What Is the Butterworth Filter?

Butterworth filter (Butterworth filter) is a type of electronic filter, it is also called the maximum flat filter. The characteristic of Butterworth filter is that the frequency response curve in the pass band is flat to the maximum, without ripple, and it gradually decreases to zero in the stop band. ^[1]

This filter was first proposed by British engineer Stephen Butterworth in a paper published in the British "Radio Engineering" journal in 1930. ^[2]

Butterworth filter features

The Butterworth low-pass filter can be expressed by the squared-frequency formula of the following amplitude: ^[3]

The characteristic of Butterworth filter is that the frequency response curve in the pass band is flat to the maximum, without fluctuation, and it gradually decreases to zero in the stop band. On the wave-diagram of the logarithmic diagonal frequency of the amplitude, starting from a certain boundary angular frequency, the amplitude gradually decreases with the increase of the angular frequency and tends to negative infinity. ^[3]

Butterworth filter is a design classification of filters, similar to Chebyshev filters, it has

Compare with other filters

The following figure is the frequency response diagram of Butterworth filter (top left) and Chebyshev filter (top right), Chebyshev filter (bottom left), and elliptic function filter (bottom right) of the same order. .