Transmission/reflection and short-circuit line permittivity measurements

Abstract

The transmission/reflection and short circuit line methods for measuring complex permittivity are examined. Equations for permittivity are developed from first principles. Robust algorithms that eliminate the ill-behaved nature of the commonly used transmission/reflection method at frequencies corresponding to integral multiples of one-half wavelength in the sample are presented. An uncertainty analysis is presented which yields estimates of the errors incurred due to the uncertainty in scattering parameters, length measurement and reference plane position. The indications from the derived equations are presented. In addition, equations for determining complex permittivity independent of reference plane position and sample length are derived. Equations that are derived for permittivity determination using the short circuit line, allow for the positioning of the sample arbitrarily in the sample holder.