A Broadband and Stable Method for Unique Complex Permittivity Determination of Low-Loss Materials

Transmission-reflection methods suffer from the increasing uncertainty in the phase of reflection scattering ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -) parameter measurements of low-loss materials. In addition, transmission <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter measurements produce multiple solutions for the complex permittivity. In this paper, we propose a broadband and stable method for unique complex permittivity determination of low-loss materials by eliminating these problems. For elimination of the phase uncertainty problem, we utilize only the amplitudes of reflection <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters and complex transmission <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters. In order to avoid multiple solutions, we express multivalued terms, which result in multiple solutions, in terms of single-valued terms. The method can work very well in limited frequency-band applications or for dispersive materials since it is based on point-by-point (or frequency-by-frequency) extraction. We measured the complex permittivity of two low-loss dielectric materials by different methods for validation of the method.