If I move either one to a separate power supply (e.g one on battery, the other on bench PSU), the problem disappears entirely. (The mixer doesn't care who it shares its power supply with.)
Now, correct me if I'm wrong, but that's what I thought the decoupling caps are there to alleviate.
The audio signal levels at the mixer are 20 to 100 times larger than those at the mike amp, and it's gain can be much lower, so they and it, are much less effected by small variations in the +-9V supplies and any noise on GND.
I forgot to mention that the large decoupling caps should be at the high current end - near where the headphone, it's amp, and +-9V and battery centre GND are connected, so that their higher charging and discharging currents don't flow anywhere near the mike input/amp. Of course you'll need some decoupling near the mike input/amp end, but the main idea is to keep any large currents from flowing in GND near the mike input/amp - because the mike, and its amp's -ve input resistor have to be connected to GND there.
With this, using a bank of caps on each rail (220u, 10u, 1u, 100n, 1n) seems to completely solve the problem. It's a simple solution, I'm just somewhat baffled as to why it made no difference the first time around.
A properly decoupled RC filter type supply for the mike voltage will always help. You can increase the value of that 47u quite a bit if needed, 47u is near the minimum, 100u-150u would be fine, if you increase it to a too massive value you sometimes get that slow oscillation/motor boating effect.
I'm still trying to wrap my head around impedance -- I think I understand how to manage input impedance, but output impedance is still kinda fuzzy,
I'll try.
Impedance is just AC resistance, at DC impedance and resistance are really the same thing, it's really just an alert that the voltages are going to be AC, and some components will act differently depending on what the actual frequency of the AC is - mainly caps which are an open circuit at DC, but turn into a resistor at AC with a resistance value that changes depending on the actual frequency of the AC.
Input and output resistance/impedance together act just like a simple 2 resistor potential divider. If you put 2 10K resistors in series across a voltage, the voltage in the middle of them would be exactly half.
If a 10K output is driving a 10K input then voltage in the middle of them(which is the only voltage that the input sees) would be half - you'd lose half the voltage you're trying to pass on to the next stage if both in and out were the same value.
and what I totally don't get is how pots inserted in between to adjust levels affect impedance. It's unclear to me whether the value of the potentiometer counts as output impedance or input impedance, and thus how to choose a value. Maybe someone can explain this to me?
Well the resistance/impedance of the pot varies with the position of the wiper, and that's the problem!
So you make the pot resistance low, and the input's resistance/impedance high so that the variations in the pot's smaller impedance (with changes of the wiper's position) don't make too much difference in comparison to the sum total impedance of the 2 of them together.
I'll draw an inverting amp and volume control in a minute, so you that can see the problem.
I've drawn it the way you originally had it with a 100K vol pot and 10K on the -ve input of the amp - which is an inverting amps input impedance.(I don't know what arrangement you've got now).
If you start with the Vol pot at near zero volume - at near the GND end, the op amps -ve input sees just its 10K resistor (GND is zero resistance) and it's easy to work out the gain it's just 100K/10K = 10X.
But, if the pot is moved to near it's middle (50K/50K) the -ve input now sees its 10K resistor plus the 50K of the pot. It's easy to miss, but the gain is not 10X now! It's gone down to 100K/(10K+50k) = 1.67X.
There are other +- effects, but in theory at least you may have noticed that the mixer's volume controls don't work properly between about the first 5% to 40%.
No picture this time. But if you get the impedances of the pot and the input of the inverting amp the right way round by reversing them, it fixes the disappearing gain problem.
10K pot,
100K -ve input resistor, and 1M feedback resistor(which is too high for the NE5532).
With the now 10K pot's wiper at near zero the gain is still 10X of course, 1M/100K = 10X.
But with the 10K pot at its middle 5K/5K, the -ve input now sees it's own 100K resistor, plus just another 5K from the pot, and the gain is now 1M/(100K+5K) = 9.5X which is quite a lot better than the 10X gain dropping down to 1.67X.
I'll post a new scheme pic when I get a round tuit so you can look for any useful bits.