Improvements in cross ratio invariance techniques for coaxial probe dielectric measurements

In coaxial probe dielectric measurements the use of a cross ratio invariance of three dielectric reference materials and one material under test (MUT) has been a common approach to calibrate and thereafter extract the complex permittivity of a MUT. Although it is generally accepted that the cross ratio is most accurate when one uses at least one reference material that resembles the MUT, there has been relatively little discussion on how different combinations of reference materials affect the accuracy of the extracted data. This work will describe two new approaches for implementing the cross ratio invariance technique by (1) measuring more than three dielectric references and selecting the three that most closely resemble the MUT, or (2) by forming a cross ratio of five reference materials and one MUT. The two approaches are evaluated through simulation and measurement by exploring the error in the extracted properties of 20 independently measured dielectric materials. For both new methods, the percent error in the extracted complex permittivity typically reduces from approximately 0.5% to 0.25% or less compared to the standard approach.