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.
So Mike's necessary conditions for a practical oscillator:
1. Initial Perturbation
2. Loop Gain > 1 (not Gain=1)
3. Loop Phase shift multiples of 360 deg.
4. Amplitude limiter
steveB said:1. loop gain > 1 for small signals
2. gain saturation to allow for gain=1 (positive feedback mode)
3. frequency selector (filter) (although sometimes the gain spectral response does this automatically)
4. Noise source or startup signal.
If we go beyond just circuits, other oscillators might require additional types of mode filters (polarization modes, spatial modes etc.)
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.
The main issue here is that the limiter (or gain saturation) is responsible for limiting the gain, and allowing gain=1 for a particular signal amplitude.
Without any additional stabilizing circuitry we have hard-limiting due to the supply rail. I think, in this case, we are not allowed to use the term "gain" for the whole signal because we have a non-linearity (no sinusoidal signal anymore). Instead, we have the possibility to use the principle of harmonic balance and can apply the condition gain=1 on the fundamental part of the signal only.
I would rather spend the time thinking about solutions to the Great Question, "Is there such a thing as a purely linear oscillator?". My best bet right now is on a linear oscillator with a linear gain control circuit where we get the pole pair so darn close to the jw axis that it can not be measured to be otherwise in any application that would use an oscillator like this. So i like to widen the required gap a little here too into the realm of necessity over perfection.
Another thing to consider is that, for OPAMPS, sometimes it is the slew rate limit (at higher frequency oscillations) that really saturates the gain. This would depend on the particular op-amp of course, but, slew rate can create reduced gain for larger amplitude signals.
Hello, well - this sounds good. Let`s come back to pure technical things.
As you have indicated, a "purely linear oscillator" is not possible.
Yes - I agree, of course, because of two reasons:
* No amplifier is really linear
* There is no way-out: We need an amplitude stabilizing mechanism, which - by nature - is non-linear.
But there is a problem: I think, it is not possible to place the pole pair so "close to the jw axis" as we would like to do.
I think, the reason is as follows:
In order to start safely (in a reasonable time) and to cope with tolerances and other uncertainties (parasitic influences) that cannot be avoided, we must include something like a "safety margin" in the pole location for start-up (at t=0).
That means, the regulation mechanism has to "live" with a considerable difference between the conditions at t=0 and t=infinity (I hope I could express my self clear enough).
Example: If we could design a Wien oscillator with a gain of 3.001 (but we cannot!) a pair of diodes across the feedback resistor would introduce a negligible distortion only.
But of course, as you have indicated, it is the aim of each engineer to design an oscillator that comes as close as possible to the ideal device.
Thank you
Regards
W.
So our first goal is to design a theoretical purely linear oscillator, then later we can take it to the practical. In theory i believe we can do this by using amplifiers, integrators, and passive networks.
Does this make sense to you?
I think, that`s what we (I mean: engineers around the world) are doing since a long time. No doubt about this.
My only concern was your sentence (which gave rise to my reply about ideal and "pure" linear circuits):
"I would rather spend the time thinking about solutions to the Great Question, "Is there such a thing as a purely linear oscillator?"."
And my answer, of course, is: NO.
...I remember some published articles with a title like this: "Slew rate stabilized oscillators".
That means, in principle it is possible to exploit the slew rate SR to limit the amplitude. I think, in fact it is the delay (resp. phase shift) caused by the SR that stops further rising of the amplitudes.
Isn't a Slew rate stabilized oscillator just a Multivibrator?
Hello to all,
I think it`s time to come back to the main question of this topic.
In my first post I did mention that there are some circuits which fulfill Barkhausens condition - but they don`t oscillate as expected.
This confirms that this condition is a necessary one only.
In post#25 I have announced a corresponding example.
Well - here is it: (see the attached pdf document).
The lower graph shows the loop gain magnitude, which reaches 0 dB at approximately 130 Hz (loop gain slightly above 0 dB).
The other graph is, of course, the phase response.
Thus, one could expect that the circuit will oscillate at 130 Hz (app.). But instead, the tran simulation reveals a squarewave above 20 kHz (not shown here). As a consequence: Barkhausen is fulfilled, but no corresponding oscillations.
Explanation to the circuit:
It is one of the 8 possible derivates based on the classical WIEN configuration - but not with equal resistors and capacitors. But nevertheless, with equal time constants R3C3=R4C4.
In order to avoid dc positiv feedback a capacitor C44 is added.
To enable a dc bias current for the non-inv. opamp input a resistor R33 was added.
It is to be mentioned that the same behaviour could be observed for an idealized opamp (as shown in the diagram) as well as a real opamp model (TL082).
Why no oscillations at 130 Hz? Does anyone have an explanation ?
Winterstone
... a perfectly linear circuit would have a difficult time actually meeting both criteria for gain and phase perfectly, and if the condition is not perfectly matched, the noise never can create a coherent oscillation ...
Hello to all,
I think it`s time to come back to the main question of this topic.
In my first post I did mention that there are some circuits which fulfill Barkhausens condition - but they don`t oscillate as expected.
This confirms that this condition is a necessary one only.
In post#25 I have announced a corresponding example.
Well - here is it: (see the attached pdf document)....
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