Chebyshev Filters

Problem:
What is a Chebyshev filter?

Solution:
The term Chebyshev refers to a type of filter response, not a type of filter. It is sometimes refered to as an equal-ripple approximation, and sometimes spelled "Tschebysheff" or some variation thereof. It features superior attentuation in the stop band, at the expense of ripple in the passband. Generally the designer will choose a ripple depth of between 0.1dB and 3dB. Chebyshev filter response, therefore, is not limited to a single value of response.

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 ripple in the passband of a Chebyshev filter. The number and position of ripples is determinined by the order of the filter. Filters with even orders generate ripple that appears above the 0dB intercept and filters with odd orders generate ripple below the 0dB intercept.

The phase response of the three filter types is shown below. The Chebyshev response has the fastest rate of phase change.



The group delay of the three filters is shown below. The Chebyshev response has the longest group delay.