# Calculating the input resistance for thermal and input current noise calculation of fixed gain InAmp

I would like to use AD8428 for amplifying very small voltages in range of 0.1 - 10Hz. I want to calculate the current noise and thermal noise on the opamp resistors. The input current noise for this frequency range is ≈ 22 pArms.

I would like to proceed to calculate the voltage noise from this value but I dont know how to proceed. The current configuration is different from what I found on the internet examples because it is a fixed gain in-amp device without feedback resistors, even more the functional block diagram consists 3 more opamps.

## Question

Can anyone describe me how to calculate input resistance what input current noise and thermal noise will see?
I would like to do it very precisely, even the values or some steps can be neglected, so please try to describe the whole process.

• Would you be satisfied using a simulator to find noise? Or, do you want to calculate the noise performance by hand? Any SPICE simulator will give a good approximation if the model of the amplifier models the necessary parameters. The SPICE model for the AD8428 includes modeling of current & voltage noise, including 1/f noise.
– qrk
Dec 5, 2022 at 19:05

The instrumentation amplifier will add its contribution, from 0.1 to 10Hz it says 40nVpp or 40nVpp/sqrt(2) = 28.3nVrms

Each one of the resistors will add its own contribution. So calculate the noise from each resistor and convert it to voltage noise. You also should consider adding in any noise from the sensor (like if it were a wheatstone bridge, you could add in the resistance noise sources from the sensor also). Calculate the noise temp here

So the 100k will be 128nVrms The 33Ω will be 2.8nVrms (and probably not worth considering)

The current noise sources from the instrumentation amplifier will also need to be accounted for, but this will depend on the source resistance.

So if the Rinput was 33Ω and the current noise source from the V- pin was 22 pArms, then the voltage noise contribution would be 33Ω*22pArms = 726nVrms (but the datasheet gives a noise figure for 150pArms, so it should be larger than that, both figures seem a little high because this is RTI before gain, so it would be on uV level of noise which seems high, so I'll do some further research later today, usually current noise is a lower voltage source)

You then add all the voltage noise sources by the sum of the squares. (not worth calculating anything under 10nVrms because it will have little contribution).

sqrt(726nVrms^2+726nVrms^2+28nVrms^2+128nVrms^2)= 1.035uVrms

so after a gain of 2000 you'd get about 2mVrms. That seems a little high so I'd check it with lt spice which should be easy.

• p-p to RMS ratio is about 8. The 100k adds only common mode noise. I guess there's contribution from current noise through both 33Ω resistors, presumably uncorrelated. Dec 5, 2022 at 21:32