A new formulation for characterization of materials based on measured insertion transfer function

A widely used method for noncontact electromagnetic characterization of materials is based on the measurement of an insertion transfer function. This function, defined as the ratio of two phasor signals measured in the presence and absence of the material under test, is related to the dielectric constant of the material through a complex transcendental equation. Solving this equation requires a numerical two-dimensional root search technique, which is often time consuming due to slow convergence and the existence of spurious solutions. In this paper, 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. Two sample materials are measured, and it is shown that their dielectric constants obtained from the exact complex equation and the new formulation are in excellent agreement. The new formulation reduces the computation time significantly and is highly accurate for the characterization of low-loss materials.