Dielectric Test Cavity for 3D Printing Filament

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I designed and built a resonant cavity to test the dielectric constant and loss tangent of filaments used in 3D printing for microwave lenses, as we are developing these lenses using this technology. We need to know these properties because they directly impact our project's success. This is a WR-90 TE101 cavity with a hole at its center where filament can be inserted easily. Perturbation theory tells us how the resonant frequency and Q will change when dielectric material is added to the cavity. The formulas for this calculation can be found on Wikipedia, specifically on the page about cavity perturbation theory: https://en.wikipedia.org/wiki/Cavity_perturbation_theory Experimental Results: Empty Cavity fc = 8.139134 GHz 3 dB Bandwidths: 3 dB = 8.138991 GHz 3 dB = 8.139271 GHz Qc = 29016.52 S11 = -25.336 dB ABS Black from Stratasys Fortus fs = 8.048269 GHz 3 dB Bandwidths: 3 dB = 8.047937 GHz 3 dB = 8.048622 GHz Qs = 11757.88 S11 = -19.974 dB Calculated Values Using Perturbation Theory er' = 2.609524 er'' = 0.003606 Commercial Vendor Specifications for ABS Black from Stratasys Fortus er' = 2.7 - 2.9 er'' = 0.0032-0.0035 Premix 20280 Custom Filament fs = 7.928404 GHz 3 dB Bandwidths: 3 dB = 7.927239 GHz 3 dB = 7.929605 GHz Qs = 3350.974 S11 = -11.327 dB Calculated Values Using Perturbation Theory er' = 4.789159 er'' = 0.018815 Commercial Vendor Specifications for Premix 20280 Custom Filament er' = 4.4 er'' = 0.004 Note that commercial dielectric test equipment is very expensive, with a price tag of $20k. However, it's possible to download and 3D print the STL files provided here. At this frequency, FDM printing might be acceptable, but STL printing is better suited for our needs. I used commercial SLA 3D printing to create my parts, which were then copper electroplated. An alternative method would be hand-painting with silver paint. The WR-90 Cavity dimensions are 0.9 in x 0.4 in x 30 mm. The hole at the center of the broad wall corresponds to the electric field maximum and is also a minimum wall current point, minimizing its impact on the cavity's operation. The hole diameter matches standard 3D printing filament at 1.75 mm. The round aperture between the commercial WR-90 coaxial to waveguide launcher and the cavity provides near-critical coupling with a diameter of 4.25 mm for the empty cavity (no filament present). This was tested using HFSS and optimized empirically. Unfortunately, regular ABS has a dielectric constant too low for our needs. We therefore ordered custom-formulated filament from Premix, which has a published dielectric constant of 4.4.