Butterworth and Chebyshev Pole Locations
The Applets below shows the relative pole location for
Butterworth and Chebyshev low pass filters in the complex
For the Butterworth approximation,
the green and red semicircles together show the unit circle
on which the Butterworth poles lie. The red poles on the
unit circle produce unstable responses and are not used to
implement the filter. The filter transfer function is derived
from the green poles on the left of the imaginary axis in the s plane.
For the Chebyshev approximation, the poles lie on the (cyan + orange)
ellipse and the filter transfer function is calculated from the cyan poles
on the left of the imaginary axis.
In the case where the Chebyshev poles are calculated to produce an
attenuation equal to the ripple at the cutoff frequency, the pole locations
are shown below. In this case the major radius of the ellipse can be
larger than unity.
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COPYRIGHT © 2005 Cuthbert Nyack.