Is there a rigorous oscillation criterion?

[MrAl]

Hello again,


Let me try to pinpoint the problem.

If you read Electricians post you'll see that he mentions that the Barky criterion does not always work. That's the general impression i got too.

If you read my last post #4 i tried to outline what was wrong. The procedure i outlined was meant to show what is wrong here as well to provide an avenue to a solution.

The very first thing that is wrong is that of the amplitude itself. With loop gain 1 (or other simplified criterion) that is not sufficient because we can not know what the output amplitude is going to be. This is a very strange problem that does not usually come up in other analyses, and that is because we usually have an input. In the oscillator circuit, the perfectly linear one, we have NO input because the input is supposed to come from the output. But when we first turn on, there is no output, so we have no idea what the input is and hence we have no idea what the output really is. I would like to call this problem #1 but usually we look at the gain first so maybe we should call it problem #2, but the problem with calling this problem 2 is that we have to know what to do about this from startup too just like the gain. So i will just refer to this problem as "The Amplitude Problem". I take the time to point this out because this is very important yet we do not see this in other circuits too much for the reasons mentioned.

So we have two problems, the AMPLITUDE problem and the GAIN problem. The GAIN problem is usually solved beforehand without too much trouble though. And please dont get me wrong, when i state the AMPLITUDE problem i do not talk about the non linear portion of the oscillator which controls the amplitude. To make sure i have this explained i will show a brief little example. This example may not show all the variables for simplicity.

In most circuits we have something like this:
Vout/Vin=f(R,C,L,s)

but in an oscillator we only have this:
Vout=f(R,C,L,s)

and what this means in the real world is that we dont know what we get out really. It could be:
Vout=0.1
Vout=1
Vout=5
Vout=100
etc.

And obviously Vout=0.000001 would not do us much good because even if that oscillator tried to put that out other parasitics could swamp it out completely and thus even though it could theoretically do that it doesnt work.

So that is the AMPLITUDE problem. We simply can not calculate this, and that is a problem as you can see. We can not calculate the output to be any particular value, and we need that. We have to know for sure what our oscillator puts out. If we need 3v out, we need 3v out. But if we cant calculate this, we can never know. But we can control the output using the loop gain.

The other problem is the placement of the poles, ie the POLE PLACEMENT PROBLEM. We have to know what the frequency output will be. This is something which we can calculate to some degree, usually pretty accurately. The problem here is that in practice we have a hard time keeping the pole placement in exactly the right place because of component variations over time and temperature for example. Once the pole position changes, we loose the oscillation one way or another.
But we do get a little lucky here, because the pole placement can be done using the gain of the circuit as a control variable. By controlling the gain in the loop we can control the pole placement.

Now examining these two problems, we see that both problems are controlled by the loop gain. So what we do is build a circuit where we control the gain and this solves the problem. But a little sub problem still exists because we still dont know what the amplitude is during start up. So we can call this the STARTUP problem.

So we have three problems in total:
1. The pole placement problem.
2. The amplitude problem.
3. The startup problem.

To address the startup problem, we maintain that the pole pair position is slightly into the RHP. It has to be far enough into the RHP to accommodate the component variations but also to ensure a timely startup. Too close to the jw axis and it could theoretically take 100 million years to start up. So this is where the first 'rigor' comes in. Calculating the sensitivities to components and other variations and making sure that the pole position meets that criterion so we get fast enough start up.

To address the amplitude problem we of course use a limiter. With the startup problem properly addressed, the limiter controls the output voltage Vout.

To address the pole position problem we get lucky because the limiter acts as a gain control. Thus, we get control over the pole position for free because we use the limiter for this too.

So what i wanted to bring out here was that we could analyze these three points of circuit operation and come up with a rigorous analysis that should show that we can always get oscillation if we construct the circuit correctly. Reviewing the above we can see that:

The pole position has to be controlled with the limiter,
The output amplitude has to be controlled with the limiter,
the startup has to be controlled by component design.

Of course in the more basic physics of it we have to also clear up a fourth problem, the ENERGY problem. We have to have sufficient energy going into the circuit in order to make up for component resistive losses.

So my suggestion is that we do a rigorous analysis of the above procedure and then simply walk it backwards to find out what is 'sufficient', if we can find that.

But this post would not be complete without at least one small mention of another point of view. This procedure i have outlined is "my" way of doing it. That doesnt mean it's the only way and i may not be the only one ever to try to do this (i know pole position placement is not new), and a question that still comes up in my mind is that is there a rigorous purely linear method out there somewhere. There very well could be. I dont have access to such a writeup however so i cant help any more than that unless someone else comes up with a better idea then i could help work out the solution. I would also ask how we could use such an analysis on the more typical non linear gain controlled oscillator. If a purely linear oscillator is too complicated we would not want to use it to replace all of our non linear ones anyway.

 

[Winterstone]

Hello MrAl, thank you for the long contribution.
Perhaps I should have mentioned that I am involved in such oscillator circuits since a long time (hardware and simulation).
Thus, I am familiar with the typical problems like pole placement, tolerances, amplitude stabilization, gain control, startup conditions, etc.
And that is exactly the background of my question. After reading several documents and relevant book chapters I am convinced that the Barkhausen criterion is a necessary condition only.

That means: Barkhausen is true - and we cannot say "Barky criterion does not always work" (by the way: Why do you say "Barky"?).
Of course, it works - within its known limits (necessary condition).

If you read my last post #4 i tried to outline what was wrong. The procedure i outlined was meant to show what is wrong here ....

I don`t understand what "was wrong"? In your post#4 I could not find a corresponding part that has shown "what is wrong here".
Please, can you clarify?
Regards
W.

 

[steveB]

Hi Winterstone,

I don't think I can offer much more than I've said here. It seems to me that all of us here understand the basics of oscillators and the importance of nonlinearity (or limiting, as MrAl calls it). By the way, a key aspect of the limiting portion of the system is that we don't generate a pure sine wave, but always have harmonics with the fundamental.

I agree the Barkhausen criteria are a necessary condition. This is why I tried to stress that the oscillation condition requires gain=1, even though we all know in practice that we start the gain higher than 1 so the oscillations can start. I think the difference here confuses people, which I think is what MikeML is having trouble with. I don't think we can just dismiss necessary conditions, unless we think the theory is wrong, but I don't think it is wrong in this case.

I personally don't see a way to have a sufficient condition for oscillation if we don't invoke the concepts from nonlinear analysis. I think nonlinearity itself might very well be a necessary condition too, at least from a practical point of view. So my answer (which is only an opinion) is that you can't have a sufficient condition for a linear system, which is why we never read about one. However, we can establish sufficient conditions once we allow nonlinearity. I tried to make a crude list that hints at sufficient conditions, but of course I'm not trying to give a definite answer here. I am just hinting that a powerful mind might be able to rigorously determine a minimal sufficient condition list. The list would start with the Barkhausen Criteria, then the requirement of nonlinearity, and then ... we can continue from there.

Since we can all make an oscillator if we need to, sufficient conditions must exist. But engineers often don't design using logic like this. We just know how to do it and we do it using the basic ideas we've just elaborated on. I just don't think sufficient conditions exist in a purely linear context. I could be wrong, of course, because proving a negative statement is one of the hardest things to do.

So, that's all I can say. I know it falls short of what you are looking for, but I'll keep reading to see if someone can penetrate further into this.

 

[MrAl]

Hello again guys,


Yes Steve that is how i always read it to be too, that non linearity was actually one of the conditions. It may have been a little informal though, but that made sense to me. And it really does not take much to work up a set of conditions that would completely describe how the circuit should work, because there are only a few mechanisms at work and all we have to do is describe them and find the limits So we're looking at a few PDE's i guess. We can do that i guess, but im not convinced that is what Winterstone wants yet anyway. He seems to be after a purely linear solution. Im not even sure if he is willing to accept an amplifier that has non linear characteristics instead of a limiter. BTW the non linear network in the oscillators function as a limiter that's why i call it that. It's function is to limit the output due to the RHP which must be present.

Winterstone:
By 'problem' i mean a problem in the Barky criterion for oscillation. A striking problem is that of the AMPLITUDE. Barky doesnt say whether the output is 1uv, 1mv, or 1000 volts AC. And there is no way to tell what the amplitude of an oscillator will be without introducing a non linearity, and that is because one that is correctly designed will have an output that increases to infinity if there were no limiter. To put it another way, with a gain of 1 as required by Barky we might have oscillation but the amplitude may be so small that it does us no good. But if the amplitude is too small, it may not appear at all, thus we have no oscillation even though we have the required gain.

ALL:
But i guess the question now on everyone's mind is: Is there a way to produce a valley of gain that is frequency dependent, such that if the amplitude tries to increase the frequency increases (or decreases) and that causes more attenuation thus lowering the gain, and if the opposite (amplitude gets too low) the frequency decreases and less attenuation, thus the gain is limited through the frequency dependency of the network. This would require a simultaneous solution for both gain and frequency.
This would look like a circuit who's pole pair moved back and forth across the jw axis very slightly over the entire operating time of the circuit.
I guess then we'd still have to ask if a change in frequency (even though small) would be considered a non linearity.

Oh yeah, i call it "Barky" for short I dont see it as disrespect but as a friendly manner in which to talk about it without typing out the whole name each time.

 

[Winterstone]

Hi Steve,
thank you for your answer.

I agree the Barkhausen criteria are a necessary condition. This is why I tried to stress that the oscillation condition requires gain=1, even though we all know in practice that we start the gain higher than 1 so the oscillations can start. I think the difference here confuses people, which I think is what MikeML is having trouble with.
.

For my opinion, it is sufficient to say that for continuous oscillation we have loop gain LG=1 (due to suitable regulation), whereas during start-up we need a design value LG>1 (because of unavoidable tolerances and other non-idealities that are not considered during design). I think, this covers everything without the danger of misunderstandings.

I personally don't see a way to have a sufficient condition for oscillation if we don't invoke the concepts from nonlinear analysis. I think nonlinearity itself might very well be a necessary condition too, at least from a practical point of view. So my answer (which is only an opinion) is that you can't have a sufficient condition for a linear system, which is why we never read about one. However, we can establish sufficient conditions once we allow nonlinearity. I tried to make a crude list that hints at sufficient conditions, but of course I'm not trying to give a definite answer here. I am just hinting that a powerful mind might be able to rigorously determine a minimal sufficient condition list. The list would start with the Barkhausen Criteria, then the requirement of nonlinearity, and then ... we can continue from there.

Yes, I agree that such a list of conditions that must be fulfilled could be a very good approach - and that`s what I am aiming at primarily. Not - as a first step - a sufficient condition, but rather something like a supplement to Barkhausen`s condition.
I also agree with you that - from the practical point of view - there is no real problem. We know many different circuit concepts that are able to oscillate. However, I am deeply interested in „System and Circuit theory“ - and, therefore, I like to know if there is a (more rigorous) oscillation condition.

Let me add some additional information: There are a few published articles dealing with the so-called „latch-up effect“ for some specific circuits.
One of those circuits is investigated by Elwakil in

https://www.google.de/url?sa=t&rct=...qoGQBw&usg=AFQjCNHJEGcodSqe7RMuv9WMommMDtxdKg

These circuits with feedback start to oscillate with rising amplitudes - however, as soon as the gain is reduced due to some non-linearities the output voltage „latches“ at a fixed voltage (e.g. power rails). And the question raises: Why?
I am pretty sure this effect has something to do with feedback systems that are known to be „conditionally stable“ only.
At the moment, I am investigating a suitable example which can illustrate the whole subject.

Thank you
Regards
Winterstone

 

[The Electrician]

I personally don't see a way to have a sufficient condition for oscillation if we don't invoke the concepts from nonlinear analysis. I think nonlinearity itself might very well be a necessary condition too, at least from a practical point of view..

steveB, are you saying that nonlinearity might be a necessary condition for oscillation to start? If so, why would that be?

 

[Winterstone]

Hello again,

Yes Steve that is how i always read it to be too, that non linearity was actually one of the conditions.

No, that`s not the case. If a circuit with feedback is able to start oscillations because of a pole pair in the RHP it will start with rising amplitudes!
All non-linearities come into play only when the amplitudes reach a certain limit that is set by the regulation mechanism (simple case: supply rail limitation)

He seems to be after a purely linear solution. Im not even sure if he is willing to accept an amplifier that has non linear characteristics instead of a limiter.

What means "not sure if he is willing to accept..."?
Where is the difference? Each suitable non-linear characteristic limits the amplitude.
Regarding linearity: See above (start-up condition).
In my foregoing posts I (repeatedly) have mentioned non-linearity. In principle, it does not matter if you stabilize the amplitude with diodes, FET control or by hard-limiting. This influences the THD only.

By 'problem' i mean a problem in the Barky criterion for oscillation. A striking problem is that of the AMPLITUDE. Barky doesnt say whether the output is 1uv, 1mv, or 1000 volts AC.

No, that`s not a „problem“. You always need a loop gain LG>1 for safe start-up. That`s for sure.
Thus - we always have rising amplitudes. That means, we can have no information about the amplitude, unless we know the properties of the amplitude stabilization circuitry. In some cases, the harmonic balance method gives us a rough information on steady-state amplitudes.
However, I am sure that this has nothing to do with the oscillation condition (main subject of this thread).

But i guess the question now on everyone's mind is: Is there a way to produce a valley of gain that is frequency dependent, such that if the amplitude tries to increase the frequency increases (or decreases) and that causes more attenuation thus lowering the gain, and if the opposite (amplitude gets too low) the frequency decreases and less attenuation, thus the gain is limited through the frequency dependency of the network. This would require a simultaneous solution for both gain and frequency.

I must confess that I don`t understand your thoughts. You want a circuit such „that if the amplitude tries to increase the frequency increases“ ? Normally, everybody who needs an oscillator wants to have an amplitude regulation that does NOT influence the frequency. Frequency stability is one of the key parameters for any oscillator!!

This would look like a circuit who's pole pair moved back and forth across the jw axis very slightly over the entire operating time of the circuit..

That`s what all stabilized oscillators do. The poles cannot be fixed at the imaginary axis. They swing from The RHP to the LHP and back. That has been proofed (theory of control systems).
Nevertheless, thank you for your effort.
Regards
W.

 

[steveB]

steveB, are you saying that nonlinearity might be a necessary condition for oscillation to start? If so, why would that be?

Hello The Electrician,

Thank you, that is a good point to stress.

No, I don't think that would be the right way to say it. The starting condition requires instability and noise, but linear behavior at the start would not interfere with that. We can use linear theory to characterize the starting instability.

However, an unstable perfectly linear circuit that can start an oscillation is not capable of maintaining a stable oscillation because we just have a divergent unbounded solution. Likewise a linear circuit that is perfectly set up to meet the Barkhausen criteria is able to sustain a stable oscillation (although it is marginally stable and not absolutely stable), but it is not capable of starting the oscillation. Note, marginal stability is of no real practical use, but it is relevant mathematically.

Hence, the Barkhausen criteria is necessary, but not sufficient to ensure oscillation. Starting the oscillation has other necessities including (apparently !!!) not meeting the Barkhausen criteria (at least not exactly).

But, a circuit that is approximately linear at the start when the signals are small, and then becomes nonlinear when the signals are larger, is still a nonlinear circuit.

 

[MrAl]

Hello again,



No, that`s not the case. If a circuit with feedback is able to start oscillations because of a pole pair in the RHP it will start with rising amplitudes!
All non-linearities come into play only when the amplitudes reach a certain limit that is set by the regulation mechanism (simple case: supply rail limitation)



What means "not sure if he is willing to accept..."?
Where is the difference? Each suitable non-linear characteristic limits the amplitude.
Regarding linearity: See above (start-up condition).
In my foregoing posts I (repeatedly) have mentioned non-linearity. In principle, it does not matter if you stabilize the amplitude with diodes, FET control or by hard-limiting. This influences the THD only.


No, that`s not a „problem“. You always need a loop gain LG>1 for safe start-up. That`s for sure.
Thus - we always have rising amplitudes. That means, we can have no information about the amplitude, unless we know the properties of the amplitude stabilization circuitry. In some cases, the harmonic balance method gives us a rough information on steady-state amplitudes.
However, I am sure that this has nothing to do with the oscillation condition (main subject of this thread).



I must confess that I don`t understand your thoughts. You want a circuit such „that if the amplitude tries to increase the frequency increases“ ? Normally, everybody who needs an oscillator wants to have an amplitude regulation that does NOT influence the frequency. Frequency stability is one of the key parameters for any oscillator!!



That`s what all stabilized oscillators do. The poles cannot be fixed at the imaginary axis. They swing from The RHP to the LHP and back. That has been proofed (theory of control systems).
Nevertheless, thank you for your effort.
Regards
W.

Hello again Winterstone,


Thanks for mis reading my entire post. It seems like you assumed too much or you just didnt take the time to read it carefully enough.

Quote MrAl:
Yes Steve that is how i always read it to be too, that non linearity was actually one of the conditions.

Quote Winterstone:
No, that`s not the case. If a circuit with feedback is able to start oscillations because of a pole pair in the RHP it will start with rising amplitudes!
All non-linearities come into play only when the amplitudes reach a certain limit that is set by the regulation mechanism (simple case: supply rail limitation)

If you read my post carefully you would have seen that i said that nonlinearity is required for limiting the AMPLITUDE, not the STARTUP.

The problems are:
STARTUP
POLE PLACEMENT
AMPLITUDE
ENERGY

STARTUP comes from the proper initial position of the RHP pair.
POLE PLACEMENT is necessary for start up and continued oscillations.
AMPLITUDE is limited with the non linear portion of the circuit.
ENERGY is required to keep the oscillation going.

Also, stabilized oscillators do not move the pole pair back and forth in the same manner as i was suggesting. They use the non linear gain or limiting. I was suggesting a different method.

I have a feeling you still dont understand this. The AMPLITUDE is a separate problem with Barky, mainly because it is not even mentioned.

Nevertheless thanks for your effort too.

ALL:
It should be clear now that the circuit works like this...

1. The RHP causes the circuit to oscillate and the amplitude increases forever, getting larger and larger.
2. Clamping the amplitude with a non linear device forces the amplitude to stay at a certain level. Side effect is some distortion.
3. Some energy input is required to keep the oscillation going because any real circuit has resistance.

Note that in this view we can keep the pole pair in the RHP and dont have to move it back into the LHP. But the closer we keep the RHP to the jw axis, the less distortion we see. The drawback here is that if the RHP is too close and component variation makes it cross the jw axis, oscillations will decrease and after some time will cease.

But there's no reason why we cant build this *so* close to a linear circuit that it behaves more like a linear circuit than a partially non linear circuit. That would be by varying the GAIN itself. By adjusting the gain we would see as an extremely close approximation to a linear oscillator as we would care to. The gain control would make such small changes to the gain per cycle that for all intents and purposes we would see what looks like a perfect sine wave output.

 

[MikeMl]

You guys are forgetting something:

In order to have oscillation, you must also have an initial perturbation. Perhaps this can come from thermal noise, numeric noise, a turn-on transient, etc. Where-ever it comes from, it has to be there...

Consider the following circuit. It is the well known 3RC oscillator network. It has an attenuation of 1/29 at the frequency where the phase shift is 180 degrees. To make an "oscillator", it would seem to be sufficient to have an amplifier with a gain of -29 to create a loop gain of 1.

Well, if there is no initial perturbation of some node away from a meta-stable state, a noiseless system will just sit there forever with no output. If a node is perturbed as in the simulation (at 10ms), that causes a transient which makes the loop "oscillate" at a constant amplitude forever if the loop gain is 1.

Note that I choose a perturbation of only 1e-15V, which is tiny compared to thermal noise in any real circuit, and that was sufficient to create a tiny periodic signal. If the Loop Gain was > 1, then even this tiny signal would grow to Volts eventually, but this is still not a useful oscillator...

Now, to turn this thing into a useful oscillator, the loop gain would have to be >1. That creates a signal that grows forever, so there has to be something to limit the growth of the output amplitude.

So Mike's necessary conditions for a practical oscillator:
Initial Perturbation
Loop Gain > 1 (not Gain=1)
Loop Phase shift multiples of 360 deg.
Amplitude limiter


ps Steve, I am not confused. I dare say I have designed more oscillators than this entire crowd put together.

 

[MikeMl]

Here is a circuit that satisfies Mike's necessary conditions for a practical oscillator:

Note startup, limiting, waveforms, and cumulative phase shift. Due to the low-pass nature of the 3RC network, the harmonic distortion is not too bad, either...

 

[Winterstone]

Thanks for mis reading my entire post. It seems like you assumed too much or you just didnt take the time to read it carefully enough.

Misreading your entire post? I think, In case of a misunderstanding not only the reader side is „guilty“.
(But why do you start again with such personal accusations? Please, stay objective.)
You have expressed yourself rather vague - that`s all, but not a problem at all. Such things happen from time to time. For such reasons we have a discussion.

If you read my post carefully you would have seen that i said that nonlinearity is required for limiting the AMPLITUDE, not the STARTUP.

That`s true - without any doubt. But the observation that „nonlinearity is required for limiting“ is self-evident and was stressed already several times in the thread. So what?

Also, stabilized oscillators do not move the pole pair back and forth in the same manner as i was suggesting. They use the non linear gain or limiting.

Yes - that`s a common misconception. Some people think that the poles - due to gain stabilization - are on the imaginary axis. But that is false. As I have mentioned - they are swinging forth and back in case of control-loop stabilization. In case of hard-limiting some specific considerations are necessary due to problems with definition of the term „gain“ (during limiting). If necessary, I can provide you with some related documents.

I have a feeling you still dont understand this. The AMPLITUDE is a separate problem with Barky, mainly because it is not even mentioned.

Yes - rely on your feelings. By the way: What is the amplitude „problem“? That the amplitude must be - or is automatically - limited is known since more than 60 years

Note that in this view we can keep the pole pair in the RHP and dont have to move it back into the LHP.

No, that´s not the case. Every good textbook and countless published articles state the opposite.
_____________________________________________________________________________

To all readers of this thread (clarification): I know in detail how feedback oscillators work, I am interested and involved in these circuits since several years.
My question is simply: Are there some additional conditions that can extend the well-known Barkhausen condition to a more rigorous oscillation criterion. The background of this question was explained in post#1.

Winterstone

 

[MrAl]

Hello there Mike,


Well, the perturbation you are talking about isnt usually discussed because it always comes in naturally at the moment the power supply is turned on. That's because as soon as one level changes it's equivalent to a step change in one of the initial conditions. But if you want to point it out anyway that's fine because in a simulation it may be needed.

The limiter you are using is the simplest form (two diodes in parallel). To get better distortion try using an LDR and LED combination with rectifier and maybe integrator. If you can measure any distortion after that i'd be surprised
It's all about adjustment. If we could adjust the gain just right, we'd have a perfectly linear oscillator. This LDR/LED circuit would be as linear as we can get...a self adjusting linear oscillator.

 

[Winterstone]

"You guys are forgetting something:
In order to have oscillation, you must also have an initial perturbation"

Hello Mike,

I don`t think we have forgotten the initial perturbation. I think, that can be a problem in simulation only because very often the power supplies of the active device are always "on".
As soon as we switch on the supply voltages at t=0 (as in reality) we have a start-up pulse that can start the oscillation built-up.
(Regarding your simulation example I have no comments. It works as expected).

Regards
W.

 

[Winterstone]

The limiter you are using is the simplest form (two diodes in parallel). To get better distortion try using an LDR and LED combination with rectifier and maybe integrator. If you can measure any distortion after that i'd be surprised
It's all about adjustment. If we could adjust the gain just right, we'd have a perfectly linear oscillator. This LDR/LED circuit would be as linear as we can get...a self adjusting linear oscillator.

Yes - you are right that an LDR-LED combination together with rectifier/integrator can lead to a very good output signal with very low THD.
But - one shouldn`t forget the time constant each control loop has. This will cause a small (very small?) amplitude modulation of the signal. Thus - perhaps a very good oscillator, but not "perfectly linear".
If this effect is of practical relevance depends on the dimensioning. But - as mentioned - I am trying to look also behind the circuit from the system point of view.

Ohh - by the way: This "amplitude modulation" is caused by a loop gain that swings between two values slightly larger or smaller than unity. Thus, it is an indication of the periodic pole movement across the imag. axis (from RHP to LHP and back).

 

[MrAl]

Hello Winterstone,

First post:
[with reference to keeping the pole in the RHP]
"No, that´s not the case. Every good textbook and countless published articles state the opposite."
Again misreading or misconstruing. You can not pull a sentence out of context and then comment on it. I dont like to keep commenting on these types of replies from you. Go back and read the whole thing please. If you need a proof of this i may be able to supply one.

Most recent post:
"Perfectly Linear", yes very very nearly perfect. That's due to the control loop which would act like a voltage regulator, and we know that we can get the output voltage of a voltage regulator (or other process) down to within a tiny tiny fraction of an error. In theory we could get this to go to zero, but i dont think it is necessary.

Also, if Mike puts one of the caps up to the DC power supply that would normally supply this circuit, the perturbation is natural as in most circuits like this.

 

[steveB]

ps Steve, I am not confused. I dare say I have designed more oscillators than this entire crowd put together.

You guys are forgetting something:

In order to have oscillation, you must also have an initial perturbation.

I don't think I said you are confused (i mentioned some people are confused by a particular concept) and I know you have designed many oscillators.

Please note that I brought up the requirement for a noise source or startup signal in post#16. I mentioned "noise" in post #6 and #28.

Also, I have several times acknowledged the need for gain>1 at startup.

When I was talking about "you having trouble with this", I was referring to your dismissal of the OP's question and the concept of gain=1 as a necessary condition for the oscillation itself.

 

[Winterstone]

Again misreading or misconstruing. You can not pull a sentence out of context and then comment on it. I dont like to keep commenting on these types of replies from you. Go back and read the whole thing please. If you need a proof of this i may be able to supply one.

MrAl, I wonder why it is not possible to communicate with you on another level
(Quotes: "I have a feeling you still dont understand this", "Go back and read the whole thing")
Is this your style to discuss technical matters?

I think, it is a normal procedure to quote that sentence only which needs a comment.
And a sentence like

"Note that in this view we can keep the pole pair in the RHP and dont have to move it back into the LHP"

contains a clear statement that in my view is not correct. That`s all.
If you like to explain or modify/correct your statement, it is up to you. I only gave my comment to this sentence.
Nevertheless, I am very interested to see the proof of your claim as announced by you (Quote: "If you need a proof of this i may be able to supply one ") .
I am looking forward.
W.

 

[Winterstone]

Hello Mike and Steve,

just for clarification regarding the value for the loop gain (LG>1 or LG=1) :

Barkhausen`s book contains both statements.
I`ll try to translate:

* For LG<1 all oscillations (if they exist) disappear,
* For LG>1 oscillation amplitudes are rising until a certain amplitude is reached corresponding to LG=1 , which is the theoretical oscillation condition for self-sustained oscillations.
(my comment: Barkhausen assumes a tube characteristic with a slightly non-linear characteristic (decreasing small signal gain).

 

[MikeMl]

...Barkhausen`s book contains both statements.
I`ll try to translate:

* For LG<1 all oscillations (if they exist) disappear,
* For LG>1 oscillation amplitudes are rising until a certain amplitude is reached corresponding to LG=1 , which is the theoretical oscillation condition for self-sustained oscillations...

My first example shows that the amplitude of oscillation is Constant with LG=1. In order for the amplitude to increase spontaneously, LG must be >1.

That is why I list LG>1 as a necessary condition. Absent LG>1, in a Practical oscillator, the output will never increase to a useful level.