Estimation of Reference Impedance in 2x-thru De-embedding With High Conductor-Loss Lines

The 2x-thru de-embedding has emerged as an attractive alternative to the classical TRL for S parameter measurement of printed circuit board and packaging devices, mainly due to its simplicity that only one THRU standard suffices to fully characterize the test fixtures over broad bandwidth. The S parameters after 2x-thru de-embedding are referenced to the characteristic impedance of the transmission line in THRU, and accurate estimation of this reference impedance (Zref) is important for subsequent renormalization and time-domain simulation. In 2x-thru literature, only constant estimate of Zref, mostly based on the time-domain reflectometry (TDR), has been reported. However, the characteristic impedance of a transmission line is frequency dependent, and the TDR may not be flat for high conductor-loss lines. In this article, we analytically show that the TDR is an increasing function in time, and propose an innovative method to estimate Zref by fitting the TDR with a causal impedance model. Simulation and measurement examples are provided to validate the proposed theory and technique, and to show the importance of using accurate Zref for renormalization in 2x-thru de-embedding.