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How do you implement a fader for a balanced summing bus?
Use a balanced fader. You could use a 2-gang stereo pot.
But what you really do is: the channel is almost invariably unbalanced, going push-pull only at the end. Put your fader in the unbalanced portion. This also means you can have post-fader gain, which you usually want (but avoid to save money).
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The summing amp has to source and sink the combined peak signal current of all channels
Yes,
.OR. the sum-amp's peak output voltage divided by the feedback resistor.
And for typical small-board gain structure, if ALL inputs are delivering maximum level, the sum-amp will voltage-clip long before it runs out of current to sink the sum of the input currents.
If a mixer is unity-gain for one input (which seems reasonable), and you drive all inputs hard, the output is much higher than any input. Sum is greater than the parts. Worst-case, all channels same 10V signal, a 100-in "unity gain" summer will output 10+10+10+10... or 10V*100 or 1,000V (or try to). For random signals (and music may be similar), dynamics and phasing will probably give an output more like the square-root of the number of inputs, or 100V, 99.99% of the time.
For many musical mixes, at any one time, there is one Star and the rest have to fit behind. If you pot-up the Star to -6dB, and four to sixteen back-up tracks at -12dB, the sum will be around 0dB. So it often makes sense to run a unity-gain summer, but mark the faders for nominal use around -10dB, with the understanding that the Star track is set a little higher (but not 0dB) and the others somewhat lower. That assumes the track levels are uniform to begin with... since they never are, you have to use some judgement too.
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Well, there is no theoretical advantage of sub-mixing.
No, but there are real practical advantages that may be compelling. A 100-in bus might end up 16 feet long, a very effective taxi-cab antenna and heavy parasitic reactance to the audio. A 100-in mix network in a box has 101 input cables, a real snarl.
And using made-up numbers we can show a significant noise advantage.
Assume the only mix-amp we have has one microVolt of input noise at any source impedance. (I said this was a made-up example, but a TL072 gives roughly this performance.) And assume we want unity-gain from any (single) input. And that all our sources are noise-free.
For the trivial case of a 1-input mixer, the output noise is 2uV. For a 2-input, it is 3uV. For 10 inputs, we get 11uV.
We see that for 100 inputs, we get 101uV.
Now try again but with ten 10-in mixers feeding an eleventh 10-in mixer (still 100 total inputs). Now the noise is only 37uV.
In today's world, we can expect much better than 1uV input noise per mix-amp. As Samuel says, we may be able to noise-match any source impedance at low Noise Figure.
With a noise-less amp, only resistor noises matter.
10-in, 909 ohms noise source, 0.3uV noise, noise gain 11, 3uV output noise
100-in, 99 ohms noise source, 0.1uV noise, noise gain 101, 10uV output noise
10*10-in to 1*10-in, 10uV output noise.
As Samuel says, with perfect amplifiers, sub-mixing has no noise advantage.