Optimal Series Resistors for On-Wafer Calibrations

The series resistor (SR) is a common on-wafer device typically used in the series-resistor (SR) calibration and for estimating the capacitance per unit length of coplanar waveguide (CPW) transmission lines. While much work has been done using SRs, this article addresses the design of the resistor itself, considering both its dc resistance value and geometry, and evaluates which resistor is the best resistor. We fabricated 48 different SRs with dc resistances ranging from approximately 1 $\Omega $ to over 6 $\text{k}\Omega $ and tested their utility in the SR calibration and in extracting the capacitance per unit length of CPW transmission lines. We found that a dc resistance near 100 $\Omega $ produces the best SR calibration when compared to multiline thru-reflect-line. For extracting the capacitance per unit length, resistors with a dc resistance near 150 $\Omega $ and shorter than 20 $\mu \text{m}$ long gave the capacitance values with the lowest uncertainty. In addition, we provide some guidance on choosing frequency bounds for the capacitance estimation. These results are of interest to anyone who performs on-wafer calibrations.