In electronics, **filter** is an electrical circuit that allows or it does not allow electrical signals to pass depending on their frequency**f**. Filters are used to suppress signals with unwanted frequencies. There are different types of filters and we have different criteria for dividing them. Due to their use, filters are divided into:

• LPF - Low Pass Filter,

• HPF - High Pass Filter,

• BPF - Band Pass Filter,

• BSF - Band Stop Filter.

We also divide filters according to their construction. For example, there are **RC filters**.

Below we have an ideal filter, i.e. one that completely suppresses unwanted signals.

Frequency | A shift | B shift |
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Examine the characteristics of this filter, i.e. determine the dependence of the gain **A** on the frequency of the signal **f** - you can choose a circuit from among four types of filters.

Gain **A** is the ratio of the amplitude of the output signal U_{0out} to the amplitude of the input signal U_{0inp}.

This is an ideal filter, so for a low-pass filter we have A = 0 for signals with attenuated frequencies, and A = 1 for passed signals.

Note that this ideal filter, however, causes a small phase shift of the output signal U(t)_{out} relative to the signal fed to its input U(t)_{inp}. - you can see it on the oscilloscope screen

In practice, we use filters for which the gain **A** for signals with attenuated frequencies is greater than zero and the phase shift is much greater.

In this simulation, at a certain frequency value **f _{0}** of the input signal U(t)

I have already written above that this is not the case in real filters. Consider RC low-pass filter. Its frequency response A(f) is as follows.

The output signal U(t)_{out} from this filter decreases gradually as the frequency **f** of the input signal increases. In other words, there is no frequency value **f _{0}** for which the value of the signal amplitude U(t)

**Filter cut-off frequency**

We will assume that in the passband of the RC low-pass filter, the value of its gain **A(f)** is A_{n}. In our ideal filter we had A_{n} = 1. In the RC filter there is no band in which **A(f)** has a constant value. Therefore, it is assumed that A_{n} is the largest value of the filter gain.

The filter cut-off frequency **f _{0}** is the frequency at which the gain of the filter