Op-Amp Gain
Closed-loop gain for inverting and non-inverting configurations.
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The engineering
Feedback makes the gain depend on two resistors instead of the amplifier — that trade of raw gain for precision is the whole op-amp idea. Note the inverting stage's input impedance is just R1, which loads whatever drives it.
Real limits arrive as gain-bandwidth product: a 1 MHz GBW part at gain 100 is a 10 kHz amplifier.
Where this math comes from
Harold Black sketched negative feedback on a newspaper aboard the Hudson River ferry in August 1927 — trading gain for distortion in telephone repeaters, an idea his own patent examiners found absurd. It is arguably the most consequential circuit idea of the century.
George Philbrick's vacuum-tube K2-W (1952) made the 'operational amplifier' a commercial building block, and Bob Widlar's µA702/µA709 ICs (1963–65) put one in every signal chain on earth.
- 1927Harold BlackNegative feedback, sketched on a ferry-ride newspaper.
- 1941Karl Swartzel (Bell Labs)Summing amplifier for the M9 gun director — the op-amp's war job.
- 1952George PhilbrickK2-W — the first commercial op-amp.
- 1965Bob WidlarµA709 monolithic op-amp; the IC era begins.
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