# Low-pass filter and its applications!

In this article, the World of Electrical presents elements that are fundamental in electrical, such as power electrical and communication systems for example. We will discuss what filters are, what is a low-pass filter, what is a low-pass filter for and how a low-pass filter works. Come on!

## What are the filters?

In electronics, this is where filters offer several applications, being widely used for signal, audio, video and data processing, as well as being used in power, telecommunications and control systems, among other applications.

As its name suggests the filter has the ability to filter, but what exactly does it filter? An electrical filter has the function of selecting or rejecting one or more frequency bands of a given electrical signal.

It is important to highlight that there are techniques that are used to obtain electric filters, that is, we have the passive technique and the active technique. Passive filters are those that use essentially passive components such as resistors, capacitors, and inductors.

Active filters can also contain passive and other elements. It is important to mention that the filters have again. For those who do not know, the gain does not have a unit of measurement and is dimensionless, it is just the relationship between the output signal and the input signal. The gain of a passive filter will always be less than 1 and the gain of an active filter can be greater than 1.

## Passive low-pass filter

Passive low-pass filters are circuits that allow the passage of low-frequency signals and reduce the intensity of high-frequency signals, that is, from a reference frequency it allows lower frequencies to pass freely and lower frequencies. high are attenuated, so your gain will be a maximum of 1.

## Passive low-pass filter – Operation

The passive low-pass filter circuits are composed of a resistor and a capacitor, which are connected in series. The output signal already filtered is in parallel with the capacitor, as well as a voltage divider, as we can see in the image below.

Circuit of a passive low-pass filter.

Before starting the explanation, it is necessary to have knowledge about some concepts of electricity and mainly how a capacitor behaves in alternating current circuits and direct current circuits.

It is possible to understand the operation of the low pass filter through two explanations, one of which we must take into account the capacitive reactance and the other way is the time of charge and discharge of the capacitor.

First, let’s understand through capacitive reactance. When the capacitor is subjected to alternating signals it has a resistance, which is defined as capacitive reactance.

With the capacitive reactance formula and considering the value of the constant capacitance, it is enough to understand the functioning of the low-pass filter. The capacitive reactance formula is in the image below.

Capacitive reactance formula.

By the formula, we can observe that if the frequency value is low, the capacitive reactance will be high and if the frequency is high, its capacitive reactance will below. That is, low-frequency signals the capacitor tends to increase its capacitive reactance and block it, and high-frequency signals the capacitor tends to lower its capacitive reactance and allow the signal to pass.

Knowing how a capacitor behaves in certain circuits and what a passive low-pass filter circuit looks like, if a load is connected in parallel with the capacitor, the high-frequency signals will pass through the capacitor and the low-frequency signals will pass through the load, characterizing a low-pass filter. This happens in the same way as a circuit with two resistors in parallel, and the current of greater intensity passes through the path of least resistance.

## Passive low-pass filter – Cutoff frequency

It is important to highlight that this analysis that we did is relatively simple, because we have not defined any reference to say what is high or low frequency, called the cutoff frequency. The cut-off formula for the passive low-pass filter is shown in the image below.

Passive low-pass filter cut-off formula.

According to the analysis we did we can see that only with the capacitor it is possible to cut the signals of higher frequency and let the higher frequency pass, but as we just saw, we need to define the cutoff frequency of the filter and for that, we need the resistor, without it it would not be possible to select the highest frequency value allowed to pass.

The cutoff frequency is also defined as the frequency at which the signal is attenuated, with the value of this attenuation being approximately 30%, that is, the output signal has approximately 70% of the input signal strength. As we said earlier, the resistor has a very important function in the circuit, as these values ​​are not random. We obtain these attenuation values ​​when the capacitive reactance is equal to the resistance, that is, when they enter resonance. If you want to better understand how certain filters behave in alternating current, the video below from the World of Electrical explains in detail and in a very simple way what electrical impedance is. This will help you better understand what capacitive reactance is.