I am trying to make a differential amplifier for one of my project. Input to amplifier is 40mV, this input is halting me to achieve higher gain, due to saturation. My question is how to limit this initial input voltage without effecting the voltage change across the sense resistor with change in load?

Below is a brief explanation of the system:

In the you can see a differential amplifier, input to this amplifier comes from sense resistor which is connect in series with certain load. Consider this load as variable resistor, which changes its value a little bit with some specific event. This event case a small voltage variation across sense resistor (few mV). I want to get 100 times amplification. But due to initial high voltage of sense resistor I am not able to achieve this. Initial voltage across sense resistor is 40mV. Now my question is how to limit this initial voltage.

Here, I want to say that I don't want to change my load or value of sense resistor. I can reduce the initial voltage drop across sense resistor by changing load or sense resistor value but this is not a good option in my case.

What I want is to limit initial voltage of the amplifier, and the main thing is that it should not effect the voltage variation of sense resistor, this variations come when I change my load under specific event.

Note: By Initial voltage I mean the voltage which I will get when I apply input voltage to my system, this will create a voltage divider between sense resistor and the load. And thus I get a voltage across sense resistor which I call initial voltage.

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