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What Is the Butterworth Filter?

Andrew Kirmayer
Andrew Kirmayer

Often used in signal processing, a Butterworth filter is generally used in audio circuitry for commercial installations, homes, and in automotive stereos. Typically made of a series of inductors and capacitors on a circuit, the filter does not create a rippling effect in the frequencies and wavelengths that pass through it, as shown in a graphical analysis. The system is therefore also called a maximally flat magnitude filter. It is named for engineer and mathematician Stephen Butterworth who first wrote about the filter in 1930.

Butterworth filters are used in many types of audio speakers. They generally provide audio crossover, which is the filtering of audio signals into different frequencies while music is played. The filters keep these frequencies separate from one another during audio processing. Volume and distortion control, for both analog and digital systems, are typically the result from the independent processing of these different audio frequencies.

Scientist with beakers
Scientist with beakers

There are different types of Butterworth filter design, typically defined by configurations called topologies. Shunt capacitors and series inductors are laid out in the Cauer topology, while a Sallen-Key topology uses resistors and capacitors as well as electronic components called operational amplifiers and buffers. The different configurations in circuitry are usually developed through mathematical formulas incorporating concepts such as polynomials, logarithms, and trigonometry.

Different equations can be used to determine the magnitude of frequency response, the electrical phase, and the timing between the input and output. The capacitors and inductors can be physically switched around to create a high-pass Butterworth filter. Another configuration of the circuit generally creates a band-pass filter, while it is also possible to make a band-stop device as well. The capacitors and inductors can be mixed in different ways to construct the desired kind of filter. There are several other kinds of filters, such as Bessel and Chebychev, which are characterized by different rates of response and loss of frequency intensity, or attenuation.

Mathematical skills are generally required for building various designs such as a low pass Butterworth filter. Numerical formulas typically help determine what the characteristics of the filter, such as cutoff frequency, will be. There are tools on the Internet, however, that can make these calculations automatically for anyone building a Butterworth filter for the first time. The low-pass type can be created by using prototype circuits for designing electronics systems, and most of the time no experience in building such a filter is necessary to make one.

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      Scientist with beakers