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Operational amplifier
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====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/ΞΌs). 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 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 V per microsecond. After 10Γ amplification, the output should be a 10{{nbsp}}V, 100 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 kHz sawtooth, rather than a 10{{nbsp}}V, 100 kHz sawtooth.{{paragraph break}}Next consider the same amplifier and 100 kHz sawtooth, but now the input amplitude is 100{{nbsp}}mV rather than 1{{nbsp}}V. After 10Γ amplification the output is a 1{{nbsp}}V, 100 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 5β100{{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 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.
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