the possibility of osillation with low amplitude

[yxo]

Hello!
I have got an abstract question a little bit. I wonder if an amplifier or another circuit can oscillate without reaching rail-to-rail amplitude if the circuit is unstable. If it is possible, do you you have such experience or could you please give me an example of a such circuit. Thank you.

 

[erikl]

This is possible, if the onset of oscillation shifts the operating point of the circuit into a region with a gain/phase condition which has lower gain and/or lower phase shift, by this counter-acting against the positive feedback and so stabilizing the low-amplitude-oscillation.

 

[tdy]

refer to a delta(sigma delta) modulation application with dc input.

 

[LvW]

Hello!
I have got an abstract question a little bit. I wonder if an amplifier or another circuit can oscillate without reaching rail-to-rail amplitude if the circuit is unstable. If it is possible, do you you have such experience or could you please give me an example of a such circuit. Thank you.

It sounds a bit contradictory - but a linear oscillator (with the goal to produce a sine wave) must have a kind of non-linearity to limit resp. stabilize the amplitude (Diodes, AGC, Fet-resistor,...).
Otherwise it will reach the upper limit (power supply) with a clipping effect - or the oscillation will decay.
The reason is simply that it is not possible to fulfill the oscillation condition exactly by finding the correct dimensioning of parts.
As a consequence - it is not possible to create a real sinusoidal wave because of the regulation effect.

 

[FvM]

refer to a delta(sigma delta) modulation application with dc input.

Limit cycles, as observed in SD modulators, are a kind of oscillations. But it requires a specific structure not applicable to linear amplifiers. By the way, the signal at the SD quantizer output is actually rail-to-rail.

Otherwise it will reach the upper limit (power supply) with a clipping effect.

Yes, in most cases. Possibly other non-linear effects act before the signal reaches the respective amlitude limits, e.g. a slew-rate limitation of an amplifier.

Just to mention another point, variable gain elements are beyond the scope of this discussion yet and offer various options to maintain stable low amplitude oscillations.

 

[tdy]

to FvM:
agreed, it seems the SD quantizer is a kind of variable gain elements from the loop point of view. can you give some other examples? it seems an interesting topic.

 

[FvM]

With the variable gain element, I wanted to address e.g. oscillators with amplitude control, or gain controlled systems with instability. Limit cycles are a different thing, I think.

I basically follow LvW's view, that an oscillator needs surplus gain, because you can't dimension it to fulfill the oscillation condition exactly. Then the amplitude rises until it reaches a serious limitation. In many cases, it's the output stage's supply voltage. But if you have e.g. a current limited output stage (an OTA) and a load impedance, the amplitude level will be considerably below the supply limits. You can find similar conditions in some low EMI crystal oscillator circuits.

 

[dick_freebird]

Many oscillators are "small signal" and in fact you
would like small-signal deterministic oscillation because
that means the design is pretty amplitude-robust
(unlike bang-bang oscillators where short-stroking
might either damp it to death, or result in a harmonic
mode like some short-chain ring oscillators)