About phase margin of inverting amplifiers

Question

Phase margin is usually defined as how far is the phase of the loop gain from -180: $$PM = \angle \text({loop \space gain}) +180^{\circ} $$

Let's suppose that we want to compute the maximum phase margin of a single-pole amplifier. For a non-inverting amplifier, this calculation is straightforward: PM(max) = -90 + 180 = 90. However, when it comes to inverting amplifiers, things can get tricky because of the initial 180 phase delay that already exists at low frequencies between the input and output.

For example, using the previous definition, one can compute PM(max) = (-180 - 90) + 180 = 90 or PM(max) = (+180 - 90) + 180 = 270. Thus, we get different answers depending on how we consider the initial phase delay (+180 or -180). However, intuition suggests that the correct value should be PM(max) = 90 because it is the amount of phase delay left until the input signal "inverts again".

What is right value of the phase margin in this case ?

Answer 1

Quote:

Phase margin is usually defined as how far is the phase of the loop gain from -180: PM=∠(loop gain)+180∘

I would not agree to this definition. The LOOP GAIN is the gain of the complete loop when it is opened at a suitable point. Hence, it contains also the summing junction and the corresponding sign (negative or positive feedback).

Therefore, the definition does not make a difference between positive and negative feedback and the phase margin is simply the "distance" to the point of instability (oscillation condition):

When the magnitude of the loop gain is unity, the phase shift of the loop gain must not yet have reached the critical value of -360 deg (and the difference to 360 deg is the margin PM).

Comment: The problem with the quoted (simplified) definition is the following: There are many circuits with negative feedback where the minus sign is NOT introduced at the summing junction but anywhere within the loop. Some other circuits have negative and positive feedback pathes at the same time. In all these cases, it is necessary to use the 360deg criterion.

Answer 2

Given that an amplifier may be inverting or non-inverting at DC, you should take that into account when calculating phase margin. So, phase margin comes down to how much the phase angle has moved (i.e. |difference|) as frequency rises to the point where the |gain| becomes unity. Then you can use the formula: -

$$PM = \text{180}-|\angle_{\text{change from DC}}|$$

For an AC amplifier with no gain at DC it's more complicated because you then have to compute the frequency where the "normal" operating point is meant to be hence, you might consider this: -

$$PM = \text{180}-|\angle_{\text{change from normal operating point}}|$$

For the above we are interested in knowing if the circuit can produce an oscillating condition when an external feedback loop is applied around the amplifier.