Uncertainty of S-Parameter Measurements on PCBs due to Imperfections in the TRL Line Standard

This paper evaluates the uncertainty of S-parameter measurements on multilayer printed circuit boards (PCBs) due to the uncertainties of the dimensions and dielectric properties of the line standard in the Thru-Reflect-Line (TRL) calibration. This evaluation is performed in two ways: one is based on repeated TRL calibrations with a randomly perturbed line standard, and the other is based on equations given by Stumper. The two methods require the uncertainties of the S-parameters of the TRL line standard, which are obtained from the uncertainties of the dimensions and dielectric properties using three-dimensional electromagnetic Monte Carlo simulation. The two methods agree well with each other. This study also shows how to apply impedance renormalization in Stumper's equations. We design the TRL standards and the devices under test (DUTs) in PCB stripline and precisely measure the cross-sectional dimensions of the fabricated striplines. Uncertainty analysis based on the measured values enables us to investigate the impact of realistic deviations in the dimensions of the TRL line standard on the S-parameter measurement uncertainty of the DUTs. Finally, as an example, we evaluated the uncertainty in the measured S-parameters of a Beatty line on the fabricated PCB.