Gap-Corrected Thin-Film Permittivity and Permeability Measurement With a Broadband Coaxial Line Technique

Abstract

A technique for measuring the high-frequency broadband complex permittivity and permeability of thin films from 50 MHz up to 18 GHz without the need for a reference sample for calibration is presented. A film for measurement is wound into a torus and inserted into a coaxial line. As a consequence, this method is suitable for measuring flexible self-supported films and coatings fabricated on flexible substrates. With the torus axis of symmetry along the coaxial direction, the electromagnetic properties of the wound torus can be deduced from the perturbed reflection and transmission coefficients of an incident wave. However, when permittivity and permeability are then obtained, there is a contribution from the effect of air gaps that cannot be avoided between layers of the wound film, which results in an underestimation of the measured permittivity and permeability. An analytical air-gap correction model has been developed to account for this air-gap effect that is then validated by experiments and shown also to be consistent with finite-element simulations. The relative effects of film thickness and air gap on a range of measured permittivity and permeability have been also elucidated.