So I'm just getting round to testing the super low cost front end for the cotton spark detection gizmo. Total BOM at Digikey prices (1ku) is about $1.85, including about 60 cents' worth of protection circuitry.
The front end amp is a TLV272IS (a splurge at 23 cents), with a couple of 100M 1206es in series for feedback.
The resistor's 1-Hz Johnson noise is sqrt(200M/60.4) nV = 1.8 uV, so the op amp's noise is no big deal at low frequency. The TLV272's datasheet gives a typical 1-Hz noise current of 0.6 fA at 1 kHz.
Turns out that the 1-Hz current noise is actually 400 times larger than that: 240 fA at 100 Hz. That's the shot noise of 180 nA!
Swapping it out for a TLC2262 gets us back down to the Johnson noise of the resistor (1.8 uV), but it's 60 cents, so it blows the budget.
I know that op amp datasheets often get the current noise wrong, but being off by a factor of 600 has to be some kind of record.