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Is it possible to construct simple circuits, that given a time-varying input, produce an output that represents the derivative or integral of the input with respect to time?

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  • $\begingroup$ Is it necessary that the circuit is somehow made up of "simple" components? Otherwise, yes, computers can certainly do this. $\endgroup$ – David M. R. Jan 29 '13 at 3:51
  • $\begingroup$ Yes my initial edit of the question had (not computers) in brackets. I'm after a very simple circuit involving resistors, capacitors and transistors. I know "simple" is subjective, so I'm happy for one to find the simplest circuit they can that allows for this. $\endgroup$ – Kenshin Jan 29 '13 at 3:53
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    $\begingroup$ @DavidM.R., can computers do this without employing algorithms with discrete time steps? How? I'm after a non digital circuit that solves the differentiation/integration empirically and exactly. $\endgroup$ – Kenshin Jan 29 '13 at 3:55
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    $\begingroup$ Start browsing for Analog Computers on the internet. Try "en.wikipedia.org/wiki/Analog_computer $\endgroup$ – DarenW Jan 29 '13 at 4:07
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Apparently what you are looking for is called an "Integrator" and a "Differentiator". (I'm not too good with circuits, so I can't judge if these are simple enough.)

See e.g. http://www.allaboutcircuits.com/vol_3/chpt_8/11.html

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    $\begingroup$ have also a look at analogue computers, built up with these as building blocks.en.wikipedia.org/wiki/Analogue_computer . when i started in physics they were compeiting with digital. $\endgroup$ – anna v Jan 29 '13 at 9:46
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As David pointed out in his answer, the circuits are called the differentiator and the integrator respectively. They use operational amplifiers (op amps) to do this.

An op-amp isn't necessarily a "simple circuit" to build, since it consists of several transistors and hundreds of resistors and capacitors, but since it's extremely easily available as an IC, it's plenty easy to build an integrator or a differentiator circuit.

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  • $\begingroup$ Back in my grandfather's day, of course, the amps were tube devices and you could do the same things with them. And they did. $\endgroup$ – dmckee Jan 29 '13 at 19:30
  • $\begingroup$ RC circuit integrates the current $\endgroup$ – Helder Velez Jan 30 '13 at 19:49

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