Broadband complex permittivity determination using a two-port U-shaped coplanar waveguide with artificial neutral network algorithm

Abstract

A two-port U-shaped Coplanar Waveguide (U-CPW) used for broadband complex permittivity measurement of high loss solutions is presented. Compared with the one-port measurement device, this two-port U-CPW coupled with artificial neural networks algorithm has the ability of reducing the multiple-solutions. Also, the measured T/R (transmission/reflection) coefficients were used instead of simulated reflection coefficients for training the neural networks that enhanced the accuracy of measurement results. Two real-valued neural networks associated with the U-CPW are used to reconstruct the two parts of the complex permittivity separately from the measured T/R coefficients. First, a large number of measured T/R coefficients of broadband frequency points of ethanol-water mixtures along with their theoretical complex permittivity are used to train two separate neural networks. Second, the trained networks are employed to reconstruct the complex permittivity of other solutions using the measured T/R coefficients. Compared with the results of Cole-Cole equation, the reconstructed results of methanol-water mixtures and ethanol-methanol mixtures at different volume fractions have been obtained with sufficient degree of accuracy in the frequency range 1–3 GHz at 20°C. For predicted values using the developed artificial neural network (ANN) architecture and those obtained from literature, the average relative errors of real and imaginary parts of complex permittivity are 2.27% and 2.12%, respectively.