3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

Abstract

This paper investigates physical dimension limits associated with the low-cost, polymer-based masked stereolithography apparatus (MSLA) 3-D printer, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 ~\mu \text{m}$ </tex-math></inline-formula> pixels defining the minimum print feature size. Based on the discretization properties of our MSLA 3-D printer, multi-step quantization predistortion is introduced to correct for registration errors between the CAD drawing and slicing software. This methodology is applied to G-band <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5^{th}$ </tex-math></inline-formula> order metal-pipe rectangular waveguide filters, where the pixel pitch has an equivalent electrical length of 8.5° at center frequency. When compared to the reference Chebyshev filter, our chained-function filter exhibits superior S-parameter measurements, with a low insertion loss of only 0.6 dB at its center frequency of 182 GHz, having a 0.9% frequency shift, and an acceptable worst-case passband return loss of 13 dB. Moreover, with measured dimensions after the 3-D printed parts have been commercially electroplated with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 ~\mu \text{m}$ </tex-math></inline-formula> thick layer of copper, the re-simulations are in good agreement with the S-parameter measurements. For the first time, systematic (quantization) errors associated with a pixel-based 3-D printer have been characterized and our robust predistortion methodology has been successfully demonstrated with an upper-millimeter-wave circuit. Indeed, we report the first polymer-based 3-D printed filters that operate above W-band. As pixel sizes continue to shrink, more resilient (sub-)THz filters with ever-higher frequencies of operation and more demanding specifications can be 3-D printed. Moreover, our work opens-up new opportunities for any pixel-based technology, which exhibits registration errors, with its application critically dependent on its minimum feature size.