Electronic – Invert Voltage 0-2V

There are plenty of ways to do what you want. There are even ICs that will do it for you (programmable voltage regulators).

But if you want to follow your path, first you need a PWM with more than 8 bits resolution (10 mV is the step, 3.3 V is the max voltage you want to reach - this is 330 steps or 9 bits), make sure that your PWM has the correct resolution.

Then you need to filter the PWM output. The "simplest" solution is indeed RC. This is not the most efficient but its ok if you can accept some ripple. Take a cuff frequency that is at least 10 times smaller than the PWM frequency for reasonable ripple attenuation (2 kHz in your case). For a first order RC filter, you select R the following way:

R = 1/(2 x pi x C x f)

Then you need to buffer to output of the filter. This can be done with an operational amplifier used as a follower. Make sure that the supply voltage of the operational amplifier is sufficient to avoid saturation and that the amplifier can supply sufficient current for your application.

You can have something like that:

^{simulate this circuit – Schematic created using CircuitLab}

Select R1/R2 to set the gain (or attenuation), select R4/(R3+R4) to set the offset, select C*R2 to set the filter frequency. Output will be opposite to your PWM setting (0=max, 255=min).

Take a peek at figs 7 and 8 in the data sheet. for +/- 5V supply, the common mode input voltage cannot be less than about 4 volts. I suspect that with your 4V supply, and ground as the negative supply, you can't get within 750 mV of ground as a common mode input. While it may operate single supply, it is not rail to rail on the input.

The fact that there is no equivalent to figs 7 and 8 for single supply operation suggests that this is not a very good choice of an instrumentation amp for a single supply emg. I don't know any rail to rail dual package, but suggest you peek at the AD623, which actually works for a common mode voltage a bit BELOW the negative rail.

If your output is stuck at Vref, that would suggest that if it were grounded you'd be stuck at the negative rail. You don't say the size of the sine wave you're using as input, but I suspect it's less than a volt, and below the valid range for common mode input given single supply use. Try putting in a DC 3 volts and see what happens.

Also, that's not how you use a reference terminal on an instrumentation amp. You offset the output stage by providing a LOW IMPEDANCE reference voltage, usually the output of an op amp.