## Saturday, January 2, 2021

### Audio Amplifier Feedback - Limitations of Dominant Pole Compensation

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, I compensated a conventional three stage audio power amplifier by adding a "Miller" compensation capacitor, which created a dominant pole. The dominant pole compensation is easy to apply, produces predictable results, the resulting amplifiers are relatively insensitive to the variations in parts and manufacturing, and thus is widely used.

The benefits of dominant pole compensation come at a cost: the open loop gain falls by 20dB/decade as the frequency grows. This brings two major limitations:

• Global loop gain and the bandwidth (that is, the frequency where the loop gain becomes unity) are linked - the more gain you want, the more bandwidth you have to provide; and
• Global loop gain falls with frequency at the rate of 20dB/decade:

With the dominant pole compensation, the bandwidth sets a limit on the global loop gain. For example, if you want to close your feedback loop at 800kHz, you loop gain at 20kHz will be 800 / 20 = 40 = 32dB. If your output stage at 20kHz produces 0.1% of third harmonic distortion without feedback, with this loop gain the distortion will be reduced by a factor of 800 / 60 = 13 (=22.5dB) to 0.0075%.

Conversely, choosing the global loop gain at a given frequency sets the bandwidth. If you wanted your distortion to go down to 0.001%, you'd need 0.1/0.001 = 100 = 40dB of loop gain at 60kHz, which translates to a 60kHz * 100 = 6MHz bandwidth.

The bandwidth of an amplifier has a practical limit. As the zero-loop-gain frequency increases, high frequency poles add to the phase lag, the impact of parasitics increases, the variations in the parameters of parts with voltage and current become more important, the construction of the amplifier requires more attention, and so on.

Generally speaking, amplifiers with the bandwidth of low single digit megahertz are fairly easy to build,  but as the bandwidth goes to 10MHz and above, it becomes complicated. For example, my model amplifier becomes unstable (its phase lag exceeds 180 degrees, and the phase margin becomes negative) if its bandwidth is set at 6MHz:

Because of that practical limit, most audio power amplifiers compensated with a dominant pole have at most 30-40dB of global loop gain at 20kHz, and often even less than that.

Limited global loop gain increases distortion in two ways:
• Error Transfer Function $ETF = {1 \over {1 - LG }}$ (see my first post on this topic) becomes larger - that is, the ability of the global loop to correct distortion at the output of the amplifier diminishes;
• A subtler effect is that the voltage at the amplifier's input increases, making the input stage less linear - this will be covered in the next post.
In addition, the loop gain falls - and distortion grows - with frequency. This has a familiar sonic signature: the bass, largely unaffected by distortion, sounds very tight and controlled on the backdrop of higher frequency mush. This is often attributed to the amplifier's high damping factor (the ratio of its output impedance to the load impedance) and/or to the massive power supply.

Some recognized experts, such as Bruno Putzeys or Vladimir Lamm, have suggested that if you don't have enough loop gain to make your amplifier sound transparent, it is better to have the loop gain, and hence distortion, approximately flat across the audio band. In this way, the distortion at higher frequencies is less conspicuous and less annoying, giving a better overall sonic experience. I will look into this in a subsequent post on transient intermodulation distortion (TIM).