How to analyze low pass filter in voltage divider?

Question

In some guitar pedals I've seen following circuit to provide a stable voltage between ground and the supply voltage (labelled as INPUT below). I think this forms a low pass filter, but I'd like to learn how to determine the frequency response. So far I've only encountered RC-filters, or more complicated ones that could however all be decomposed into RC-filters.

There are two variations, the one on the left seems to be more common, and it is a special case for R3=0 of the one on the right:

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

Are you aware of voltage divider rules and Thevenin's Theorem: -

Can you see that R3 can merge into the value formed by the paralleling of R1 and R2 then, if rescaled the value of R1 and R2 it becomes the original circuit you drew.

Answer 2

So far I've only encountered RC-filters, or more complicated ones that could however all be decomposed into RC-filters.

These are normal RC filters, it's just that the R is made up of several Rs rather than one.

We always consider power supplies to be 'AC ground'.

The first filter has an effective R to ground that is just R1 parallel with R2, often written R1||R2. The normal formula for that is 1/(1/R1+1/R2), which is probably the quickest way to do it on a calculator with reciprocal button. Rearranging slightly, the quickest way to do it in your head is probably (R1.R2)/(R1+R2). Once R1 and R2 are very different, R1||R2 is approximately the smaller of the two, which is usually accurate enough for filter frequency calculations.

The second filter has an effective R to ground of R1||R2 + R3