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Capacitor-input filters are a common thing. However, what is the theory behind this and can someone show me some evidence of before and after using them? I read the wikipedia page on this and it seems a bit technical for a new comer - too many concepts at once. Can anyone care to explain more simply?

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It's a low-pass filter which attenuates high-frequency signals and allows low-frequency signals to pass through it. Basically, the capacitors pass high frequencies better than low frequencies so high frequencies are shunted to ground, and don't appear on the output. The inductor works in the opposite fashion, and passes low-frequency signals much better than high-frequency ones.

If you find the theory behind that type of filter difficult, make one for yourself and try it out with a suitable signal generator and oscilloscope.

Where I once worked, I designed a system that met all the EMC requirements in our preliminary testing, apart from a VHF emission from the RS-232 cables that connected it to the host PC. An additional little PCB by the RS-232 connector with Pi filters as in that article solved the problem and the system passed the formal tests without any problems.

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I'm not going to explain the pi configuration, but you can understand much of its function when you look at the individual components.
The impedance of a capacitor is inversely proportional with frequency: the higher the frequency, the more it conducts. So high frequency disturbances are shortcut to ground. Also, the impedance of the coil is proportional with frequency: the higher the frequency the less it conducts. So the high frequency disturbances which haven't been filtered away by the capacitor will be blocked by the coil.

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