# How does a capacitor work as a filter?

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I understand that capacitors will charge until it’s “full” and voltage and current = 0 because no more electrons can go through. In AC circuits, capacitors will charge and discharge according to the ups and downs of the sin graph. But how does this filter noise?

Noise being different frequencies than the sin wave that we want?

In: Physics

You can look at a capactor as a resistance with a low resistance at high frequency and high resistance at low frequency. In the case of DC it let nothing trough. To what degreree this happen at different freqiunsis depend on the capacitance of the

A simple filter do not filter out noise it blocks different frequencies to different amount. If you have a system where you for some reason have nose at a higher frequency then the signal you can filter it out with a filter that let low frequencies too and block high frequencies.

That would be called a low pass filter and a very simple open looks like [this](https://qph.cf2.quoracdn.net/main-qimg-7ab20326bdddb4a7a1e65322743ea15b) The capacitor let trough the high frequencies to ground but low frequencies continue on the upper line. You can look at it as a low frequency signal will change slow enough so the capacitor get changed to the same voltage with low delay compared to the length of a period. A high frequency signal will have a shorter period and then the capacitor will not get change fast enough so all change is used to change up the capacitor and do not pass on in the circuit

If you have noise at lower frequency then the signal you use a high pass filter and let the high frequencies trough. A simple filter will look like [this](https://qph.cf2.quoracdn.net/main-qimg-ac9b2cfe1b3c208700a1635062c40e8a)The resistor and capacitor is swapped.

Put a high pass filter after a low pass filter with appropriate component values and you can select a frequency range that can pass troug. That is called a band pass filter. [https://www.allaboutcircuits.com/uploads/articles/capacitive-band-pass-filter-circuit.png](https://www.allaboutcircuits.com/uploads/articles/capacitive-band-pass-filter-circuit.png)

A capacitor does not allow DC through because it fills up. The closer a signal is to DC (the lower its frequency), the more difficulty it has passing through a capacitor.

This also means that you can have a shunt capacitor – one that allows AC signals to go straight to ground instead of continuing down the wire. This gets rid of them. Meanwhile DC signals cannot pass and so the AC component can be removed.

Combining both, or adding an inductive filter too, can allow us to select a particular range of frequencies that we want to allow through a wire.

Lets say you send sine waves through a capacitor. **At a low frequency the capacitor fills long before the wave changes sign**. A fast frequency does not last long enough for that, it changes sign before it gets close to full and then even depletes it again.

But even for high frequencies it isn’t just letting them through unhindered. **The fuller a capacitor already is, the less current will flow** in (at any fixed voltage). So the slower a sine wave changes, the more it fills the capacitor, and thus the less current will flow on average.

But **the ratio of voltage per current is _resistance_**. So what we have observed is that a capacitor acts like a resistor, but not one of fixed value. Instead **the capacitor acts like a resistor that depends on frequency**; slow waves face high resistance, higher frequencies lead to low resistance. If you do the math you will find that the resistance is proportional to 1/frequency.

In practical terms this means that **putting a capacitor in series will strongly hinder low frequencies**, while letting high ones through. A _high pass filter_, it lets high frequencies pass through. **If instead you put a capacitor in parallel to a device, then all high frequencies will be diverted through the capacitor**, the device will mostly get the low ones. A _low pass filter_.

For all intents and purposes you can see DC as AC of zero frequency whenever it matters.

Okay, but to understand filtering you need one more crucial ingredient: **the superposition principle**.

Certain basic components such as resistors, capacitors, inductances(coils), transformers, and a bunch more are (almost) _linear_. This means that **combining two inputs leads to the combined result of whatever they would do individually**.

Lets as an example look at the combination of a low frequency and a high frequency wave such as a radio signal (sound waves, 20-20000 Hz) on a carrier wave (megahertz range or above). Say we again put a capacitor in parallel to our sensor or a loudspeaker:

– Most of the high frequency wave is diverted through the capacitor and thus not seen by our sensor.
– The low frequency wave however flows mostly through he sensor, as the capacitor acts like a high resistance.

Thus by the superposition principle our sensor will primarily see the low frequency part. It filters the carrier wave of the radio signal and leaves us with the sound part. This is far from the only or best way to make a radio receiver, but it definitely is a starting point.

Lastly it should be noted that _inductances_ such as coils act exactly the opposite way: they strongly block high frequencies but let low ones through.

A capacitor can accommodate AC signals because, as you say, they fill and empty and refill. It turns out this isn’t a binary thing, where DC is blocked and anything wave-shaped sails right through.

The impedance of a capacitor is 1/jωC where ω is the angular frequency of the signal and C is the capacitance. So if you have a really high-frequency signal the impedance is tiny, low-frequency sees higher impedance, and DC’s frequency is effectively zero so it sees a capacitor as an open circuit/brick wall.

So the higher frequency you are, the more capacitive circuits like you; you can use capacitance to make a “high-pass” filter where high frequencies go through and low freq/DC gets blocked. With inductors you can make low-pass filters which do the opposite (friendly to DC, block high frequency) and by combining those we can make band-pass filters where too high *and* too low freqs get blocked.