Measurement of Complex Permittivity using Artificial Neural Networks Azhar Hasan and Andrew F. Peterson School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA 30332-0250, USA ABSTRACT In this paper, a Neural Network based methodology is presented to measure the com- plex permittivity of materials using monopole probes. A multilayered Artificial Neural Net- work, using the Levenberg Marquardt back propagation algorithm is used to back solve the complex permittivity of the medium. The pro- posed network can be trained using an analyt- ical model, numerical model, or measurement data spread over the complete range of param- eters of interest. The input training data for the non linear inverse problem of reconstruct- ing the complex permittivity comprises the com- plex reflection coefficient of the monopole probe. For the results presented in this paper, the net- work is 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 gives 99% ac- curate 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, depends upon the accuracy and robustness of the model / system used to generate the training data. The analytical model used in this paper has 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 ana- lytical or numerical model, or reflection coeffi- cient training data generated through a series of measurements. The methodology is likely to be employed for experimental measurements of complex permittivity of dissipative media. keywords: Neural Network, Complex Permittivity, Measurement, Monopole Probe, Reflection Coeffi- cient 1 . Introduction There is a vast range of topics across a whole variety of disciplines which find their basis in di- electric characterization of materials. Depending upon the application of interest, dielectric profiles are investigated in different segments of the fre- quency spectrum. Due to ever increasing interest in applications at microwave frequencies, the research presented in this paper is focused on the frequency range from 2.5 - 5 GHz. Different resonant and non- resonant methods have been reported in the research literature for measuring the complex permittivity of materials [2]. A monopole probe immersed into the material under investigation is considered a simple and efficient technique for determining the electri- cal properties of the medium. The input impedance of a monopole probe immersed in an approximately semi-infinite dielectric medium provides valuable information for extracting the complex permittivity of the medium. In the method reported in [3],the normalized impedance of the monopole probe is expressed as a rational function of order three and the coefficients of the function are determined based on the profile of a standard medium. Based on the rigorous expression for the impedances of monopole antennas in half space by Gooch et al. [1], various in-situ procedures are reported in the literature for solving the non-linear inverse problem of calculating complex permittivities [4, 5, 6]. Neural networks using the back-propagation algorithm have demonstrated the ability to recon- struct the permittivity profile of lossless stratified medium from complex reflection coefficients [7]. For a dissipative medium, the complex-valued na- ture of the permittivity makes the problem incom- patible with conventional neural networks, which are designed to process real-valued data. One possi- ble approach is to use a complex valued back prop- agation neural network, which might result in better accuracy, but these are considered more difficult to implement [8]. Another possible approach is to split the network into two networks, one dealing with the real part and the other dealing with the imagi- nary part (with both using real valued input data). Such an approach, for a broad-band evaluation of