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The power supply units of PCs and other devices incorporate multiple DC power supplies. A power supply line provided by a power supply unit is referred to as a power rail.
The entire range from the maximum voltage of a power line (VCC) to its minimum voltage (GND or minimum negative voltage, VEE) is referred to as rail-to-rail.
Op-amps having a common-mode input voltage range that almost covers the GND-VCC or VEE-to-VCC range are called rail-to-rail input op-amps (or full-swing op-amps).
The output stage may also be rail-to-rail. Op-amps with rail-to-rail input and output voltage ranges are called rail-to-rail input/output op-amps.
The differential input stage of most of the conventional op-amps is composed of P-channel MOSFETs. When the input voltage is close to VDD, op-amps with a differential input pair composed of P-channel MOSFETs do not provide a normal output, because a current source enters the linear region and gain is reduced.
Op-amps with a differential input pair composed of N-channel MOSFETs do not provide a normal output when the input voltage is close to GND.
Conversely, op-amps with a differential input pair composed of P-channel MOSFETs provide a normal output even when the input voltage is close to GND.
The input stage of rail-to-rail input op-amps, which consist of an N-channel differential MOSFET pair and a P-channel differential MOSFET pair connected in parallel, covers almost the entire voltage range from GND to VDD.
The following documents also contain related information:
Basics of Operational Amplifiers and Comparators
Is there any way to amplify a signal with a voltage close to the power supply level?
Are there any considerations for using an op-amp at low voltage?
What is the common-mode input voltage of an op-amp?
Product web page
Operational Amplifiers and Comparators
Operational Amplifier ICs and Comparator ICs
Input and output full range