Impact of Z_Ref Estimation for Transmission Line Characterization Based on 2X-Thru Calibration

When using 2x-thru calibration for PCB transmission line characterization, accurate estimation of the reference impedance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathrm{Z}_{\text{ref }})$</tex> is crucial to the accuracy of the renormalized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S$</tex> parameters. In this paper, we compare three different methods of estimating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Z}_{\text{ref }}$</tex>: the mid-point method, initial-value method, and an analytic method. The results show that (i) initial value method is accurate at high-frequency, but not so at lowfrequency, (ii) constant- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{ref }}$</tex> methods can have incorrect DUT TDR regardless of the chosen <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Z}_{\text{ref }}$</tex>, and (iii) analytic method using frequency-dependent <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z_{\text{ref }}$</tex> produces better results.