Noise introduced by current cancellation in low noise amplifiers

[Atomillo]

Hi!

Recently, I was reading the "Design by the Masters" episode in chapter 5 in the AoE where they describe the input amplifier of the HP34420A nanovoltmeter.

I found interesting how they used a current source to cancel the input bias current, because as discussed in various threads related to building a homemade nanovoltmeter, a low noise preamplifier is much easier to make if one tolerates a high bias current. Thus, might be this concept could be used in a preamp using AD8428s.

However, how does the noise of the op amp used in the current source affect the noise perfomance of the amplifier? They are using a normal op amp in the HP34420A, so presumably it's input noise is somehow not a factor. But then, what are the sources of noise in such a circuit? I at first glance would say that the Johnson noise of the 10Meg resistor is fatal, but this obviously doesn't meet the published specs.

Thanks for any help!

[Kleinstein]

The 10 M resistor is used to control the current. As a current cource the noise (in the current) gets larger with a smaller resistor. So a 22 M resistor would  be slightly better than the 10 M resistor if the range is sufficient.

The bias current in the 34420 amplifier to compensate for is in the 100pA, maybe 1 nA range and thus relatively small.

The AD8428 has a much higher input current and also variations in the current. A compensation can not correct for the dirft and noise of the input current, but can only add a little more current noise. So even with compensation of the input current the AD8428 is not good for high impedance sources (e.g. > 1 K). Ideally it wants a source impedance below 100 Ohms.

[Atomillo]

So, the noise added by the current cancellation is simply
Rs^2*(I.op-amp^2+I.R^2) (i.e the noise current of the op amp and of the resistor times the impedance of the thing you are measuring).

But then what is the effect of the voltage noise of the op amp in the shown circuit? If I understand correctly, does this generate a very small current noise and then this again is multiplied by Rin?

Finally, the idea regarding  the AD8428 was to null it periodically, and in doing so both measure it's offset and the bias current. Then, do like an AZ amplifier, substract it's offset but also program the bias current in the current source. Current noise would increase but bias current would decrease right?

Many many thanks for your help and time!

[Kleinstein]

The voltage noise of the auxiliary OP would add an noise current of the voltage noise divided by 10 M. Similar the johnson noise of the 10 M resistor is divided by the 10 M to get the current noise from the 10 M resistor. So even with a relatively noisy OP for the compensation this would not be much extra noise.

Using an Auto zero mode to compensate for both the offset voltage and bias current is unusual, though not impossible. The compensation would be only for the lower frequency part, but not for the higher frequency part and this the change during the active use. The extra measurement of the bias takes some time and it could be hard to do both in parallel. So this would add time lost to actually measuring the input.

[Atomillo]

Yes, the main problem with bias current aside from the associated current noise is the offset that is created when it flows through the source impedance.

The idea was to use a switch to connect the input of the amplifier to a TIA. Because the input of the TIA should be at ground, both voltage offset and current bias could be measured at the same time.

Of course that's just theory, in practice the TIA would add its own voltage offset to the mix. However, the op amp used in the TIA could have a bias current as high as it wanted, since you have all time used in the actual measurement to measure this current and calibrate it out. Thus, a low offset low drift unit could be used.

I'm still reading though CHP. 8 of AoE as well as all the resources present in this forum regarding low voltage measurements and noise, so please excuse if any of this is wrong or just plain stupid.