Measurement of Complex Permittivity using Artificial Neural Networks

In this paper, a neural-network-based methodology is presented to measure the complex permittivity of materials using monopole probes. A multilayered artificial neural network, using the Levenberg Marquardt back-propagation algorithm, is used to back solve the complex permittivity of the medium. The proposed network can be trained using an analytical model, numerical model, or measurement data spread over the complete range of parameters of interest. The input training data for the nonlinear inverse problem of reconstructing the complex permittivity comprises the complex reflection coefficient of the monopole probe. For the results presented in this paper, the network was trained using the analytical model for impedances of monopole antennas in a half space by Gooch et al. [1]. In addition to computational efficiency, the proposed approach gave 99% accurate results in the frequency range of 2.5-5 GHz, with the values of permittivity varying across a range of 3-10 for the real part, and 0-0.5 for the imaginary part. The accuracy and the effective range of real and imaginary components of the complex permittivity that can be reconstructed using this approach depend upon the accuracy and robustness of the model/system used to generate the training data. The analytical model used in this paper had a limited range for the values of loss tangent that it can model accurately. However, the performance of the back-solving algorithm remains independent from any specific model, and the scheme can be successfully applied using any reliable analytical or numerical model, or reflection-coefficient training data generated through a series of measurements. The methodology is likely to be employed for experimental measurements of complex permittivity of dissipative media.