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Is there any way to amplify a signal with a voltage close to the power supply level?

Op-amp with a differential input pair composed of P-channel MOSFETs
Op-amp with a differential input pair composed of P-channel MOSFETs

In order to amplify a signal with a voltage close to the power supply level, use a rail-to-rail op-amp instead of a typical op-amp. The correct operation of a non-rail-to-rail op-amp is not guaranteed when the input is outside the common-mode input voltage range and close to VDD.
The differential input pair of a typical op-amp is composed of P-channel MOSFETs as shown in the following equivalent input circuit.

It is necessary to operate all the MOSFETs of an op-amp in the saturation region in order to prevent unwanted output distortion etc. Therefore, the following equation must be satisfied:
|VDS| > |VGS| - |Vth|
Qp1, which acts as a current source, enters the linear region when the input voltage is between VDD and (VSD of the circuit’s current source) + (VSG of the differential input pair). An op-amp enters the linear region when an input voltage within (VSD of the circuit’s current source) + (VSG of the differential input pair) is below the supply voltage. This voltage range is out of the common-mode input range. An input voltage in this range results in an output distortion or a reduction in gain. It is therefore necessary to operate op-amps in the common-mode input voltage range.

The differential input pair of a rail-to-rail op-amp is composed of a pair of differential P-channel MOSFETs and a pair of differential N-channel MOSFETs connected in parallel. Therefore, a rail-to-rail op-amp can be used with an input voltage between GND and VDD.

Is there any way to amplify a signal with a voltage close to the power supply level?
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