New formulation for evaluating complex permittivity of low-loss materials

A widely used method for non-contact electromagnetic characterization of materials is based on the measurement of an 'insertion transfer function'. This function is related to the complex dielectric constant of the material through a transcendental equation which can be solved numerically using a two-dimensional root search technique. Solving this complex equation is often time consuming due to slow convergence and the existence of spurious solutions. In this article, a new formulation is presented which facilitates the evaluation of complex dielectric constant of low-loss materials by means of real equations, thus requiring only one-dimensional root search techniques. A wooden slab is characterized using the new formulation. The results for loss tangent and dielectric constant are in excellent agreement with those obtained from the complex equation.