Passive filters do not require an external energy source to operate. Such simple filters consist of resistors and capacitors or coils. The latter two components are suitable because their resistance varies with frequency, behaving very differently at low and high frequencies.
As the name suggests, it passes the low frequencies and blocks the higher frequencies. The cut-off frequency is the point at which the output (gain) starts to decrease, specifically where the power ratio is halved (-3 dB).
A low-pass filter can be easily built from a resistor and a capacitor. Based on the principle of voltage dviders, the two components are connected in series. The output signal of the filter is the voltage across the capacitor, and because a capacitor behaves like a small resistor at high frequency, the output voltage will be low.
$ f_c = \dfrac{1}{2 \pi ⋅ R ⋅ C } $
Coils can also be used to form a low-pass filter, but here they are connected in the opposite order, with the resistor voltage as output. At high frequencies, the coil is a large resistor causing a low output voltage.
$ f_c = \dfrac{R}{2 \pi ⋅ L} $
If frequencies below the cut-off frequency need to be blocked, a high-pass filter is needed. In both low-pass and high-pass filters, the filtering of frequencies is gradual, with a 20 dB reduction in signal strength per decade starting from the cut-off frequency, so it is obviously not instantaneous.
A resistor and a capacitor (RC) can be used to build a high-pass filter where the output of the voltage divider is the voltage across the resistor, so at high frequencies the capacitor causes the output voltage to be high.
$ f_c = \dfrac{1}{2 \pi ⋅ R ⋅ C } $
The principle is the same as for all previous RC and RL passive filters. In the voltage divider, there is a coil at the output, across which a low voltage is measured at low frequencies, thereby filtering low frequencies.
$ f_c = \dfrac{R}{2 \pi ⋅ L} $