The Reference Impedance in 2x-thru Calibration, and its Estimation for High Conductor-loss Transmission Lines

Abstract

<p>The 2x-thru calibration has emerged as an attractive alternative to the classical TRL for S parameter measurement of printed circuit board and packaging devices, due to its simplicity that only one THRU standard suffices to fully characterize the test fixtures, thus eliminating the LINE measurement in TRL and also overcoming the bandwidth limit. Although various 2x-thru calibration tools are available nowadays, there are still some issues that have not been studied in detail. This paper addresses the following two fundamental questions: (i) what is the reference impedance (Zref) of the S parameters after 2x-thru calibration? (ii) what is the time-domain reflectometry (TDR) response of the THRU for high conductor-loss transmission lines, and how to estimate Zref given such TDR? For problem (i), we rigorously show that the Zref is equal to the characteristic impedance of the center transmission line in the THRU standard, and provide the important interpretation for the S parameters in terms of the traveling-wave and pseudowave concepts. For problem (ii), we show that the TDR impedance is a monotonically increasing function instead of constant, and we propose a new method to estimate the characteristic impedance by fitting the TDR with a causal impedance model. Simulation and measurement examples are provided to validate the proposed theory and techniques. In the last example, we also compare five commercial/open-source 2x-thru calibration tools; the results reveal that with the proposed method of impedance estimation, better accuracy can be achieved. </p>