Firstly, there are many blog videos on this subject...watch a few!
One very recent with Dave on Eeevblog...Dave just did one on offset voltage and another on offset current.
I might need to use dual supply op amp like OP07. How does the supply stability affect performance:
The power supply will always need to within the operating voltage limits of the op amp. If the power supply voltage dips to a point that it cannot deliver the required output voltage, then the output will clip. In other words the power supply voltages need to be in excess of the required output voltage by some few volts.
1. do the supply voltage needs to be regulated?
A good op amp has good power supply variation rejection, so unless you are doing something with precision and tiny voltages, the power supply just has to be in the operating range and sufficient for the + and - output swing.
2. I'm thinking of using charge pump for negative rail. How will 1V drop on negative rail affect performance. Is it that bad if positive and negative rails differ that much if you don't need the output to go near the rails?
If your signal doesn't go near the rails, then the rails only need to exceed the expected output voltage by in either direction by a few colts. The power supplies can be very different for the VDD and VEE, so long as their different voltages are high enoiug to meet the requirement of your output swing and the min. operating voltage of the op amp. Some op amp outputs cannot reach the rails, so the power supply must be boosted above the max. output signal voltage in either polarity so that the op amp output range can be achieved.
2a. Datasheet of OP07 sais ?VIO/?VCC = 7µV/V. I don't understand ?VIO here. Does it mean that there could be 7 µV offset on either input or output for each change of 1V on the supply? 7 µV on the output is not a big deal, but if it's on the input it'll be multiplied.
Yes, it means that 7uv offset change for each volt change. Correct, it will be multiplied, that's the job of the op amp..but the change is very small unless you are chasing after micro volts or expect to achieve very high gain settings.
. What if the supply rails are stable, but not quite matched - let's say +10V, -9V. If the offset is compensated will the opamp work correctly
4. How does supply internal resistance affect performance? Charge pumps have high internal resistance.
Yes it will work correctly.
Charge pump internal resistance will cause their output to drop at large currents. Make sure your charge pump can supply the current you need without drooping enough in output voltage to upset your circuit.