Unexpected behavior of simulated differential amplifier

Question

I need to measure a current from 1uA to 1A with a CM voltage up to 18v. I decide to go with a differential amplifier as per the following figure:

The expected Gain should be 50 V/V (=R5/R4) but at low currents it is much higher and not linear.

The gain reaches the expected value only starting from about 130mA and continuously decrease a bit all over the measurement range.

Since the Gain is not constant at all, I cannot calculate the current measuring Vout.

Is this unexpected behavior related to something wrong in the simulation (maybe because the opamp model) or am I missing something important in the circuit (I not able to test the circuit for a while)?

I have tried to buffer the differential amplifier input:

but I got fancy results:

Answer 1

The problem with using a simple differential amplifier is that the required matching of the resistors becomes prohibitively, impossibly tight at any price. Also, measuring 1uA with a 0.1Ω shunt is unlikely to be successful.

If you want 1uA change for 18V common mode voltage change, that means 100nV/18V, or about 5 parts per billion. Inexpensive 'precision' resistors might give you 50ppm/°C drift and matching within maybe 0.1%. (1000ppm), so basically it isn't going to happen.

If you redesign your circuit to avoid the excessive common-mode sensitivity and accept more realistic specifications it is possible, using the op-amps you have.

A high-side current source proportional to the voltage across the shunt is the obvious approach, assuming the current you are measuring is unidirectional. Offset of that op-amp is 100uV max so you can expect an offset error in the measured current of +/-1mA maximum just from that.

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So, to summarize, there are two distinct problems with your approach. The differential amplifier (common-mode rejection) and trying to get too much dynamic range, as bobflux mentions. Unfortunately, if you can't significantly relax your requirements that means you essentially have to swap out shunt values. A good 6.5 digit benchtop multimeter would almost do what you want if I loosely interpret the latter (100nV resolution with a few hundred nV peak noise), but that kind of analog design is non-trivial.