Bipolar high-dynamic range current sensing

I'm working on a project that will necessitate bipolar current measurement across a wide current range. It will need to accurately measure current from 750 mA down to 1 nA, although greater. The amplifier I'm using is an ADA4254, and my ADC is a 24-bit LTC2449.

My preliminary design involved two sense resistors connected to a relay. One resistor was 15 O, and the other was 56 kO. The ADA4254 has programmable amplification up to 128 V/V. See the diagram below.

This should work handsomely for my purpose, except that this circuit will be replicated 48 times, and relays are big and comparatively expensive. So I was wondering if I could do away with the relay altogether.

A 15 O resistor is pretty well the largest resistor I could use (15 O * 750 mA = 11.25 V).

The voltage across the sense resistor at Imin is 15 O * 1 nA = 15 nV. Once amplified, that would be 1.92 uV.

The resolution of the ADC is (5/2)/2^24 = 149 nV. Note that I divided by 2 because the operation is bipolar.

Since 1.92 uV >> 149 nV, I should be able to achieve sufficient resolution, however I do not have a lot of experience with very small signals and I have some potential concerns, so my questions are as such:

1. Is this practically achievable?
2. Given that the sense resistor cannot be particularly close to the op-amp (~3.5 cm), would this pose a risk of amplifying noise at very low currents?
3. Does anyone see another feasible solution?

Thanks all!

• With the 15 $\Omega$ resistor, won't 1 $\mu\Omega$ of resistance be equivalent to the LSB of your converter? Can you control the resistance of your interconnects, and the resistor itself, to 1$\mu\Omega$ over temperature and with aging? Forty times? What is the specified accuracy and linearity of your converter? What level of accuracy (not resolution) do you need? Jul 4 at 18:29
• Wiring is to be done as it is for thermocouple wiring ( junctions, length of wires ... ) ... Jul 4 at 18:36
• The system will be able to calibrate for trace resistances and resistance error. I don't know of any resistor that would be able to maintain its resistance to within 1 uO over even a modest temperature range. This device will end up generating a lot of heat, but we are only using passive air-flow cooling. Jul 4 at 21:08
• The total error of the ADC is 15 ppm of Vref, and the linearity is 5 ppm of Vref. As for the accuracy of our system, we are aiming for +/- 10 nA. Jul 4 at 21:12
• @AMacDonald You have a dynamic range of $10^9$! And you said bipolar, as well??? This is not for the faint of heart. You will need to specify your needed resolution over this range. (It is likely that the resolution you need at one end of the scale is very different from the resolution at the other end, so you need to specify many details here, I think.) And do I take it that you have a dead-band between - 1 nA and + 1 nA, where you "don't care?" And yes, something is achievable if that's all you are asking. The question is more about the resulting details.
– jonk
Jul 4 at 21:49

No, this is not at all achievable with the circuit topology you're suggesting.

It's not even a question of accuracy, it just flat-out won't work for a very simple reason: The ADA4254's input current is bigger than the current you want to measure (it's up to 14nA depending on temperature). This means that the amplifier will add a current that randomly varies between -14nA and +14nA to your 1nA signal, so you'll just measure garbage.

You could instead build an OpAmp-based transimpedance amplifier with a very large (i.e. 100 MΩ) switchable feedback resistor. Of course, you will have to select an OpAmp with a very low input current (about 10pA or less, i.e. LMC662), otherwise you'll have the same problem as with the ADA4254. The OpAmp will keep the input burden voltage close to zero while producing a large output voltage that can be digitized easily. You will also have to add a high power Class-AB output stage to the OpAmp to drive the low-value feedback resistors for the higher current ranges. Switching the feedback resistors can be accomplished with JFETs for the lower ranges and relays for the higher ones. You'll also need a lot of feedback resistors to switch between, i.e. 100MΩ, 1MΩ, 10kΩ, 100Ω, and 1Ω - or more depending on your resolution requirements.

Keeping the PCB free from contaminants will also be a big problem, you will have to clean it very thoroughly because stuff like finger grease can easily cause unacceptable leakage currents. Precision instruments often use point-to-point wiring mounted on teflon posts for this very reason.