Editing Operational amplifier (section)

== Applications ==
[[Image:Generic 741 pinout top.png|thumb|[[Dual in-line package|DIP]] [[pinout]] for 741-type operational amplifier]]
{{Main|Operational amplifier applications}}

=== Use in electronics system design ===
{{Unreferenced section|date=September 2024}}
The use of op amps as circuit blocks is much easier and clearer than specifying all their individual circuit elements (transistors, resistors, etc.), whether the amplifiers used are integrated or discrete circuits. In the first approximation op amps can be used as if they were ideal differential gain blocks; at a later stage, limits can be placed on the acceptable range of parameters for each op amp.

Circuit design follows the same lines for all [[electronic circuit]]s. A specification is drawn up governing what the circuit is required to do, with allowable limits. For example, the gain may be required to be 100 times, with a tolerance of 5% but drift of less than 1% in a specified temperature range; the input impedance not less than one [[megohm]]; etc.

A basic circuit is designed, often with the help of [[electronic circuit simulation]]. Specific commercially available op amps and other components are then chosen that meet the design criteria within the specified tolerances at acceptable cost. If not all criteria can be met, the specification may need to be modified.

A prototype is then built and tested; additional changes to meet or improve the specification, alter functionality, or reduce the cost, may be made.

=== Applications without feedback ===
Without feedback, the op amp may be used as a [[voltage comparator]]. Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found since such devices can quickly recover from full-on or full-off ''saturated'' states.

A ''voltage level detector'' can be obtained if a reference voltage ''V''<sub>ref</sub> is applied to one of the op amp's inputs. This means that the op amp is set up as a comparator to detect a positive voltage. If the voltage to be sensed, ''E''<sub>i</sub>, is applied to op amp's (+) input, the result is a noninverting positive-level detector: when ''E''<sub>i</sub> is above ''V''<sub>ref</sub>, ''V''<sub>O</sub> equals +''V''<sub>sat</sub>; when ''E''<sub>i</sub> is below ''V''<sub>ref</sub>, ''V''<sub>O</sub> equals −''V''<sub>sat</sub>. If ''E''<sub>i</sub> is applied to the inverting input, the circuit is an inverting positive-level detector: When ''E''<sub>i</sub> is above ''V''<sub>ref</sub>, ''V''<sub>O</sub> equals −''V''<sub>sat</sub>.

A ''zero voltage level detector'' (''E''<sub>i</sub> = 0) can convert, for example, the output of a sine-wave from a function generator into a variable-frequency square wave. If ''E''<sub>i</sub> is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square. Zero-crossing detection may also be useful in triggering [[TRIAC]]s at the best time to reduce mains interference and current spikes.

===Positive-feedback applications===

[[Image:Op-Amp Schmitt Trigger.svg|right|thumb|300px|Schmitt trigger implemented by a non-inverting comparator]]

Another typical configuration of op amps is with positive feedback, which takes a fraction of the output signal back to the non-inverting input. An important application of positive feedback is the comparator with hysteresis, the [[Schmitt trigger]]. 

Some circuits may use ''positive'' feedback and ''negative'' feedback around the same amplifier, for example [[triangle wave|triangle-wave]] [[oscillator]]s and [[active filters]].

===Negative-feedback applications===

==== Non-inverting amplifier ====
[[Image:Op-Amp Non-Inverting Amplifier.svg|frame|An op amp connected in the non-inverting amplifier configuration]]
In a non-inverting amplifier, the output voltage changes in the same direction as the input voltage.

The gain equation for the op amp is
:<math>V_\text{out} = A_\text{OL} (V_+ - V_-).</math>

However, in this circuit ''V''<sub>−</sub> is a function of ''V''<sub>out</sub> because of the negative feedback through the ''R''<sub>1</sub> ''R''<sub>2</sub> network. ''R''<sub>1</sub> and ''R''<sub>2</sub> form a [[voltage divider]], and as ''V''<sub>−</sub> is a high-impedance input, it does not load it appreciably. Consequently
:<math>V_- = \beta V_\text{out},</math>

where
:<math>\beta = \frac{R_1}{R_1 + R_2}.</math>

Substituting this into the gain equation, we obtain
:<math>V_\text{out} = A_\text{OL} (V_\text{in} - \beta V_\text{out}).</math>

Solving for <math>V_\text{out}</math>:
:<math>V_\text{out} = V_\text{in} \left( \frac{1}{\beta + \frac{1}{A_\text{OL}}} \right).</math>

If <math>A_\text{OL}</math> is very large, this simplifies to
:<math>
  V_\text{out} \approx \frac{V_\text{in}}{\beta}
                     = \frac{V_\text{in}}{\frac{R_1}{R_1 + R_2}}
                     = V_\text{in} \left(1 + \frac{R_2}{R_1}\right).
</math>

The non-inverting input of the operational amplifier needs a path for DC to ground; if the signal source does not supply a DC path, or if that source requires a given load impedance, then the circuit will require another resistor from the non-inverting input to ground. When the operational amplifier's input bias currents are significant, then the DC source resistances driving the inputs should be balanced.<ref>An input bias current of 1&nbsp;μA through a DC source resistance of 10&nbsp;kΩ produces a 10&nbsp;mV offset voltage. If the other input bias current is the same and sees the same source resistance, then the two input offset voltages will cancel out. Balancing the DC source resistances may not be necessary if the input bias current and source resistance product is small.</ref> The ideal value for the feedback resistors (to give minimal offset voltage) will be such that the two resistances in parallel roughly equal the resistance to ground at the non-inverting input pin. That ideal value assumes the bias currents are well matched, which may not be true for all op amps.<ref>{{cite web |author=Analog Devices |title=Op Amp Input Bias Current |date=2009 |id=Tutorial MT-038 |publisher=Analog Devices |url=http://www.analog.com/static/imported-files/tutorials/MT-038.pdf |access-date=2014-05-15 |archive-date=2015-02-13 |archive-url=https://web.archive.org/web/20150213055046/http://www.analog.com/static/imported-files/tutorials/MT-038.pdf |url-status=dead }}</ref>

==== Inverting amplifier ====
[[Image:Op-Amp Inverting Amplifier.svg|frame|right|An op amp connected in the inverting amplifier configuration]]

In an inverting amplifier, the output voltage changes in an opposite direction to the input voltage.

As with the non-inverting amplifier, we start with the gain equation of the op amp:

:<math>V_\text{out} = A_\text{OL} (V_+ - V_-).</math>

This time, ''V''<sub>−</sub> is a function of both ''V''<sub>out</sub> and ''V''<sub>in</sub> due to the voltage divider formed by ''R''<sub>f</sub> and ''R''<sub>in</sub>. Again, the op-amp input does not apply an appreciable load, so

:<math>V_- = \frac{1}{R_\text{f} + R_\text{in}} \left( R_\text{f} V_\text{in} + R_\text{in} V_\text{out} \right).</math>

Substituting this into the gain equation and solving for <math>V_\text{out}</math>:

:<math>V_\text{out} = - V_\text{in} \frac{A_\text{OL} R_\text{f}}{R_\text{f} + R_\text{in} + A_\text{OL} R_\text{in}}.</math>

If <math>A_\text{OL}</math> is very large, this simplifies to

:<math>V_\text{out} \approx -V_\text{in} \frac{R_\text{f}}{R_\text{in}}.</math>

A resistor is often inserted between the non-inverting input and ground (so both inputs see similar resistances), reducing the [[input offset voltage]] due to different voltage drops due to [[bias current]], and may reduce distortion in some op amps.

A [[Capacitive coupling|DC-blocking]] [[capacitor]] may be inserted in series with the input resistor when a [[frequency response]] down to DC is not needed and any DC voltage on the input is unwanted. That is, the capacitive component of the input impedance inserts a DC [[complex zero|zero]] and a low-frequency [[complex pole|pole]] that gives the circuit a [[bandpass]] or [[high-pass]] characteristic.

The potentials at the operational amplifier inputs remain virtually constant (near ground) in the inverting configuration. The constant operating potential typically results in distortion levels that are lower than those attainable with the non-inverting topology.{{cn|date=January 2025}}

===Other applications===

* audio and video [[preamplifiers]] and [[Buffer amplifier|buffer]]s
* [[differential amplifier]]s
* [[differentiator]]s and [[integrator]]s
* [[Filter (signal processing)|filter]]s
* [[precision rectifier]]s
* precision [[peak detector]]s
* voltage and current [[Voltage regulator|regulators]]
* [[analog calculator]]s
* [[analog-to-digital converter]]s
* [[digital-to-analog converter]]s
* [[electronic oscillator|oscillator]]s and [[signal generator]]s
* [[Clipper (electronics)|clipper]]
* [[Clamper (electronics)|clamper]] (dc inserter or restorer)
* [[Log amplifier|log and antilog amplifiers]]

Most single, dual and quad op amps available have a standardized pin-out which permits one type to be substituted for another without wiring changes. A specific op amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors.