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RE: Phase Distortion, dv/dt, and Slew Rate

The maximum output level, maximum frequency, and maximum slew rate are related by:

dV/dt = 2 * pi * Vmax * fmax

fmax is the maximum frequency the circuit may be expected to encounter
Vmax is the maximum output voltage

So the wider the bandwidth, the higher the slew rate required. And for a power amp, the higher the power output, the higher the slew rate required. For a given maximum slew rate, you can trade off maximum output against bandwidth.

Often discussions of slew rate drift into TIM and how it is related to NFB. I've heard it said several times anecdotally that early solid state designs had low open-loop bandwidth and needed a lot of NFB to achieve low distortion and to achieve the desired bandwidth (Google gain-bandwidth tradeoff). But if their slew rate was also low, then they could run into slew rate limiting that NFB cannot fix.

You wrote:

Now picture two sine waves or other signals of fixed "shape" but shifting frequency. I'm thinking here of two (or more) voices singing in unison but with vibrato. As they independently slide around the central frequency the phase relationship varies unpredictably. So the needed slew rate varies too, but the peak slew rate could be very high. Now add a chorus of voices or instruments all doing vibrato and you have a Fourier function that has a whole mess of high-frequency components.

If the circuit is linear, then summing up a bunch of different voices at different pitches superimposes their frequency content but doesn't generate new frequencies. For example, summing a sine wave at f1 with another sine wave at f2 just results in a signal containing f1 and f2. If f1 and f2 are close together, then you may hear a beat frequency at f1-f2 but there is no such frequency component in the signal. In this case, human auditory processing is working like an envelope detector.

Assuming we're working with linear circuits (or at least approximately linear), the required slew rate is dependent on the bandwidth of the signal and the output level per the formula above. It doesn't really matter how complex the signal is, just its maximum bandwidth.

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