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It is my experience that:
Operational amplifiers are particularly useful when their gain and bandwidth is significantly curtailed by negative feedback of part of their output signal. Depending on how this is done, an operational amplifier with feedback circuit can be configured (for example) as an analog signal high-fidelity wide-band audio amplifier, an analog signal inverter, an analog signal mathematical integrator, an analog signal differentiator.
It was not unusual for operational amplifiers with rated voltage gain of 100000 [i.e 100 decibel (db)] to have negative feedback applied that reduced their gain reduced to 20 db (i.e. voltage gain of 10) or so, to ensure their stability and hence their reliability.
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An op amp is best used as either an operational amplifier or an oscillator.
op amp have very hight voltage gain with small input voltage
Op amp use in many operation like adding interating and many other maths operation
They are used as a sort of new "super" circuit element that allows you make all sorts of other circuits whereby the desired parameters are given by regular linear component values rather than silicon device properties. Mostly they are used to make amplifiers of various kinds.
The most basic usage is as either an inverting or noninverting amplifier.
Mainly for amplification or attenuation purpose..
And signal modification (Delay or Shift)
To provide gain at DC and audio frequencies.
WIDE BAND AF AMPLIFIER.
OSCILLATOR.
BUFFER.
COMPARATOR.
CONSTANT CURRENT SOURCE.
CONSTANT VOLTAGE SOURCE.
DETECTOR.
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TOO MANY WAYS, A WHOLE BOOK TALKS ABOUT THIS SUBJECT.