Problem encountered while amplifying load cell signal with LM358
If you replace the LM358 with an instrumentation amplifier then theoretically would work. Practically you will face one another problem, that is nulling. 

Most instrumentation amplifiers requrire a REF input that has to be driven with a low impedance source, aka opamp. The purpose of REF is the null setpoint at zero load for your load cell, but this ref voltage gets only subtracted/added to the amplified signal. Therefore if the diferential signal at zero load is non-zero it gets aplified, so there is only little headroom left for the working range. The REF voltage is then subtracted/added to the already amplified signal.

The best approach is to subract/add tare (zero) before it gets amplified, thus having almost the entire supply voltage as operational range. Those are not classic instrumentational amplifiers

Fortunatelly there are some special instrumentation amplifiers, called indirect current feedback  instrumentation amplifier.



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