Miniaturization of superconducting filters using Hilbert fractal curves

This work presents novel compact high-temperature superconductor microstrip resonators and filters based on the Hilbert space-filling fractal curve. Several Hilbert resonator configurations have been assessed by using a full-wave electromagnetic simulator and their miniaturization performance has been investigated, emphasizing the parameters which allow obtaining good tradeoff between compact size and losses. These resonators have proved to be useful for filter design. A four-pole 2.45-GHz quasi-elliptic filter and a four-pole 1.9-GHz Chebyshev filter have been realized by patterning 10 mm×10 mm Y₂Ba₃Cu_7-δO thin films on MgO substrates. Insertion losses of the order of 0.2 dB have been measured, showing good agreement with the simulations.