The Operational Amplifier

The name is literal. John Ragazzini and his colleagues at Columbia coined it in a paper of May 1947 about wartime work on gun directors, and the amplifiers in question were called operational because they performed mathematical OPERATIONS - adding, scaling, integrating, differentiating - inside a machine that solved the differential equations of a shell in flight while the shell was still in the gun. The circuit is Black's feedback amplifier with the loop closed by two impedances instead of two resistors, and the argument for it needs no electronics at all. Give the amplifier enormous gain and an inverting input. For the output to sit anywhere sensible, that input must be within microvolts of zero, so no current goes into the amplifier and whatever arrives through the input resistor has to leave through the feedback element. That is Kirchhoff, and it means the answer is a ratio of two components. Put a capacitor in the feedback path and the same argument gives you an integral. It is the same integral the wheel-and-disc machine performed with friction sixteen years earlier, and it wins for a reason that has nothing to do with accuracy: both are good to about a tenth of a per cent, and one takes a day of gearing to set up while the other takes a few minutes of patch cords. It loses on one column, and that is worth knowing. A friction wheel parked at a radius stays there all day; a charged capacitor leaks, and the amplifier's own offset voltage and bias current are integrated along with the signal. A general-purpose bipolar op-amp integrating onto a microfarad will hit the supply rail in under two minutes with no input at all. That is why every analogue computer has a reset button and no differential analyser ever needed one.