# What does it mean for amplifiers to be stable only down to N gain, where N > unity?

This is related to

which is about unity gain stability.

But what exactly does it mean if some op-amp is said to be only stable to, say, gain 3 rather than all the way down to unity gain?

Guesses:

Does this gain 3 refer to open-loop gain? (The amplifier has an adequate phase margin at the upper frequency where open-loop gain is 3, but not beyond?)

Or does it refer to closed-loop gain? (The amplifier will be stable up to its unity open-loop gain frequency, if the closed-loop gain is not less than 3?)

• If it's not unity gain stable, it has to be stable under some conditions, or what's the use of it? So, they're telling you, this op-amp is not unity gain stable, and the minimum gain where it is stable is A. – The Photon Oct 19 '12 at 19:25

To expand on my comment, they are talking about closed loop gain.

If an op-amp is not unity gain stable, it has to be stable under some conditions, or what's the use of it?

So, if they say the op-amp is "gain-of-3 stable", they're telling you, this op-amp is not unity gain stable, and the minimum gain where it is stable is 3.

• So, basically, interpretation B. – Kaz Oct 19 '12 at 20:32
• I can add more later, but now that I re-read what you wrote, I think the two interpretations are equivalent, but there is also some confusion introduced when you use some "non-standard" terminology. – The Photon Oct 19 '12 at 20:47
• Main thing is, an amplifier is either stable or it isn't, it isn't stable "up to some frequency". If it were unstable at any frequency, noise would cause it to oscillate. – The Photon Oct 19 '12 at 20:49
• Yes, I understand. It's not use if you just want to use the amplifier up to 500 Khz, when it's oscillating at 3 Mhz. – Kaz Oct 20 '12 at 0:03
• The Photon-your comment is not correct, sorry. Either a circuit with feedback is stable - or it is not. It cannot be stable/unstable "at or up to" a certain frequency. That means, if a circuit oscillates at 3 MHz you cannot use it at any frequency. It is simply an oscillator - that`s all. – LvW Jul 28 '15 at 7:04

I'm not an expert on this, still learning myself, but in my search for an intuitive grasp on op-amps I've found it very helpful to think about closed-loop gain as percentage of feedback.

Unity gain is 100% feedback. In other words, if the output is off by 10mV, the error signal fed back to the inverting input is 10mV; 100% of the error.

If the op-amp is set up with a gain of 10, say with a 10k and 1k resistor, then the feedback is only 10%. An error of 10mV will only apply 1mV to the inverting input.

I'm not sure how accurate it is, but I think of op-amps as being "twitchy", meaning for a small input it wants to produce a big output (like over-react in the twitchy characterization). Accordingly, they're more stable when you "water down" the feedback you give them. And the op amp is not likely to be happy if you want to feed it a big input and expect it to make a teensy adjustment in its output, even if that fulfills the "make its inputs equal rule" of an ideal op-amp.

Increasing closed-loop gain (reducing feedback percentage) does reduce the op-amp's bandwidth though, a decade for each order of magnitude of closed-loop gain, so a balance must be struck. For example, a 10MHz op-amp would be reduced to 1MHz at 10% feedback (closed-loop gain of 10).

As I understand it, all op-amps are inherently unstable. The only question is whether you let the manufacturer compensate it for you or whether you want to do that yourself. Unity-gain stable op-amps are compensated by the manufacturer. This makes them easy to deploy in a lot of circuits as the designer need add no compensation circuitry. However it does close off the possibility of choosing a compensation network (circuit) perhaps more suitable for the specific application. So it's a design choice.

• +1 for mentioning the GBWP trade-off. There is an lower AND upper limit to most design decisions. – rudolfbyker Mar 11 '17 at 8:46

The only thing that matters is the LOOP GAIN Ao*B. That is the gain around the complete loop consisting of active device (gain Ao) and feedback circuit (factor B). The classical stability criterion applies to this loop gain and we require that either (a) the phase of the loop gain is already beyond -360 deg if the loop gain magnitude reaches 0 dB or (b) the loop gain magnitude is smaller than 0 dB at that frequency where the loop gain phase is crossing the -360deg (0 deg) line. Note that the mentioned -360deg contain the -180deg phase inversion introduced by the inverting opamp terminal for negative feedback.

Now - because a larger closed-loop gain requires a smaller feedback factor B (if compared with unity gain) the corresponding loop gain Ao*B is smaller. According to the feedback theory, less feedback gives less bandwidth - which means that the phase shift introduced by the opamp is also smaller. Hence the stability is improved in any case - however, in some cases it is even necessary to use less feedback (larger closed-loop gain) because more feedback leads to instability (violation of the above stability criterion).