Comparison of corrected calibration independent transmission coefficient method to estimate complex permittivity

Abstract

The accuracy of estimation of the frequency dependent complex permittivity of dielectric materials is important for medical applications to perform in situ chemical analysis. The achieved accuracy depends on the measurement apparatus and the methods used for permittivity estimation. Calibrating the sensor before use is not always possible nor is it desirable. The transmission coefficient S21 method is usually used because it does not require accurate calibration of the measurement apparatus. In this paper we analyze the disparity, observed in the literature, in the estimated permittivity at lower frequencies when the transmission coefficient method and small embedded sensors are used to estimate permittivity. Our results indicate that the large disparity of the permittivity at lower frequencies in the transmission coefficient S21 method is caused by the fact that the method neglects the multiple reflections at the air material interfaces. Here we propose a new method, extending the transmission coefficient method, to contend with the large disparity at lower frequencies in the existing methods whilst preserving the desirable properties of the method, namely not requiring accurate calibration of the apparatus before use. The proposed method is compared with other calibration dependent and independent methods using Ansoft's HFSS simulation software. The accuracy of these methods is then also verified using on chip coplanar waveguides (CPW) measurements in 1–30GHz. Results indicate that the accuracy in dielectric estimates can be improved by taking into account both transmission and reflection coefficients (multiple reflection model) and reducing the CPW metal layer thickness. Further improvement in the accuracy in this method for short CPW can be achieved if a material of known permittivity can be used as a reference.