Barkhausen's criterion have 2 condition:
1. Gain is >=1 and phase is 0/180 degree. that means positive feed back.
If Ideal opamp is having unity gain even though it is not able to oscillate untill its gives, 0/180 degree of phase shift.

Hope you can get my explanation.

varunkant2k said:

No!, Barkhausen's criterion have 2 condition:
1. Gain is >=1 and phase is 0/180 degree. that means positive feed back.
If Ideal opamp is having unity gain even though it is not able to oscillate untill its gives, 0/180 degree of phase shift.
Hope you can get my explanation.

Click to expand...

Thanks for reply - however, I didn't get your explanation.
As I have mentioned - Barkhausen's condition is met by both alternatives (opamp real resp. ideal).
But only one configuration shows (by simulation) oscillatory behaviour.

Oscillation occurs:
why? system is positive f/b: even a very small amplitude signal amplifies and starts oscillating
Why not: system is damped enough to die down the output signal. [It is negative f/b and have phase <2*pi*n (n = 0,1,2,)]

so case 1:
Ideal opamp with,
gain >/= 1 and 0 degree phase: will oscillate;
gain < 1 and 0 degree phase: will not oscillate;

Hope something you can get.
Better refer some references for stability. That will be helpful

varunkant2k said:

so case 1:
Ideal opamp with,
gain >/= 1 and 0 degree phase: will oscillate;

Click to expand...

Don't you mean 180 degree phase shift? zero degree phase shift won't oscillate.

Back to the original question, you've only stated that your real opamp has unity gain, but you haven't specified the feedback phaseshift. Also, since the other part of the requirement for oscillation is equal-or-greater than gain of 1, if your real opamp circuit is unity gain even a tiny change in gain (below unity) will stop oscillation. In your simulation if you specify G=1, it will be EXACTLY 1; that's not the case in the real world.

barry said:

Don't you mean 180 degree phase shift? zero degree phase shift won't oscillate.
Back to the original question, you've only stated that your real opamp has unity gain, but you haven't specified the feedback phaseshift. Also, since the other part of the requirement for oscillation is equal-or-greater than gain of 1, if your real opamp circuit is unity gain even a tiny change in gain (below unity) will stop oscillation. In your simulation if you specify G=1, it will be EXACTLY 1; that's not the case in the real world.

Click to expand...

Barry, thanks for reply - however it does not answer my question at all.
I am rather familiar with oscillator circuits - and, in particular, with conditions for oscillation. Please, read my reply #4 carefully, and you will see that I did not speak about a unity gain opamp, but rather on the well known oscillation criterion which requires unity loop gain. That's a big difference.

I repeat: I have no technical problems because I can explain the behaviour. My (probably small) problem is: How to describe the circuit - as an "oscillator" or not?
As mentioned in my first posting - it is more or less a "linguistic" question. For example, because "english" is not my mother tongue I don't know exactly if an arrangement of parts that includes an artificial (non-existing) part like an ideal opamp may be called "circuit" ? Or does the term "circuit" imply that it can exist as hardware unit?
Thanks
LvW

it might help if you explain where the osciallation is actually coming from.

Keep in mind that DDS systems are often called "numerically controlled oscillators". a gain of 1 doesn't seem to apply here either.


also, given that terminology is fluid (eg mf/mmf vs uf/nf), I'd say you'd be able to find a mixture of people who give the model various names -- osciallator, oscillatory, degenerate case, limit-cycle, etc...

This seems to fall under the category of concepts we sometimes use as a reference for real world devices:

ideal resistor (noiseless, infinite watt rating)
ideal capacitor (zero loss of charge, zero ESR)
ideal inductor (zero capacitance, never saturates)
ideal amplifier (straight wire with gain)
ideal transistor,
etc.

As we know, these don't exist in real life. Nevertheless they are useful concepts which we compare with real life behavior. Thus we are better able to understand real life devices.

We have the ideal op amp with its various characteristics. Infinite gain, infinite bandwidth, infinite slew rate, etc.

Perhaps these concepts ought to include the characteristic you bring up. Ability to sustain oscillations in the configuration you described.

Somewhere there ought to be a list of circuits that (a) work even though they shouldn't, and we don't understand why, and (b) circuits that don't work even though they should, and we don't understand why. However most of the time it happens due to real life characteristics and we can explain why a circuit does or doesn't work. If I could think of a good example off the top of my head, I'd bring up one that fits (a) or (b) above.

I think it's O.K. to name the construct comprised of ideal components a circuit, even it can't be implemented with real devices. But it would be reasonable to state the circuit's purpose very clearly, e.g. as a border case to demonstrate a principle. An the reader would want to know about possible utilizations, e.g. necessary modifications to turn the "theoretical" in a real oscillator.

Finally, I would prefer an illustrative example of the said circuit category.

BradtheRad - thank you.
I think you've understood the core of my my problem - and I agree to your examples. I`ll try to find a trade-off for my description of that particular circuit under discussion.
Thank you all for today.
LvW

---------- Post added at 21:57 ---------- Previous post was at 21:55 ----------

FvM, thanks for your suggestions.
I will present an example (or two) very soon.

As promised yesterday, here are two examples illustrating my explanations/comments/statements in former postings (see pdf attachement)
Contrary to the examples as mentioned by BradtheRad (pointing to the fact that we always live with idealizations and simplifications) these two examples reveal a fundamental difference between ideal and real: Ideal works and real not at all !

Finally, I like to repeat: I do not need explanations "why or why not" because I can explain the behaviour. My only concern is if it is allowed to use the terms "amplifier" resp. "oscillator" for the "circuits" as shown in the attachement.

Perhaps it is interesting to add the following: There is an article from A.S.Elwakil (Cairo University) who has very good reputation in the field of analog electronics - published in 2006 (Analog Integr. Circuits and Signal Processing, 48, p 239-245). In this article he is investigating in detail the behaviour of a circuit as shown as example #2 in my attachement. He is using the term "oscillator" and explains what should be done to stabilize the output amplitude.
And - all of this for an amplifier that never can be realized (ideal opamp !). By the way, he does not mention that the behaviour will be completely different for real amplifiers (immediate saturation, no stable operating point).

LvW

Here comes the attachement

Thanks for providing the instructive examples.

I tend to classify both circuits as a kind of simulation artefacts or fake circuits. They only exist due to the properties of the SPICE solver, that doesn't care for the plausibility of it's solution, in this case the gain sign of a feedback loop. This leads to the curosity of a stationary oscillation in transient solution, nevertheless the loop phase has wrong polarity in AC simulation.

Although the SPICE results suggests stable feedback amplifier respectively functional oscillator circuits , you can prove that they aren't referring to other criteria. In my opinion, the point how these circuits are faking functionality isn't primarly ideal component behaviour. The amplifier circuit e.g. still works with limited GBW. It's the simulator's unawareness.

circuit 1: recall that a/(1+ab) really doesn't matter on the sign once the open loop gain is large enough (despite polarity). a model that uses this equation without checking for any boundary conditions will give "correct" linear behavior even when connected backwards... eg 1000/(1000+1) ~= -1000/(-1000+1).

circuit 2: I have to guess the same issue.

recall that a/(1+ab) really doesn't matter on the sign once the open loop gain is large enough

Click to expand...

In which sense the sign doesn't matter? Without doubt in the sense, that you can calculate a solution with consistent node voltages. But not necessarily in the sense, that the solution can be implemented in a functional analog circuit.

Thank you both for replying.

permute said:

circuit 1: recall that a/(1+ab) really doesn't matter on the sign once the open loop gain is large enough (despite polarity). a model that uses this equation without checking for any boundary conditions will give "correct" linear behavior even when connected backwards... eg 1000/(1000+1) ~= -1000/(-1000+1).

circuit 2: I have to guess the same issue.

Click to expand...

Yes, I never claimed that the simulator is wrong. In contrary, each simulation program (even hand calculation) will give the same result, which is correct by 100%.
However, I disagree with you regarding the role of the open loop gain. It does not matter at all how large it is, the only property that matters is the missing time delay in the ideal opamp model.
Thus, there is no error and everything is calculated/simulated correctly. But each real-world amplifier has a delay (time constant). Therefore, these results are totally unrealistic and can never be prooved by measurements.

Quote FvM:The amplifier circuit e.g. still works with limited GBW. It's the simulator's unawareness.

I don't think so. Limited GBW means time delay within the feedback loop leading to realistic results (no stable operating point, output saturation for both circuits)

I don't think so. Limited GBW means time delay within the feedback loop leading to realistic results (no stable operating point, output saturation for both circuits)

Click to expand...

Yes you are right, I confused two different setups. Even a very high GBW makes the OP immediately jump out of it's pseudo bias point.