3-D printed bandpass filters with coupled vertically extruded split ring resonators

The additive manufacturing process of multimaterial extrusion offers performance advantages using functional materials including conductors while making accessible the third dimension in the design of electronics. In this work we show that the additional geometrical freedom offered by this technique can be exploited for the design and realisation of filters made of three- dimensional (3D) resonators that exhibit enhanced characteristics. The coupling properties of 3D grounded square split ring resonators (SRRs) are initially explored. We demonstrate by simulations and experiments that SRRs with finite height display significantly stronger coupling compared to equivalent thin printed circuit structures. The observed trend can be exploited for designing filters with wider operational bandwidths for a given footprint, or miniaturized layouts and enhanced compatibility with fabrication limits for minimum feature size and spacing without performance degradation. This concept is demonstrated by presenting results of full-wave simulations for sample bandpass filters with identical footprint but formed by coupled 3D square SRRs of different heights, showing that filters with taller resonators exhibit increasingly wider bandwidths. Two filter prototypes with centre frequencies at 1.6 GHz and 2.45 GHz are manufactured by multimaterial 3D printing. The measured characteristics of these prototypes are found to be in good agreement with numerical simulations taking into account the effect of the lossier metallic and dielectric materials used in 3D printing and confirm the predicted larger bandwidth of the filters made of 3D SRRs with marginally higher insertion losses.