An operational amplifier (often op amp, op-amp, or opamp) is a DC-coupled electronic amplifier with a differential input, a (usually) single-ended output voltage, and an extremely high gain. Its name comes from its original use of performing mathematical operations in analog computers. The voltage-feedback opamp (VFOA or VFA, the focus of this article) amplifies the voltage difference between its two inputs, while the less common current-feedback op amp (CFOA) amplifies the current between its two inputs. By using negative feedback, the characteristics of an op amp application circuit (e.g., its gain, input and output impedance, bandwidth, and functionality) can be determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op amp itself. This flexibility has made the op amp a popular building block in analog circuits. Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standard integrated circuit op amps cost only a few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost over US$100. Op amps may be packaged as components or used as elements of more complex integrated circuits. The op amp is one type of differential amplifier. Other differential amplifier types include the fully differential amplifier (an op amp with a differential rather than single-ended output), the instrumentation amplifier (usually built from three op amps), the isolation amplifier (with galvanic isolation between input and output), and negative-feedback amplifier (usually built from one or more op amps and a resistive feedback network).
Operation
The amplifier's differential inputs consist of a non-inverting input (+) with voltage V+ and an inverting input (−) with voltage V−; ideally the op amp amplifies only the difference in voltage between the two, which is called the differential input voltage. The output voltage of the op amp Vout is given by the equation
V out = A OL ( V + − V − ) , {\displaystyle V_{\text{out}}=A_{\text{OL}}(V_{+}-V_{-}),}
where AOL is the open-loop gain of the amplifier (the term "open-loop" refers to the absence of an external feedback loop from the output to the input).
Open-loop amplifier The magnitude of AOL is typically very large (100,000 or more for integrated circuit op amps, corresponding to +100 dB). Thus, even small microvolts of difference between V+ and V− may drive the amplifier into clipping or saturation. The magnitude of AOL is not well controlled by the manufacturing process, and so it is impractical to use an open-loop amplifier as a stand-alone differential amplifier. Without negative feedback, and optionally positive feedback for regeneration, an open-loop op amp acts as a comparator, although comparator ICs are better suited. If the inverting input of an ideal op amp is held at ground (0 V), and the input voltage Vin applied to the non-inverting input is positive, the output will be maximum positive; if Vin is negative, the output will be maximum negative.
Closed-loop amplifier
If predictable operation is desired, negative feedback is used by applying a portion of the output voltage to the inverting input. The closed-loop feedback greatly reduces the gain of the circuit. When negative feedback is used, the circuit's overall gain and response are determined primarily by the feedback network, rather than by the op-amp characteristics. If the feedback network is made of components with values small relative to the op amp's input impedance, the value of the op amp's open-loop response AOL does not seriously affect the circuit's performance. In this context, high input impedance at the input terminals and low output impedance at the output terminal(s) are particularly useful features of an op amp. The response of the op-amp circuit with its input, output, and feedback circuits to an input is characterized mathematically by a transfer function; designing an op-amp circuit to have a desired transfer function is in the realm of electrical engineering. The transfer functions are important in most applications of op amps, such as in analog computers. In the non-inverting amplifier on the right, the presence of negative feedback via the voltage divider Rf, Rg determines the closed-loop gain ACL = Vout / Vin. Equilibrium will be established when Vout is just sufficient to pull the inverting input to the same voltage as Vin. The voltage gain of the entire circuit is thus 1 + Rf / Rg. As a simple example, if Vin = 1 V and Rf = Rg, Vout will be 2 V, exactly the amount required to keep V− at 1 V. Because of the feedback provided by the Rf, Rg network, this is a closed-loop circuit. Another way to analyze this circuit proceeds by making the following (usually valid) assumptions:
When an op amp operates in linear (i.e., not saturated) mode, the difference in voltage between the non-inverting (+) and inverting (−) pins is negligibly small. The input impedance of the (+) and (−) pins is much larger than other resistances in the circuit. The input signal Vin appears at both (+) and (−) pins per assumption 1, resulting in a current i through Rg equal to Vin / Rg:
i = V in R g . {\displaystyle i={\frac {V_{\text{in}}}{R_{\text{g}}}}.}
Because Kirchhoff's current law states that the same current must leave a node as enter it, and because the impedance into the (−) pin is near infinity per assumption 2, we can assume practically all of the same current i flows through Rf, creating an output voltage
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