Abstract
3-D additive printing technology has been employed recently for the manufacturing of a wide variety of tunable radio frequency (RF) components. In particular, this article is focused on the extraction of magnetically tuned 3-D printed materials suitable for RF circuits. The design and modeling of tunable RF circuits require an accurate electromagnetic (EM) characterization of the 3-D printed dielectric [polylactide (PLA)] as a primary substrate, magnetic particles (CoFeO) as the tunable component in the composite substrate, and copper traces at RF frequencies. The extraction of complex permittivity, permeability, and conductivity parameters is reported over broadband (50-7000 MHz) and narrowband Wi-Fi bands (2.4 and 5.4 GHz) using the best fitting of EM simulated to measured scattering ( S ) parameters. Broadband characterization is performed using best-fit modeling of three different physical lengths of microstrip transmission lines that are fabricated on unknown 3-D printed PLA substrates. Error analysis of this approach was evaluated on commercially available RT/Duroid substrate as a baseline. An accurate narrowband extraction procedure around the resonance frequency of 3-D printed annular ring resonators (ARRs) at 2.4 and 5.4 GHz is performed by the best fitting of simulated material RF properties to measured results. Further modeling improvements are presented through completely 3-D printed circuits that include the bottom and top copper traces with extracted conductivity of one tenth of bulk copper. Moreover, a 50-MHz tuning of ARR operating at Wi-Fi bands is observed and complex permeabilities are extracted at zero and 2-kG external magnetic field for the 3-D printed composite substrate.