Editing Operational amplifier (section)

==Op-amp characteristics==
<!-- [[Ideal and real op-amps]] redirects here, to "Op-amp characteristics" -->
=== Ideal op amps ===
[[Image:Op-Amp Internal.svg|thumb|250px|right|An equivalent circuit of an operational amplifier that models some resistive non-ideal parameters.]]

An ideal op amp is usually considered to have the following characteristics:<ref>{{cite web |url=http://www.ti.com.cn/cn/lit/an/slaa068b/slaa068b.pdf |title=Understanding Basic Analog – Ideal Op Amps |url-status=live |archive-url=https://web.archive.org/web/20161227060510/http://www.ti.com.cn/cn/lit/an/slaa068b/slaa068b.pdf |archive-date=2016-12-27 }}</ref><ref>{{cite web |url=http://research.cs.tamu.edu/prism/lectures/iss/iss_l5.pdf |title=Lecture 5: The ideal operational amplifier |url-status=dead |archive-url=https://web.archive.org/web/20161123045824/http://research.cs.tamu.edu/prism/lectures/iss/iss_l5.pdf |archive-date=2016-11-23 |access-date=2016-12-26 }}</ref><ref>{{Cite book |last=Schlaepfer |first=Eric |url=https://tubetime.us/wp-content/uploads/2018/10/Ideal-Op-Amp-Datasheet.pdf |title=IC01 Ideal Operational Amplifier |publisher=Perfect Semiconductor |year=2018 |access-date=2022-12-20}}</ref>

* Infinite [[open-loop gain]] ''G'' = ''v''<sub>out</sub> / ''v''<sub>in</sub>
* Infinite [[input impedance]] ''R''<sub>in</sub>, and so zero input current 
* Zero [[input offset voltage]] 
* Infinite output voltage range
* Infinite [[bandwidth (signal processing)|bandwidth]] with zero [[phase shift]] and infinite [[slew rate]] 
* Zero [[output impedance]] ''R''<sub>out</sub>, and so infinite output current range
* Zero [[Electronic noise|noise]]
* Infinite [[common-mode rejection ratio]] (CMRR)
* Infinite [[power supply rejection ratio]].
 
These ideals can be summarized by the two {{em|golden rules}}:
# In a closed loop the output does whatever is necessary to make the voltage difference between the inputs zero.
# The inputs draw zero current.<ref name=AoE>{{Cite book |last1= Horowitz |first1= Paul |last2= Hill |first2=Winfield |title= The Art of Electronics |publisher= Cambridge University Press |year= 1989 |location= Cambridge, UK |url= https://books.google.com/books?id=bkOMDgwFA28C&pg=PA177 |isbn=0-521-37095-7}}</ref>{{rp|177}}

The first rule only applies in the usual case where the op amp is used in a closed-loop design (negative feedback, where there is a signal path of some sort feeding back from the output to the inverting input).  These rules are commonly used as a good first approximation for analyzing or designing op-amp circuits.<ref name="AoE"/>{{rp|177}}

None of these ideals can be perfectly realized. A real op amp may be modeled with non-infinite or non-zero parameters using equivalent resistors and capacitors in the op-amp model. The designer can then include these effects into the overall performance of the final circuit. Some parameters may turn out to have negligible effect on the final design while others represent actual limitations of the final performance.

=== Real op amps ===
Real op amps differ from the ideal model in various aspects.

;Finite gain
:[[Open-loop gain]] is finite in real operational amplifiers. Typical devices exhibit open-loop DC gain exceeding 100,000. So long as the [[loop gain]] (i.e., the product of open-loop and feedback gains) is very large, the closed-loop gain will be determined entirely by the amount of negative feedback (i.e., it will be independent of open-loop gain). In applications where the closed-loop gain must be very high (approaching the open-loop gain), the feedback gain will be very low and the lower loop gain in these cases causes non-ideal behavior from the circuit.
;Non-zero [[output impedance]]
:Low output impedance is important for low-impedance loads; for these loads, the voltage drop across the output impedance effectively reduces the open-loop gain. In configurations with a voltage-sensing negative feedback, the output impedance of the amplifier is effectively lowered; thus, in linear applications, op-amp circuits usually exhibit a very low output impedance.
:Low-impedance outputs typically require high [[quiescent current|quiescent (i.e., idle) current]] in the output stage and will dissipate more power, so low-power designs may purposely sacrifice low output impedance.
;Finite [[input impedance]]s
:The ''differential input impedance'' of the operational amplifier is defined as the impedance ''between'' its two inputs; the ''common-mode input impedance'' is the impedance from each input to ground. [[MOSFET]]-input operational amplifiers often have protection circuits that effectively short circuit any input differences greater than a small threshold, so the input impedance can appear to be very low in some tests. However, as long as these operational amplifiers are used in a typical high-gain negative feedback application, these protection circuits will be inactive. The input bias and leakage currents described below are a more important design parameter for typical operational amplifier applications.
;Input [[capacitance]]
:Additional input impedance due to [[parasitic capacitance]] can be a critical issue for high-frequency operation where it reduces input impedance and may cause phase shifts.
;Input current
:Due to [[biasing]] requirements or [[Leakage (semiconductors)|leakage]], a small amount of current<ref group="nb">Typically ~10 nanoamperes, nA, for [[Bipolar junction transistor|bipolar]] op amps, tens of picoamperes, pA, for [[JFET]] input stages, and only a few pA for [[MOSFET]] input stages.</ref> flows into the inputs. When high resistances or sources with high output impedances are used in the circuit, these small currents can produce significant voltage drops. If the input currents are matched, ''and'' the impedance looking ''out'' of ''both'' inputs are matched, then those voltages at each input will be equal. Because the operational amplifier operates on the ''difference'' between its inputs, these matched voltages will have no effect.<!-- (unless the operational amplifier has poor [[Common-mode rejection ratio|CMRR]], which is described below). CMRR is usually much better than matching of currents, so not relevant. --> It is more common for the input currents to be slightly mismatched. The difference is called input offset current, and even with matched resistances a small ''offset voltage'' (distinct from the input offset voltage below) can be produced. This offset voltage can create offsets or drifting in the operational amplifier.
;Input offset voltage
:Input offset voltage is a voltage required across the op amp's input terminals to drive the output voltage to zero.<ref>{{cite book |first=D. F. |last=Stout |title=Handbook of Operational Amplifier Circuit Design |publisher=McGraw-Hill |date=1976 |isbn=0-07-061797-X |pages=1–11}}</ref><ref group="nb">This definition hews to the convention of measuring op-amp parameters with respect to the zero voltage point in the circuit, which is usually half the total voltage between the amplifier's positive and negative power rails.</ref> In the perfect amplifier, there would be no input offset voltage. However, it exists because of imperfections in the differential amplifier input stage of op amps. Input offset voltage creates two problems: First, due to the amplifier's high voltage gain, it virtually assures that the amplifier output will go into saturation if it is operated without negative feedback, even when the input terminals are wired together. Second, in a closed loop, negative feedback configuration, the input offset voltage is amplified along with the signal and this may pose a problem if high precision DC amplification is required or if the input signal is very small.<ref group="nb">Many older designs of operational amplifiers have offset null inputs to allow the offset to be manually adjusted away. Modern precision op amps can have internal circuits that automatically cancel this offset using [[chopper (electronics)|chopper]]s or other circuits that measure the offset voltage periodically and subtract it from the input voltage.</ref>
;Common-mode gain
:A perfect operational amplifier amplifies only the voltage difference between its two inputs, completely rejecting all voltages that are common to both. However, the differential input stage of an operational amplifier is never perfect, leading to the amplification of these common voltages to some degree. The standard measure of this defect is called the [[common-mode rejection ratio]] (CMRR). Minimization of common-mode gain is important in [[#Non-inverting amplifier|non-inverting amplifiers]] that operate at high gain.
;Power-supply rejection
:The output of a perfect operational amplifier will be independent of power supply voltage fluctuations. Every real operational amplifier has a finite [[power supply rejection ratio]] (PSRR) that reflects how well the op amp can reject noise in its power supply from propagating to the output. With increasing frequency the power-supply rejection usually gets worse.
;Temperature effects
:Performance and properties of the amplifier typically changes, to some extent, with changes in temperature. Temperature drift of the input offset voltage is especially important. 
;Drift
:Real op-amp parameters are subject to slow change over time and with changes in temperature, input conditions, etc.
;Finite [[bandwidth (signal processing)|bandwidth]]
:All amplifiers have finite bandwidth. To a first approximation, the op amp has the frequency response of an [[integrator]] with gain. That is, the gain of a typical op amp is inversely proportional to frequency and is characterized by its [[gain–bandwidth product]] (GBWP). For example, an op amp with a GBWP of 1&nbsp;MHz would have a gain of 5 at 200&nbsp;kHz, and a gain of 1 at 1&nbsp;MHz. This dynamic response coupled with the very high DC gain of the op amp gives it the characteristics of a first-order [[low-pass filter]] with very high DC gain and low cutoff frequency given by the GBWP divided by the DC gain.{{paragraph break}}The finite bandwidth of an op amp can be the source of several problems, including:{{glossary}}{{term|Stability}}{{defn|Associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead to [[electronic oscillation|oscillation]] in some feedback circuits. For example, a sinusoidal output signal meant to interfere destructively with an input signal of the same frequency will interfere constructively if delayed by 180 degrees forming [[positive feedback]]. In these cases, the feedback circuit can be [[BIBO stability|stabilized]] by means of [[frequency compensation]], which increases the [[Gain margin|gain or phase margin]] of the open-loop circuit. The circuit designer can implement this compensation externally with a separate circuit component. Alternatively, the compensation can be implemented within the operational amplifier with the addition of a [[Frequency compensation#Dominant-pole compensation|dominant pole]] that sufficiently attenuates the high-frequency gain of the operational amplifier. The location of this pole may be fixed internally by the manufacturer or configured by the circuit designer using methods specific to the op amp. In general, dominant-pole frequency compensation reduces the bandwidth of the op amp even further. When the desired closed-loop gain is high, op-amp frequency compensation is often not needed because the requisite open-loop gain is sufficiently low; consequently, applications with high closed-loop gain can make use of op amps with higher bandwidths.}}{{term|Distortion, and other effects}}{{defn|Limited bandwidth also results in lower amounts of feedback at higher frequencies, producing higher distortion, and output impedance as the frequency increases.}}{{glossary end}}{{paragraph break}}Typical low-cost, general-purpose op amps exhibit a GBWP of a few megahertz. Specialty and high-speed op amps exist that can achieve a GBWP of hundreds of megahertz. For very high-frequency circuits, a [[current-feedback operational amplifier]] is often used.
;Noise
:Amplifiers intrinsically output noise, even when there is no signal applied. This can be due to internal thermal noise and flicker noise of the device. For applications with high gain or high bandwidth, noise becomes an important consideration and a [[low-noise amplifier]], which is specifically designed for minimum intrinsic noise, may be required to meet performance requirements.


====Non-linear imperfections====
[[File:Inverting Amplifier Signal Clipping.png|thumb|The input (yellow) and output (green) of a saturated op amp in an inverting amplifier]]
;Saturation
:Output voltage is limited to a minimum and maximum value close to the [[power supply]] voltages.<ref group="nb">That the output cannot reach the power supply voltages is usually the result of limitations of the amplifier's [[#Output stage|output stage]] transistors.</ref> The output of older op amps can reach to within one or two volts of the supply rails. The output of so-called '''{{vanchor|rail-to-rail}} op amps''' can reach to within millivolts of the supply rails when providing low output currents.<ref name="rail-to-rail" />
;Slew rate limiting
:The amplifier's output voltage reaches its maximum rate of change, the [[slew rate]], usually specified in volts per microsecond (V/μs). When slew rate limiting occurs, further increases in the input signal have no effect on the rate of change of the output. Slew rate limiting is usually caused by the input stage saturating; the result is a constant current {{mvar|i}} driving a capacitance {{mvar|C}} in the amplifier (especially those capacitances used to implement its [[frequency compensation]]); the slew rate is limited by {{math|d''v''/d''t'' {{=}} ''i''/''C''}}.{{paragraph break}} Slewing is associated with the ''large-signal'' performance of an op amp. Consider, for example, an op amp configured for a gain of 10. Let the input be a 1{{nbsp}}V, 100&nbsp;kHz sawtooth wave. That is, the amplitude is 1{{nbsp}}V and the period is 10 microseconds. Accordingly, the rate of change (i.e., the slope) of the input is 0.1&nbsp;V per microsecond. After 10× amplification, the output should be a 10{{nbsp}}V, 100&nbsp;kHz sawtooth, with a corresponding slew rate of 1{{nbsp}}V per microsecond. However, the classic '''741''' op amp has a 0.5{{nbsp}}V per microsecond slew rate specification so that its output can rise to no more than 5{{nbsp}}V in the sawtooth's 10-microsecond period. Thus, if one were to measure the output, it would be a 5{{nbsp}}V, 100&nbsp;kHz sawtooth, rather than a 10{{nbsp}}V, 100&nbsp;kHz sawtooth.{{paragraph break}}Next consider the same amplifier and 100&nbsp;kHz sawtooth, but now the input amplitude is 100{{nbsp}}mV rather than 1{{nbsp}}V. After 10× amplification the output is a 1{{nbsp}}V, 100&nbsp;kHz sawtooth with a corresponding slew rate of 0.1{{nbsp}}V per microsecond. In this instance, the 741 with its 0.5{{nbsp}}V per microsecond slew rate will amplify the input properly.{{paragraph break}} Modern high-speed op amps can have slew rates in excess of 5,000{{nbsp}}V per microsecond. However, it is more common for op amps to have slew rates in the range 5–100{{nbsp}}V per microsecond. For example, the general purpose TL081 op amp has a slew rate of 13{{nbsp}}V per microsecond.  As a general rule, low power and small bandwidth op amps have low slew rates. As an example, the LT1494 micropower op amp consumes 1.5 microamp but has a 2.7&nbsp;kHz gain-bandwidth product and a 0.001{{nbsp}}V per microsecond slew rate.
;Non-[[linear]] input-output relationship
:The output voltage may not be accurately proportional to the difference between the input voltages producing distortion. This effect will be very small in a practical circuit where substantial negative feedback is used.
;Phase reversal
:In some integrated op amps, when the published common mode voltage is violated (e.g., by one of the inputs being driven to one of the supply voltages), the output may slew to the opposite polarity from what is expected in normal operation.<ref>{{cite web
 |url=http://www.analog.com/static/imported-files/tutorials/MT-036.pdf
 |title=Op Amp Output Phase-Reversal and Input Over-Voltage Protection
 |year=2009
 |publisher=Analog Devices
 |access-date=2012-12-27
 |archive-date=2012-12-02
 |archive-url=https://web.archive.org/web/20121202205518/http://www.analog.com/static/imported-files/tutorials/MT-036.pdf
 |url-status=dead
 }}</ref><ref>
 {{cite web
 |url=http://www.edn.com/contents/images/45890.pdf
 |title=Bootstrapping your op amp yields wide voltage swings
 |last1=King
 |first1=Grayson
 |last2=Watkins
 |first2=Tim
 |date=13 May 1999
 |publisher=Electronic Design News
 |access-date=2012-12-27
 }}{{dl|fix-attempted=yes|date=July 2020}}</ref> Under such conditions, negative feedback becomes positive, likely causing the circuit to ''lock up'' in that state.

====Power considerations====
;[[current limiting|Limited output current]]
:The output current must be finite. In practice, most op amps are designed to limit the output current to prevent damage to the device, typically around 25&nbsp;mA for a type 741 IC op amp. Modern designs are electronically more robust than earlier implementations and some can sustain direct [[short circuit]]s on their outputs without damage.
;Limited output voltage
:Output voltage cannot exceed the power supply voltage supplied to the op amp. The maximum output of most op amps is further reduced by some amount due to limitations in the output circuitry. ''Rail-to-rail op amps'' are designed for maximum output levels.<ref name="rail-to-rail">{{cite web |url=https://www.ti.com/lit/an/sloa039a/sloa039a.pdf?ts=1623104120425&ref_url=https%253A%252F%252Fwww.google.com%252F |title=Application of Rail-to-Rail Operational Amplifiers |publisher=[[Texas Instruments]] |access-date=2021-06-08}}</ref>
;Output sink current
:The output sink current is the maximum current allowed to sink into the output stage. Some manufacturers provide an output voltage vs. the output sink current plot which gives an idea of the output voltage when it is sinking current from another source into the output pin.
;Limited dissipated power
:The output current flows through the op amp's internal output impedance, generating heat that must be dissipated. If the op amp dissipates too much power, then its temperature will increase above some safe limit. The op amp must shut down or risk being damaged.
Modern integrated [[FET]] or [[MOSFET]] op amps approximate more closely the ideal op amp than bipolar ICs when it comes to input impedance and input bias currents. Bipolars are generally better when it comes to input ''voltage'' offset, and often have lower noise. Generally, at room temperature, with a fairly large signal, and limited bandwidth, FET and MOSFET op amps now offer better performance.