Automatic Pole Zero Placement

If the filter is a low pass or band pass, and is a Butterworth, Chebyshev I, Chebyshev II, Hourglass, or Elliptic, then all pass poles and zeros may be automatically positioned by checking the Delay Equalize box on the FilterSolutions Main control panel. Enter the desired order of the delay equalizer in the adjacent text box, and create the filter. If Passband is checked, FilterSolutions will attempt to create a group delay with a minimum possible standard deviation within the pass band. To delay equalize out to a specified attenuation, uncheck Passband and enter the desired attenuation to equalize out to.

The ideal frequency graph of a filter created with an automatic delay equalizer will display the standard deviation of the group delay within the pass band in the upper left corner. This displayed value is updated in real time when poles and zeros are manipulated and the RTU box is checked.

For large filters, it is often possible to reduce the group delay standard deviation more by manually adjusting the all pass poles and zeros after performing an automatic equalization.

 

Band Pass Filter Delay Equalizers

Band pass delay equalization creates a special problem because the delay equalizer all pass sections do not necessarily have a prototype. Medium width band pass filters require equalizers that do not have a prototype, and narrow band filters require an equalizer that is most efficiently constructed using a prototype. For bandwidth to pass band ratios above 0.20, FilterSolutions uses a nonprototype equalization solution, and for ratios of 0.20 or less, a prototype solution is used.

 

Digital and Transmission Line Equalizers

Due to the inherent warping of the frequency axis, filters that have been successfully equalized for the ideal case may still exhibit undesired group delays when implemented as digital or transmission line filters. When this happens, it is necessary to manually equalize the digital or transmission line filter using real time pole/zero manipulation.