## Saturday, December 19, 2020

### Audio Amplifier Feedback - A Realistic Power Amplifier and its Phase Margin

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

In the last post on this topic, I mentioned that any real amplifier has multiple poles, which cause phase lag at the amplifier's output. The lag increases with frequency, and it affects the behavior of the amplifier placed in a feedback loop. As the phase shift at the intercept frequency (where the amplifier's open loop gain equals to the closed loop gain, and thus the loop gain is unity) approaches 180 degrees, the signal at the output of the starts exhibiting overshoot and ringing:

If the phase lag at the intercept frequency reaches 180 degrees , the amplifier becomes unstable - this is called the Barkhausen stability criterion.

The difference between 180 degrees and the actual phase lag at that frequency is called the phase margin and is an indicator of how close the amplifier to instability. A practical requirement is to have at least 30 degrees of phase margin - that is, the phase lag at $180 - 30 = 150$ degrees or less - at the frequencies where the loop gain is between 10db and -10dB.

Let me look at a realistic example of a conventional three-stage audio power amplifier with the desired closed loop gain of 10 (=20dB):

It has multiple poles, and at the crossover 0dB frequency (about 6MHz), when its open-loon gain (green line) reaches the desired closed-loop gain set by the feedback network (blue line), the phase at the output lags that at the input by over 240 degrees, indicating the negative phase margin of about -60 degrees:

With a negative phase margin, the amplifier is unstable and will oscillate:

To make it stable, one needs to compensate it - to make somehow the phase lag at the intercept frequency less than 180 degrees. The simplest way is to increase the closed loop gain by modifying the feedback network. If we, for example, set the closed loop gain at 3,000 (or 70dB), the intercept frequency moves from 6MHz to 300kHz, and the gain margin becomes positive 50 degrees, making the amplifier stable:
The problem with this approach is, of course, that no one needs an audio power amplifier with the gain of 3,000.

Thankfully, there are more practical ways to compensate this amplifier, and I will look at them in the next posts.