Differential amplifier
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A differential amplifier is a type of an electronic amplifier that multiplies the difference between two inputs by some constant factor (the differential gain). A differential amplifier is the input stage of most operational amplifiers, or op-amps. Given two inputs <math>V_{in}^{+}<math> and <math>V_{in}^{-}<math>, a perfectly symmetrical differential amplifier gives an output <math>V_{out}<math>:
<math>V_{out} = A_d(V_{in}^{+} - V_{in}^{-})<math>
where <math>A_d<math> is the differential-mode gain. Practical amplifiers are never perfectly symmetrical which means that the amplifier also produces some output even if both inputs are at the same potential (so called common-mode gain <math>A_c<math>):
<math>V_{out} = A_c\frac{V_{in}^{+} + V_{in}^{-}}{2}<math>
The common-mode rejection ratio is usually defined as the ratio between differential-mode gain and common-mode gain:
<math>CMRR = \frac{A_d}{A_s}<math>
Note that a differential amplifier is a more general form of amplifier than one with a single input; by grounding one input of a differential amplifier, a single-ended amplifier results.
Differential amplifiers are found in many systems that utilise negative feedback, where one input is used for the input signal, the other for the feedback signal. A common application is for the control of motors or servos, as well as for signal amplification applications. In discrete electronics, a common arrangement for implementing a differential amplifier is the long-tailed pair, which is also usually found as the differential element in most op-amp integrated circuits.