#### Low-pass filter

_{c}

Figure 1: Frequency response of a 1st-order low-pass filter

#### Low-pass filter

In the field of electronics, a low-pass filter is a type of filter
that permits signal components with frequencies below a particular cut-off frequency f_{g} to pass through.
On the other hand, signal components with higher frequencies are attenuated.
Typically, these filters are passive two-port networks that are made up of resistors, coils, and capacitors.

The filter function can be explained as a voltage divider, where the capacitor's reactance is dependent on the frequency. For direct current or very low frequencies, the capacitor's reactance is almost infinitely high, resulting in the maximum output voltage. For very high frequencies, however, the reactance approaches zero, creating an almost short-circuit for the output voltage.

(1)

- X
_{c}= reactance of the capacitor - U
_{e}= input voltage - U
_{a}= output voltage

_{c}

Figure 2: Frequency response of a 2nd-order low-pass filter

The cut-off frequency is calculated as follows:

(2)

- f
_{c}= cut-off frequency

Jumps in the DC voltage at the input are transmitted to the output after a charging or discharging process.

When a coil is used in place of a resistor, it creates a 2nd order filter. The order number of the filter increases based on the number of frequency-dependent components used. One way to achieve this is by connecting multiple filters of a lower order in a series.

The cut-off frequency of the 2nd order filter is X_{C} = X_{L}.
It can be calculated with:

(3)