Electronic – Can some clamp meters measure voltage through their clamp

Just because the battery voltage is 3V doesn't mean there isn't some sort of switching regulator to boost the voltage. However, even if there isn't it is possible to achieve using just a single 3V rail, 2 op-amps, a couple of resistors, and a photodiode.

You just need an op-amp which can operate on low voltages. You will either need to bias the non-inverting reference point, or put an capacitor switch pump to generate a negative rail.

Here's an example with a dual op-amp package, one which is used to provide a virtual ground reference.

You'll want an op-amp which has very low noise, low input bias current, and low input offset current. Something like this TL032.

^{simulate this circuit – Schematic created using CircuitLab}

The output is \$V=I_D R_G\$. Make \$R_G\$ small enough to avoid saturating the op-amp, but large enough to give you the full resolution. This is designed to operate with a differential voltage sensor, you can in theory measure Vout+ single-endedly, but it won't necessarily work as well because you'll miss out on fluctuations on the 1.5V reference.

Oh, and it probably goes without saying that this circuit doesn't include any of the logic/adc stuff. That is all extra, but simple microcontroller with a differential ADC should be sufficient to get a reading (these can operate in the 3V range as well).

Since you want very high resolution (and, presumably, accuracy), I don't believe any simple op amp will do the trick. Nor, for that matter, will any conventional current sensor IC. You are looking for 10 uA out of 200 mA, or .005%. Alternatively, this is a bit less than 15 bits resolution.

I suggest a rather different approach. Use a sense resistor as you have shown, but use a floated power supply to provide for a 2 MHz, 16-bit A/D converter. Use a high-speed optocoupler to transmit serial data from the ADC, along with a clock and sync channel (so you'll need 3 total). Run the A/D in continuous mode. Use the optocoupler outputs to reconstruct the current.

Go to Mouser and search the optocoupler section by speed, and you'll find a number of 50 MHz optocouplers. Since a 2 MHz sample rate will provide 2 x 16 MHz, or 32 MHz, these optos should do the job just fine.

Make sure you use power supplies rated for 100 volts of isolation.