See attached pic for circuit, just to be sure we're on the correct page. For simplicity of analysis, we'll denote R1/C1 as 1st-stage components and R2/C2 as 2nd-stage.

Yes, this is what I was thinking about.

So it's clear that the stages are impedance matched. Of course, this assumes that the output impedance of the uC pin providing the PWM signal and input impedance of the non-inverting input of the buffer are very small and very large, respectively (which is a reasonable assumption). QED.

Mm... sorry I don't see it.

I do agree that the additional term ( j w R_1 C_2 ) in m y transfer function is irrelevant at both extremes:

* If w = 0 (DC) then the term is just nulled.

* If w -> inf then the term is irrelevant compared to the quadratic term w^2

But in the transition region, the term has "some" influence. (it doesn't change drastically the response, but it's there nonetheless). So yes, if you're just drawing the bodeplot by hand for a quick check you can ignore it. But in the analytical solution, it must be present. If you're ok with an approximate solution, you might as well drop all the linear terms and just keep the constant one and the quadratic one.

The first stage if you consider it connected to a non-negligible load :

Which clearly shows the "extra" term and later on simplifies itself to (j w R_1 C_2).

And btw, I LOVE this codecogs instant online latex business! Thanks for the indirect link!!

Yes, the stuff is just awesome :p

Not sure if they really like hotlinking to it but meh ...