Hourglass Filters

The Hourglass filter's distinguishing trait is that the reflection zero frequencies are exactly the inverse of the transmission zero frequencies. The Hourglass Filter is similar to the Chebyshev Type II Filter, but has a sharper cut off, higher group delay, and greater stop band attenuation. The pass band also contains a slight equiripple characteristic, which makes it a special case of the Elliptic filter. The distinguishing feature of the Hourglass filter is that the reflection zeros are the reciprocal of the transmission zeros.

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

The Hourglass Filter was first derived  by Dr. Byron Bennett of Montana State University, and is documented in IEEE Transactions on Circuits and Systems, December 1988, volume 12 page 1469.

Below are examples of 5th order Hourglass low pass, high pass, band pass and band stop filters and low pass step response. The stop band ratio is 1.2 in all cases shown. Compare the stop band attenuation and the group delay to that of the Chebyshev II and Elliptic Filters.