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Following excerpt from a text says Figure a and Figure b are equivalent:

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But in practice when Figure b is used we are recommended to use a 10k or upto 100k resistor between the inverting terminal and the amplifier ground. Otherwise saturation is observed.

In practice Vin can be a battery or a transducer which is powered by a galvanically isolated power supply.

Regarding Figure b why does this issue happen in practice even though Vin is floating? Why such resistor necessary?

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The amplifier inputs will require a bias current, however small.

Without a component to provide that current, the voltage on both inputs will quickly head off to one rail or the other, as the bias current charges the input capacitance, and any stray capacitance that the Vin source has to ground.

Even a very very low input bias current amplifier, say one with FET inputs, will need this, it just takes longer for them to saturate than a bipolar amplifier input would.

There are some amplifiers that provide this bias resistor internally, and so do not need an external resistor. They are few and far between, but when you find one, it will say 'self biassed inputs' in the data sheet.

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