Amplifier circuit with positive feedback - stability?

[twomilimeter]

I know that we can determine the stability of an amplifier with negative feedback loop by evaluating the gain and phase margin.

How do we determine the stability of an amplifier with positive feedback loop?

Thanks.

 

[betwixt]

Unless you are exceptionally careful, amplifiers with positive feedback are NOT stable, in fact the more general name for them is 'oscillator'.

Brian.

 

[dedalus]

Loop gain must be less than 1.

 

[flatulent]

This is called a regenerative amplifier. It was commonly used in the early days of AM broadcasting receivers because the valves were so expensive. The user had a knob to adjust the feedback amplitude until just before it oscillated. This effect also made the bandwidth narrower which was a good thing in that application.

 

[LvW]

Unless you are exceptionally careful, amplifiers with positive feedback are NOT stable, in fact the more general name for them is 'oscillator'.
Brian.

Unfortunately, it is not so simple! Some more requirements have to be met (oscillation condition)

Dedalus: Loop gain must be less than 1.

This is by far not a sufficient answer, since the gain of each loop will be less than 1 at one frequency!

 

[biff44]

An amplifier with a loop gain of greater than one is not necessarily unstable. You can do a simple experiment to prove this. Try to take a two port amplifier and make a feedback oscillator out of it. To do so you will need an amplifier, and some sort of frequency resonant circuit in the feedback path. After playing around with it, you will find that there have to be TWO conditions for it to oscillate:

1: round trip open loop gain of >1
2: round trip open loop phase shift of approximately 0, 2Π,4Π....

Another example is a simple conrol loop. You will find that classical feedback control loops can have a unity gain MUCH GREATER than unity, and be perfectly stable. A phase locked loop might have 80 dB of low frequency open loop gain, and yet be stable, for example. The key is that the round trip phase shift must stay withing certain limits.

So at what point in the phase shift do you start to call it "positive" feedback, vs. "negative" feedback? If your definition of "positive" feedback is anything other than 180 degrees, then yes, you play around with the phase and gain and maybe get it stable.

Once it IS stable, you have to be a little careful to keep it that way. If when you first turn on the amp's power supply, it momentarily sweeps thru an unstable condition, it will stay there and oscillate, for instance.

Added after 10 minutes:

Other examples of quasi stable amplifiers, like the regenerative amplifier, abound. Take a simple microwave oscillator. If you let it free run it is, obviously, and "unstable amplifier" However, if you instead inject a small amount of an input signal to it, you can have what is called an "injection locked amplifier", where the output is a highly amplified copy of the input signal. So there is an "amplifier" that is operating in very stable mode (providing a highly amplified but exact copy of the input signal), even though in itself is is an unsable oscillator when an input signal is missing.

You can find the same examples in locked lasers, etc.

 

[LvW]

Now I have time to go somewhat into details:

When speaking about feedback it is very important to know the terms.
* negative feedback means: Feedback to the inverting input terminal. This sounds simple, however, you should note that each negative feedback at higher frequencies turns into positive feedback due to phase shifting of real amplifiers. But this positive feedback will not harm you when for these signals the loop gain amplitudes are below unity.

* Positive feedback also for low frequencies is achieved by feeding back to the non-inverting input. For amplifiers this is done always in conjunction with appropriate negative feedback (which must dominate because of stability reasons).

* An amplifier with positive feeedback only cannot work as an amplifier - it is a kind of Schmitt-Trigger (switching capabilities between output extreme values).
Exception: The example given by FLATULENT with very small amount of positive feedback (pos. feedback can narrow the bandwidth, as negative feedback will enlarge it).

*Oscillator condition: If the positive feedback leads to a loop gain of unity at one frequency only and if the loop gain drops down for lower and for higher frequencies, than you have a harmonic oscillator. This is only a simplified description as oscillating properties of amplifiers with feedback are a rather complicated area.

*As an example: In all textbooks dealing with the subject a necessary oscillation criterion (Barkhausen rule) is mentioned. However, no book contains a formulation for a sufficient oscillation criterion! That means, up to now, I couldn´t find such a criterion. I would be happy if somebody could show me that I am wrong!!!

* From the above: To answer the question - in principle, there is no difference in loop gain measurement (simulation) between negative and positive feedback. But it becomes complicated if you cannot open both loops at the same time (that means: at the same node).
The problem is: For two different feedbacks (negative resp. positive), then you have three different loops (positive open, negativ open, both open) with three different loop gains. And it is not easy to decide and to know which loop of the three dominates and sets the margin. This depends on the specific topology.

* Finally: Feedback is one of the most involved and challenging phenomenon within the field of analog electronics.

Added after 19 minutes:

................
Another example is a simple conrol loop. You will find that classical feedback control loops can have a unity gain MUCH GREATER than unity, and be perfectly stable. A phase locked loop might have 80 dB of low frequency open loop gain, and yet be stable, for example. The key is that the round trip phase shift must stay withing certain limits.
........

More than that - normally one is interested in a very high loop gains becaus of many wanted properties associated with it. However, at a phase shift of 360 deg it should be less than unity (I suppose, that was the meaning of the contribution from DEDALUS).
But - as another example for the complicated subject of loop gain - there is something called "conditional stability" which allows a loop gain even larger than unity at a phase shift of 360 deg. !

 

[betwixt]

This blew out of proportion. I said "Unless you are exceptionally careful", meaning if you don't take care an unintended oscillator is formed. I fully agree with the technical analysis and (brings back memories) I have built 'Q multipliers' and regenerative AM receivers in the past, in fact I used to listen to local US stations from the UK with single transistor receivers. That was in the days before a trillion local AM stations came on air here and zapped the whole AM band !

Brian.