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I was reading datasheet of MCP6072. I saw a parameter namely "phase margin" (table 1-2, page 4). As far as I know, "phase margin" is a control engineering term, and implies the phase difference between input and output when the gain is unity. I don't understand the meaning of this term in opamp terminology. The typical phase margin of this opamp is given to be 57o. That what does it mean?

hkBattousai
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4 Answers4

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The phase margin PM is a measure for the stability of a system with feedback. And, thus, it also applies to operational amplifiers. The PM is defined for the LOOP GAIN of the system - that means: open the loop at a suitable node and measure/simulate the gain and the phase around the complete loop. Then ,the PM is the DIFFERENCE between the measured phase and -360 deg (that means: The "distance" to the oscillation condition, positive feedback) at the frequency which gives unity loop gain. Without taking the phase inversion at the inverting input into account, the PM is the "distance" to -180 deg.

Now, for an opamp the most critical situation arises for 100% feedback (unity gain operation). In this case, the feedback factor is unity and the Loop gain is identical to the open-loop gain Ao of the opamp. Normally, only this condition is used to specify the PM in the opamp´s data sheet.

Summary: The PM as given for an opamp is the DIFFERENCE between the opamp´s phase shift and -180 deg at the unity-gain frequency.

LvW
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An op-amp is a "control system" and the phase margin is defined as the difference from -180 degrees of the phase of the open-loop transfer function when the magnitude is unity. This allows you to predict the stability and response of the system when you close the loop with a given amount of feedback.

An op-amp is typically compensated with a dominant pole, so the transfer function is approximately Ao/(1+s/wo) where wo is the dominant pole frequency and Ao is the DC gain- This implies a phase margin of 90 degrees. In practice, the Ft of the transistors causes additional phase shift and the dominant pole is set so that the 0dB crossover occurs with reasonable phase margin.

John D
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    @VladimirCravero LvW has it right, it's not the feedback network, it's the entire open loop transfer function. On a datasheet they can't know what you're going to wrap around an op-amp, so they specify phase margin of the open loop transfer function of the amplifier itself. Make a unity gain buffer out of it and you will know the phase margin. Pure resistive feedback to give more gain will be more stable than that, i.e. the datasheet number is the worst case in "normal" operation. (Though there are plenty of situations like capacitive loads that can cause trouble.) – John D Apr 20 '14 at 16:34
  • The OL transfer function of an opamp characterized by a dominant pole has a phase margin that's practically 90°. You've got your pole at a few Hz, cross the 0db at some 100kHz so the phase is 90° for all practical purposes. If you close the loop instead, and \$\beta=1\$, then the pole shifts very near the unity gain frequency and the phase margin decreases. – Vladimir Cravero Apr 20 '14 at 16:43
  • @VladimirCravero I disagree, if they cross unity at 90 degrees phase margin (by placement of the dominant pole) they are giving up bandwidth. Typically they would cross unity at a somewhat lower but still acceptable phase margin like 60 degrees. Then with a feedback factor of unity, the phase margin of the system IS the phase margin of the op-amp open loop characteristic, and the bandwith (closed loop pole) moves out to the open loop crossover. – John D Apr 20 '14 at 17:04
  • @JohnD I can't believe we are discussing this, I think we are saying the same thing in two different ways. How can a pole that is 4 or 5 decades before the unity gain frequency affect it's phase? it'd be something like arctan(10^4) that is something like 99.99% of 90°... Maybe you are implying that there are other poles after the unity gain frequency? – Vladimir Cravero Apr 20 '14 at 17:18
  • @VladimirCravero Yes, you have it- There are tons of poles at high frequency due to the Ft of all the transistors making up the op-amp. These cause lots of phase shift at higher frequencies, and op-amp designers put the dominant pole in such a place to maximize bandwidth such that the high frequency poles only contribute moderate phase lag. So the resulting phase margin is not 90 degrees, but something less. – John D Apr 20 '14 at 17:25
  • @JohnD now I can't disagree... Finally :D – Vladimir Cravero Apr 20 '14 at 17:26
  • phase margin is measured from loop gain, not open-loop gain. it has to include the feedback network – endolith Apr 18 '16 at 14:43
  • @endolith depends on what you mean by open-loop gain. If you define open loop gain to include the "feedback factor" then the definition of phase margin is OK. If you consider just the op-amp open loop gain then the phase margin from looking at the gain/phase is only valid at unity gain. (Feedback factor=1) – John D Apr 19 '16 at 15:24
  • Well "open-loop gain" = \$A\$ is defined without the feedback factor, while "loop gain" = \$−A⋅β\$ includes it. http://cc.ee.ntu.edu.tw/~lhlu/eecourses/Electronics2/Electronics_Ch9.pdf#page=2 Yes, if \$β = 1\$ they are the same. – endolith Apr 19 '16 at 16:00
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    I think you're technically right for an op-amp, though with general feedback control systems I hear (and use) the term "open loop gain" for the entire system including feedback, and the Bode plots for stability analysis are usually titled "open-loop gain and phase". An op-amp has a more defined "open loop gain" on the datasheet so maybe the term "loop gain" is more appropriate for that case. Thanks! – John D Apr 19 '16 at 16:58
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Phase Margin is the amount of phase shift margin at unity gain which could cause instability or Oscillation.

90 deg is theoretical ideal, 0 is NG , 45 deg will have some overshoot, 60 deg is practical solution. Phase margin shows tradeoff between rise time and overshoot.

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Op-amps are used with feedback, this makes it possible for them to oscillate, which is bad unless you are designing an oscillator!

The phase margin basically states how stable the op-amp is, i.e. phase angle distance from the point of oscillation, in the worst-case configuration of unity gain.

The addition of stray input & output capacitance, but especially load capacitance, can cause a phase shift that reduces the stability margin.

Typically a small resistor is added to the output to compensate for a "large" capacitive load, but this of course reduces the effective gain. Input capacitance is usually less of a problem, but it too can be compensated.

Many op-amps are internally compensated for typical usage conditions, but not all are.

Dave Null
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