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I would like to create a circuit with a button. When this button is pressed, a circuit should be closed for a fixed amount of time. Right now, I have managed to get the desired effect using an arduino, but that seem way overkill for my needs.

I have found similar questions, like this one on EE, but my requirements are different. I need the circuit to be closed for 1 to 50 milliseconds (the value would be selectable using a potentiometer). Is the 555 timer suitable for this kind of durations?

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Yes, you could use NE555 in a monostable one-shot configuration. There is a lot of posts/docs about it. Just use google.

Another solution, simpler, is something like this:

oneshot

For a 5V supply, if you vary R1 between 10Ohm and 1kOhm, you get a one-shot pulse that powers RLoad for a time between ~1ms and ~50ms (this is not tight tolerance). The load shouldn't be much more than 50mA, otherwise, you need to adjust other parameters.

There is one thing to take care, however, is that you can run into missed or shorter pulses problems if the switch is closed/opened/closed too fast (200ms of opening time between two button presses seems to be enough to guarantee you won't run into those problems).

Note: The load can be powered by a voltage different from the switch voltage without effect on the delay time.

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It's not coincidence that you found 555. Fixed time means you have to measure time. 555 is classic to make sawtooth wave, compare it to reference and restart by discharge sawtooth capacitor.

Milliseconds time is just fine for 555. By the way, the circuit is called monostable.

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