The Chebyshev filter

The Butterworth filter provides a good approximation to the ideal low pass characteristics for values of Ω near zero, but has a low fall-off rate in the transition band. The Chebyshev filter has ripples in either the pass band or the stop band but has a sharper cut-off in the transition band. Thus, for filters of the same order, the Chebyshev filter has a smaller transition band than the Butterworth filter. We now look at the analog low pass Chebyshev filter. There are two types of the Chebyshev filter.

Type I (Chebyshev I) is an all-pole filter. It has equiripple nature in the pass band and monotonically decreases in the stop band. For N = order of the filter, the value response looks as below (N = 5 and N = 6 illustrated). The magnitude, |H(jΩ)|, is a symmetric function of Ω.

Type II (Chebyshev II or Inverse Chebyshev) filter has both zeros and poles. It has a monotonically decreasing shape in the pass band and an equiripple behavior in the stop band.

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