Sequential tuning of coupled resonator filters using Hilbert transform derived relative group delay

A sequential tuning technique for coupled resonator filters using the Hilbert transform derived relative group delay is demonstrated. It is shown that the S₂₁ group delay contains sufficient information for filter tuning and that this group delay can be derived from the magnitude of S₂₁ using the Hilbert transform. This technique allows for the cost of the required tuning hardware to be decreased by an order of magnitude compared to a complete VNA setup. Measured results for the tuning technique using a 3-pole 3% bandwidth filter at 14 GHz are shown with an achieved return loss of 13 dB demonstrating the usefulness of the technique for coarse filter tuning.