Measurement of Substrate High-Frequency Complex Dielectric Constant With 2-D Spatial Distribution

A high-frequency (HF) S-matrix-based measurement of complex permittivity with a microstrip resonant ring (MRR) and coplanar waveguide (CPW) transmission line (TL) is developed. The permittivity characterization technique exploring the MRR resonance frequency and CPW TL insertion loss enables originally to consider the spatial distribution uniformity. The MRR is coupled with access TL and the CPW integrates hole and transition section to improve the transmission performance. The MRR and CPW parameter theoretical influences around 2 and 10 GHz are examined from 3-D electromagnetic (EM) simulation. As a proof of concept (POC), different batches of domestic and RO4350B substrates are tested and compared. Due to the domestic substrate instability, the CPW and CPW physical parameter effects need to be compared by RO4350B substrate test. High-precision dielectric constant $\varepsilon (x$ , $y$ ) and loss tangent $\tan \delta (x$ , $y$ ) at 2- and 10-GHz frequencies are measured with respect to the dielectric surface coordinates ( $x$ , $y$ ). The measured differences between $\varepsilon (x$ , $y$ ) and $\tan \delta (x$ , $y$ ) at various coordinate positions compared to the average values are assessed. The precision of dielectric constant testing can reach 0.004. The domestic substrate relative permittivity presents inhomogeneous property at the considered test frequencies.