Analytical and experimental investigation of substrate permittivity and loss up to 67 GHz

In this paper, we characterize the substrate permittivity and overall loss of different planar transmission lines (TL) such as microstrip (MS), coplanar waveguide (CPW) and grounded CPW (GCPW) using on-wafer probes and a thru-reflect-line (TRL) calibration technique. The theory for calculation of the related effective permittivity from S-Parameter measurements is given and numerical simulations are being used for a fast and precise mapping of the effective permittivity ε_{r, eff} to the physical value ε_r of the TL´s substrate. The method presented can be used for higher frequencies, as long as single mode operation of the TLs is ensured. Thus, an overview on higher order modes in TLs and design rules to suppress them is given. The results up to 67GHz for the aforementioned TL on a conventional RF substrate are presented and used to evaluate approximate models known from publications.