op-amp unity gain stability

[Kdog44]

Biased on the bode plot of an op-amp's open loop gain, how could one tell if the op amp is unity gain stable?

[planet12]

To be able to find this, the plot will need to have phase as well as amplitude.

Many others can explain this better than me - the magic google phrases are "phase margin" and "gain margin" - you're looking to find the phase margin at the point the gain drops through 0dB, and that said phase margin is greater than 45 degrees ("Nyquist stability criterion" if you want to get all technical about it).

This all assumes a standard dominant-pole compensated op-amp - which most are. If you've got strange dips then rises in gain things get more complicated.

[LvW]

..... and that said phase margin is greater than 45 degrees .

Theoretically, the circuit is "stable" even for a phase margin of some degrees only. However, if this margin is too small (for example, less than 45 deg) the step response will exhibit heavy overshoot or ringing. If the margin is larger than app. 65 deg. there will remain a very small overshoot only.

[planet12]

..... and that said phase margin is greater than 45 degrees .

Theoretically, the circuit is "stable" even for a phase margin of some degrees only. However, if this margin is too small (for example, less than 45 deg) the step response will exhibit heavy overshoot or ringing. If the margin is larger than app. 65 deg. there will remain a very small overshoot only.

Quite right - I put the 45 degrees figure in as that is the common rule of thumb for the minimal "usefully stable" margin.

[T3sl4co1l]

To be able to find this, the plot will need to have phase as well as amplitude.

Not necessarily.  If the response isn't terribly pathological, you can tell phase shift from attenuation rate: every 20dB/decade is 90 degrees.  http://en.wikipedia.org/wiki/Minimum_phase#Relationship_of_magnitude_response_to_phase_response

Fortunately, most simple components, amps and circuits are like this, so it's handy to know.  A component-level example: you can tell the inductivity, or Q, or loss, or whatever of something like a ferrite bead based on the slope of the impedance: rising at 20dB/decade it's inductive, flattening out it's resistive, descending and it's capacitive.  (It's interesting because some materials -- nanocrystalline common mode chokes are one example -- exhibit a slope over a useful range which is not a multiple of 20dB/dec!)

Tim

[LvW]

To be able to find this, the plot will need to have phase as well as amplitude.

Not necessarily.  If the response isn't terribly pathological, you can tell phase shift from attenuation rate: every 20dB/decade is 90 degrees.capacitive.  (It's interesting because some materials -- nanocrystalline common mode chokes are one example -- exhibit a slope over a useful range which is not a multiple of 20dB/dec!)

Perhaps it is helpful to add that the above rule (90 deg for each 20dB/dec drop) gives a set of asymptotes which can (and must be !) be used to find the approximate real phase response. As an example, many opamps have a second pole in the vicinity of the transition frequency (where the open-loop gain crosses the 0 dB line). Hence, the asymptotic attenuation rate now will be 40dB/dec. Hence, the phase margin will be roughly between 90 deg and 0 deg: 45 deg approximately.