If a particular circuit doesn't oscillate then it likely is not actually meeting the Barkhausen criterion due to the components in the actual circuit not being exactly what was used to calculate the criterion.
If the loop gain is greater than 1, and the net phase shift around the feedback loop is 0 or multiples of 360 deg, it will oscillate...
My confusion from your post stems from the phrase "harmonic oscillator". I call them just "oscillators". Are you referring to an oscillator which also generates power at harmonics of a fundamental frequency?
Hi,
Harmonic oscillator is a general phrase used to describe oscillators even of only one frequency.
But as far as creating an oscillator, my advice is to abandon the Barkie criterion altogether and place one complex pole pair on the jw axis. Since this is not only very hard to do it also makes it impossible to calculate the output amplitude from the component values...something we can usually do. Combining these two difficulties we can satisfy them both by placing the single pole pair slightly into the right half plane and also limiting the amplitude using a pseudo non linear scheme. To figure out what gain we need we could look at the root locus. Also, no other poles in the RHP.
The rigor would come in when we go to place the pole pair. We'd have to make sure that component variations do not pull the pair back to the left half plane or else we'll loose the oscillation over time.
... - why there are some other circuits with feedback that do NOT oscillate - in spite of the fact that they are able to meet the Barkhausen criterion.
Therefore, my question is:
If an active circuit with feedback shall produce self-contained oscillations, what are the requirements that must be fulfilled to operate as a harmonic oscillator?
...there are circuits that meet Barkhausens criterion - and do not oscillate. That`s the point of my question...
Could you post an example? I suspect that an actual circuit that is supposed to oscillate, and doesn't, it is because the circuit analysis was not rigorous enough, i.e. parasitics not accounted for, gains not up to spec, parts tolerances, etc.
Therefore, my question is:
If an active circuit with feedback shall produce self-contained oscillations, what are the requirements that must be fulfilled to operate as a harmonic oscillator?
If you accidently make an oscillator, then loop Gain>1 while phase shift is multiples of 360deg. If you are trying to make an oscillator, then loop gain wasn't high enough, or the phase shift wasn't right.
Let me say it in mathematical terms:
I think, the well-known Barkhausen criterion is a necessary one only.
And I am wondering if somebody has heard about an oscillation criterion that is sufficient.
No steve, I have built many oscillators, and I am here to state that the Gain MUST be > 1 for any practical oscillator.
It looks to me that Winterstone has sucked us (yet again) into one of these "How Many angels can dance on the head of a pin" forum exchanges. I, for one, am not going to play...
And I am wondering if somebody has heard about an oscillation criterion that is sufficient.
.
It looks to me that Winterstone has sucked us (yet again) into one of these "How Many angels can dance on the head of a pin" forum exchanges. I, for one, am not going to play...
The linear analysis tool just is ill-suited to deal with the nonlinearity that provides the sufficient conditions.
The Barkhausen criteria is somewhat ambiguous for a linear system. We can define a linear system to select for frequency, but not for amplitude. .........
And, let's not forget that frequency domain theory become very questionable (and must be used with care) once the system becomes nonlinear.
...... Are you looking for a sufficient condition for a linear circuit, or are you allowing us to specify that including nonlinearity is needed in order to establish the sufficient conditions.
I ask because I have seen sufficient criteria for stable oscillations.
loop gain > 1 for small signals
gain saturation to allow for gain=1 (positive feedback mode)
frequency selector (filter) (although sometimes the gain spectral response does this automatically)
Noise source or startup signal.
In their paper they demonstrate a circuit with loop gain greater than 1 and loop phase shift of 360° (at some particular frequency) which didn't oscillate when the loop was closed.
So, I think what Winterstone is getting at is that Nyquist's criterion can be both necessary and sufficient to indicate the condition for oscillation, whereas Barkhausen's may fail.
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