Given the ionization chamber’s tiny currents and the huge resistors required to turn them into voltages, reviewing the thermal noise I generally ignore seems in order…
The RMS noise voltage of an ordinary resistor:
vn = √ (4 kB T R Δf)
The constants:
- kB – Boltzman’s Constant = 1.38×10-23 J/K
- T – temperature in kelvin = 300 K (close enough)
Mashing them together:
vn = √ (16.6x10-21 R Δf)
vn = 129x10-12 √ (R Δf)
For a (generous) pulse current of 20 fA, a 10 GΩ resistor produces a mere 200 μV, so wrap a gain of 100 around the op amp to get 20 mV. An LMC6081 has a GBW just over 1 MHz, giving a 10 kHz bandwidth:
vn = 129x10-12 √ (10x109 10x103) = 1.3 mV
Which says the noise will be loud, but not deafening.
A 100 GΩ resistor increases the voltage by a factor of 10, so you can decrease the gain by a factor of ten for the same 20 mV output, which increases the bandwidth by a factor of ten, which increases the noise by a factor of … ten.
Ouch.
With the same gain of 100 (and therefore 10 kHz bandwidth) after the 100 GΩ resistor, the output increases by a factor of ten to 200 mV, but the noise increases by only √10 to 4 mV.
The LMC6081 has 22 nV/√Hz and 0.2 fA/√Hz input-referred noise, neither of which will rise above the grass from the resistor.
With 10 kHz bandwidth, the pulse rise time is:
tr = 0.34 / BW = 0.34 / 10 kHz = 34 μs
The LMC6081 has a 1 V/μs slew rate that poses no limitation at all for these tiddly signals.
That’s significantly better than the stacked Darlingtons and might be Good Enough for my simple needs.
The Smell of Molten Projects in the Morning 