page_title: Chebyshev filter
section_title: Type II Chebyshev filters (inverse Chebyshev filters)
hierarchical_section_title: Chebyshev filter / Type II Chebyshev filters (inverse Chebyshev filters)
caption_attribution_description: Gain of a fourth order type II Chebyshev electronic filter as a function of normalized frequency, with ε = 0.01
context_page_description: Chebyshev filters are analog or digital filters having a steeper roll-off than Butterworth filters, and have passband ripple or stopband ripple. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the passband.
  This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials.
  The type I Chebyshev filters are called usually as just "Chebyshev filters", the type II ones are usually called "inverse Chebyshev filters".
  Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the passband but a more irregular response in the stopband are preferred for some applications
  .
context_section_description: Also known as inverse Chebyshev filters, the Type II Chebyshev filter type is less common because it does not roll off as fast as Type I, and requires more components. It has no ripple in the passband, but does have equiripple in the stopband.  The gain is:
  In the stopband, the Chebyshev polynomial oscillates between -1 and 1 so that the gain will oscillate between zero and
  and the smallest frequency at which this maximum is attained is the cutoff frequency . The parameter ε is thus related to the stopband attenuation γ in decibels by:
  For a stopband attenuation of 5 dB, ε = 0.6801; for an attenuation of 10 dB, ε = 0.3333. The frequency f₀ = ω₀/2π is the cutoff frequency.  The 3 dB frequency fH is related to f₀ by:
caption: The frequency response of a fifth-order type II Chebyshev low-pass filter with 
    
      
        
          ε
          =
          0.01
        
      
      {\displaystyle \varepsilon =0.01}
exif: {}