60 GHz square open-loop resonator (SOLR) based on planar Goubau line (PGL) technology
Résumé
This study presents the design, fabrication, and measurement of a square open-loop resonator (SOLR) on high resistivity silicon substrate feed with a planar Goubau line (PGL), which is a very low-loss transmission line around 60 GHz fabricated through a very simple and low-cost process. Electromagnetic simulations using ANSYS high frequency structure simulator are performed for the PGL structure, in order to determine the PGL characteristics (impedance, losses and quality factor) versus the line width. The geometrical parameters of the SOLR structure are studied to observe their impact on reflection and transmission properties. An equivalent lumped element circuit is extracted from the distributed planar design to study and optimise the resonating structure using Advanced Design System. This electrical circuit response is successfully compared to the planar electromagnetic structure one, and a parametric study permits to better understand the role of the different circuit elements. Field displays lead to a better understanding of the SOLR behaviour. For measurement purpose of the fabricated structure, a coplanar waveguide-PGL transition is optimised with 0.9 dB losses. Simulation and measurement results show good performances for filter applications with 1 dB losses and small size at 60 GHz for 10% bandwidth. through electromagnetic simulations using ANSYS high frequency structure simulator (HFSS) software. Besides, an equivalent lumped element circuit is proposed to optimise the resonator response. In order to measure the fabricated SOLR with coplanar probes, we need a coplanar waveguide (CPW)-PGL transition, a simple design CPW-planar Goubau type was first studied for THz BioMEMS application [10, 11], this design was also presented for millimetre-wave applications in [3]. In this work, we have optimised the design defined in [3] after adding a glass wafer below the filter to reduce the probe station metallic chuck effect on the field distribution. Finally, experimental results are compared with simulated data obtained through electromagnetic modelling as well as the related equivalent lumped element circuit. 2 PGL structure The proposed PGL structure (Fig. 1a) consists of a 1 μm thick gold conductor line (σ = 4.1 × 107 S/m) deposited on a bi-layer substrate: 350 μm high resistivity silicon substrate (ε = 11.6, σ = 0.025 S/m) on a 500 μm glass substrate (ε = 11.6, tan δ < 0.001); the glass substrate has been added to keep away the effect of the metallic surface of the measurement bench. Fig. 1b shows the electrical field distribution of the 50 µm width PGL, which is clearly confined near the metallic wire. The PGL acts as a high-pass filter; substrate's permittivity and thickness have been essentially modified in [3] to reduce the cutoff frequency. The PGL characteristic parameters (characteristic impedance Z C , attenuation coefficient α, and quality factor QL) are extracted from electromagnetic simulations using HFSS by applying a parametric study to the gold conductor width. Fig. 2a shows an impedance varying at 60 GHz from 100 to 40 Ω for PGL width varying from 50 to 500 µm. Very low attenuation coefficients α between 0.05 and 0.08 dB/mm along with a very high-quality factor defined as QL = β/(2 × α) (with β the phase constant) and of values between 185 and 300 are obtained for the same width variation (Figs. 2b and c).
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