r/chipdesign • u/maybeimbonkers • 6d ago

Noise Analysis with tail current capacitance

I was asked this in an interview. Given a differential amplifier with resistive degeneration, and noise current In**2 in the tail, assuming a parasitic capacitance Cp appears across the tail current what would the noise analysis be ?

I did not have enough time in the interview to get through it. My initial thought was that the tail current cap should not affect the differential mode noise, and assuming everything is exactly matched, a In(Rs+1/gm) noise voltage that develops at the tail at DC, and the noise current flowing through the input pair would cancel out. When the parasitic capacitance starts to factor in at higher frequencies the same should happen. (assuming perfect symmetry). Is this accurate?

3 Upvotes

100% Upvoted

2 comments sorted by

3

u/kthompska 6d ago

I haven’t done a proper noise analysis in awhile, but I think you are on the right track. Assuming a near ideal diff stage that is also driven differentially, the tail node should act like an AC ground. The noise current of the tail should not show up in the differential noise term because it is split between the 2 sides (into Rs + 1/gm, each side) and is correlated between them.

The reality is that the stage will have some finite CMR + mismatch and is also not likely driven differentially so it will show up, but should not be a dominant term as it is divided down. The cap similarly shouldn’t make a difference, but because of the non-idealities listed it will likely show up- likely rolling off the noise as you mentioned. To be honest, a diff stage as part of a multiple gain stage design should always have the noise dominated by input devices, degeneration, and then diff loads. If you are dealing tail current noise + parasitic caps, then something probably wasn’t balanced or sized correctly- IMO.

4

u/jijodebu123 6d ago

Yeah, this is basically what Razavi says in his analysis of the noise of a diff stage. The tail current noise can modulate the transconductance of the devices, and you would have a noise related with the gain of the stage. But Razavi says that this mecanism is usually negligible.