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.
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