Pin-Gap Correction of Coaxial Calibration Standards for TRL or LRL Calibration

In this paper, a novel method is proposed by which to correct the pin gaps of coaxial calibration standards for Thru-Reflect-Line (TRL) or Line-Reflect-Line (LRL) calibration. This method is a post-process in which the pin-gap correction is applied to the measured S-parameters of the device under test (DUT) after TRL or LRL calibration. It is based on the perturbation equations derived from the sensitivity-coefficient approach. These equations enable us to obtain the correction quantity of the DUT-S-parameter due to the pin gaps. We verify the proposed method by simulation for a 2.4 mm coaxial line, and the result shows that the pin-gap correction works successfully. Because the method is based on the perturbation equations, the smaller the pin gap, the better the correction results. Nevertheless, we can achieve sufficient correction results within the range of the pin-gap to at least 10 times the nominal value. In addition, the proposed pin-gap correction can play the role of impedance renormalization, even though the two LRL calibration lines have different characteristic impedance. Finally, we demonstrate the correction method for a 2.4 mm coaxial LRL calibration kit through measurement.