I'm still figuring out analog electronics with my waveform generator project. It has a 9V power supply that I split into +/-4.5V rails with an op amp virtual ground (the subject of an earlier question). The +4.5V side powers an ATmega328P that generates an 8-bit digital waveform on pins D0-D7. Those lines go through an R2R resistor network to generate an analog signal in the rough range of 0-4V. Then I use the negative power rail and an op amp to center the signal on the 0V virtual ground.
So it works, but the waveform is noisy as hell. I kind of expected this, but not this bad. It's not breadboard noise because it's soldered on a real prototype board. There is relatively little noise across the positive and negative rails, so I think the noise is mostly in the virtual ground. (I know that "ground" doesn't normally have noise, but this is a virtual ground and the "noise" is relative to a theoretical 0V point centered between the +4.5V and -4.5V rails.)
I measured the noise between the virtual ground and the +4.5V rail and used the FFT function of my oscilloscope to see if there were any dominant frequencies. I am not so good at reading this but nothing stands out.
I tried capacitors of different values across the virtual ground and +4.5V rail. A 10pF capacitor did nothing. But a 10uF capacitor reduced the noise dramatically!
The stairstepping is due to the 8-bit resolution of the waveform and my not having a capacitor to smooth it out. I know the frequency of the stairstepping and the frequency of the waveform, and knowing the resistance of the R2R network (10k) I was able to calculate that a 1nF capacitor would filter out the stairstepping, and it does.
But what I don't understand is, how do I calculate the value of the capacitor necessary to eliminate the virtual ground noise? I think I need a low-pass filter that just allows my waveform through. That's an RC filter, but what's R? Do I use the resistance of my load and use that to calculate C?
Best Answer
R in the R-C filter is the output impedance of the opamp driving your virtual ground, at the frequencies of interest - the noise frequencies.
At low frequencies it'll be very low (open-loop output Z / open-loop gain, assuming the opamp is used as a unity gain buffer) but it'll rise as gain reduces with frequency. Link to opamp's datasheet for more help.
Looking at your previous question, you may simply need to decouple the opamp input ... in which case R is simply (R1 and R2 in parallel), where R1 and R2 are the voltage divider on the opamp input.