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This paper presents the design and analysis of guided wave notch filters using the Lagrangian formulation for metamaterials. It is shown that the application of the Lagrangian is a convenient and effective way to select an appropriate filtering structure and determine the necessary configuration for desired filter performance. A WR-187 waveguide horn antenna is investigated with notch filters composed of broadside coupled and gap coupled split ring resonators. It is shown that broadside coupling offers significant tunability in a compact size. The filter exhibits an operational bandwidth from approximately 3.9–5.7 GHz with 40–150 MHz of instantaneous bandwidth. The fabrication of the horn antenna and split ring resonators is presented along with simulated and measured data that confirms the approach.

A WAVEGUIDE HORN ANTENNA WITH COUPLED RESONATOR NOTCH FILTER DESIGNED BY THE LAGRANGIAN FORMULATION FOR METAMATERIALS