Considerations on impedance matrix determination for accurate passive device characterization

For accurate RLCG-parameter extraction the measured S-parameter matrix needs to be converted to the Z-matrix. However, there exist three different definitions of S-parameters and consequently three different formulas of converting S-matrix into Z-matrix. In this article, we present an overview of existing S-parameters definitions and examine the uncertainties associated with the S-matrix to Z-matrix transformations. Further, we introduce an error estimator describing the inaccuracy one makes performing the incorrect transformation. We compare de-embedded measurement results of an inductor manufactured in Si-based MCM-D technology. We show that using wrong transformation can easily lead to erroneous or even catastrophic results.