Theoretical introduction
Introduction
Electrical filters are electrical systems that pass electric waveforms contained in a specific frequency band and attenuate waveforms of other frequencies.
In practice, this definition means that any system that performs operations on an electrical signal in the frequency domain can be called an electrical filter. Filters are most often used to remove unwanted components from the signal, usually interference and noise. They can be divided according to the type of frequency response into filters:
- low-pass,
- high-pass,
- band-pass,
- band-stop.
Idealized characteristics of these filters are shown in Figure 1.
The part of the frequency response that is passed through the filter is called the passband of the filter, and the part of the frequency response that is attenuated is called the stopband. For low-pass and high-pass filters, the cut-off frequency \(\omega_g\) is defined, at which the filter gain drops by 3dB. For band-pass and band-notch filters, the center frequency \(\omega_0\) and the filter band \(\Delta \omega \) are defined. The ratio of the center frequency to the bandwidth is called the filter quality \( Q = \frac{\omega_0}{\Delta \omega} \).
Ideal filters have constant gain in the passband and infinite attenuation in the stopband. The slope of the filter characteristic is vertical. Such filters are impossible to implement in practice, real filters approximate the characteristics of ideal filters.