What is a Butterworth Filter?
The term Butterworth refers to a type of filter response, not a type of filter. It is sometimes called the Maximally Flat approximation, because for a response of order
n, the first (2n-1) derivatives of the gain with respect to frequency are zero at frequency = 0. There is no ripple in the passband, and DC gain is maximally
The following figures are representative of a low pass filter. The response characteristics are mirror imaged for high pass filters.
The designer can see that there is no ripple in the passband of a Butterworth filter or a Bessel filter. The Butterworth filter, however, has a flatter response in the
passband. There is a continuum of filter characteristics, of which Bessel is one, and Butterworth another; but anything in between is possible - it just wouldn't have
a name. The Chebyshev response continues the continuum beyond Butterworth, which is the last characteristic for which there is a flat passband.
The phase response of the three filter types is shown below. The Butterworth response is a compromise between Bessel and Chebyshev.
The group delay of the three filters is shown below. The Butterworth response is a compromise between Bessel and Chebyshev.