New Methods for Series-Resistor Calibrations on Substrates With Losses Up to 110 GHz

We present two new methods to perform series-resistor calibrations on substrates with losses. Lossless calibration substrates, which are required by the traditional calibration comparison technique, are not needed. The proposed methods rely on multiline thru-reflect-line-calibrated series-resistor and series-capacitor data. The first method uses closed-form equations and the second method is based on multifrequency optimization. The proposed methods are based on a fundamental assumption that the resistance and the inductance of series-resistor standards fabricated with thin-film technologies are frequency-independent. In addition, an improved version of the traditional calibration comparison technique is proposed and is used as the benchmark technique. By measurement results on a high-resistivity silicon substrate up to 110 GHz, the validity of the proposed approaches is demonstrated.