Opamp noise: When is a resistor in the signal path?
All resistors contribute to noise. Looking at the circuit more carefully I notice two things.
- The noise sources of R1 and R2 encounter a very large divider providing about 60dB of attenuation to their noise.
- Those noise sources encounter a very strong low-pass filter further dropping their noise spectrum.
But that has nothing to do with “being in the signal path”, if R3 was larger and the capacitors smaller, then their noise contribution would dominate, while keeping the same topology and frequency response.
“Being in the signal path” is at best some sort of mnemonic device that leads you to the right design choices (I.e., make R3 small), but it is not a circuit analysis tool.
When a resistor is “in the signal path” it really means that both it and the signal are equally affected, and there is nothing you can do in the design to reduce that noise that will not also affect the signal. So you should make that noise contribution as small as possible, or try to avoid it altogether.
I have designed low-noise circuits in which some of the major noise contributors are the current source transistors biasing the transistor at the tail of differential pairs (on the opposite corner of the IC). There really can’t be something further away from the “signal path” than that.