Chebyshev Type II Filters

The Chebyshev Type II Filter, also known as the Inverse Chebyshev Filter, contains a Butterworth style, or maximally flat, pass band, a moderate group delay, and an equiripple stop band.

Like the Butterworth Filter, the pass band attenuation of the Chebyshev Type II Filter is defined to be -3.01 dB. However, FilterSolutions allows the user the option of selecting any pass band attenuation in dB's that will define the filters cut off frequency.

 

Derivation:

The characteristic equation of the Chebyshev I filter is:

 

Asymmetrical Band Pass Filters

If it is desired to create asymmetrical band pass filters, the steps are to create a Chebyshev I asymmetrical filter, then revolve the K(s) numerator roots about the respective corner frequencies. This process creates a flat stop band, but slightly corrupts the pass band. The filter pass band is fixed using numerical iterations at the expense of stop band quality.

Using left half plane poles only, the transfer function is: