Group delay shaping - advanced example

 

Example 1:
The following examples show how addition of complex conjugate transmission zero pairs, can equalize the group delay at the expense of decreased isolation outside the pass band and/or increased circuit complexity.

A reference Ku band filter without group-delay shaping is shown in the CMS screen-dump below. The filter must have 80 dB isolation above 15.1 GHz.

 This non-equalized filter can be implemented through a 9'th order design with two finite transmission zeroes placed above the pass-band.
  

 
Example 2
This Ku band filter has the same center frequency, bandwidth and stop band rejection as the filter from Example 1 - but 3 complex transmission zero pairs have now been added in the pass band - along with the two existing finite zeroes.  

The parameters of the complex transmission zeroes (values of real- and imaginary parts) have been found by a few trials. 

Max group delay variation within 100 MHz sub-band is now 0.8 ns, which is 3.5 times less compared to the non-equalized filter above.
In order to maintain 80 dB rejection above 15.1 GHz it has been necessary to increase the filter order to 12.
Compared to example 1 above - 3 extra poles and 6 extra X-couplings are added.

This example also illustrates how group delay shaping can be used to give a certain GD-tilt within the pass-band, e.g. as compensation for an opposite tilt elsewhere in the system.