Saturday, December 5, 2020

Audio Amplifier Feedback - Amp with Frequency Dependent Gain

In the last posts, I looked at the feedback theory basics and at how it applies to an opamp in both inverting and non-inverting configuration.

No amplifier can have a constant gain over an infinite bandwidth, as that would require infinite power. Any real amplifier's gain sooner or later goes down as the frequency goes up. For example, for most opamps designed in the past 50 years, their open loop gain (that without any feedback applied) starts going down at 100Hz or less:

The open loop gain Aol keeps going all the way down to unity (0dB) at a rate 20 dB/decade. At the same time, the phase (dashed line) at the output starts lagging that at the input (the opamp has a pole):

Eventually, the lag reaches (almost) 90 degrees. (Should there be more poles, each would add its own 20 dB/decade decline to the gain and up to 90 degrees phase shift. For now, I am going to look at just one pole.)

If such an opamp is connected to a feedback network (a resistor voltage divider) with gain 1/10:

setting the closed loop gain Acl=1/B at x10, or 20 dB, the error transfer function ETF and signal transfer function STF become frequency dependent:

At low frequencies, the magnitude of STF is 20dB, and the phase is constant - feedback stabilizes the gain of the opamp. The magnitude of ETF is -80dB (in this example), that is, any distortion that the opamp may generate will be reduced by a factor of 10,000. As frequency goes up, however, the open-loop gain Acl falls, and ETF grows. At 20kHz, ETF is only -27dB, so the distortion is reduced by only 20 times.

Loop gain LG is the product of open loop gain Acl and feedback network gain B, which is the same at the ratio of Acl and 1/B and, on the log plot, is simply the vertical distance between Acl and 1/B curves. The point where Acl meets 1/B is the crossover point - the loop gain become unity (0 dB), and feedback ceases to stabilize the STF and correct any distortion:

For large loop gains, ETF is approximately equal to loop gain, so commonly, it is the loop gain and not the ETF that is considered the measure of feedback's power to correct distortion. The more loop gain, the more distortion is reduced by feedback.

Loop gain falling with frequency shifts the spectrum of uncorrected distortion to higher frequencies, which creates a peculiar sonic signature - the bass, largely unaffected by distortion, become incredibly powerful and "tight", which is frequently attributed to the low damping factor or massive power supply of the audio amplifier.

There is an opinion, not scientific but useful, that, in case an amplifier has insufficient loop gain to correct distortion, it is sonically better to have loop gain, and thus distortion, approximately equal across audio range of frequencies, rather than allow loop gain to fall, and distortion to grow, with frequency as above.

Next week, I will look into what happens when the amplifier has multiple poles.

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