Calibration of vector E-field probe in tissue equivalent liquid using waveguide method in the frequency range from 5100 MHz to 5500 MHz

This paper proposes a vector-based calibration method for determining the magnitude and phase response of an electric field (E-field) probe immersed in a rectangular waveguide cell filled with tissue equivalent liquid representing the human body. The probe calibration bench is based on S-parameter measurements in the frequency range from 5100 MHz to 5500 MHz; it consists of a WR187 waveguide cell, an E-field probe associated with an opto-electronic converter, a positioner and a vector network analyzer. An analytical model of the probe calibration is developed using the measured S-parameters of the calibration bench and of the waveguide cell, to determine the magnitude and phase of the probe correction factor. A polynomial regression has been applied on the magnitude of the measured transmission coefficient of the calibration bench to limit the impact of noise caused by the probe system. The correction factor derived from S-parameter measurements gives consistent results with the dispersion value less than 3% for three positions of the probe in the liquid. Uncertainty contributors, including liquid characterization, waveguide-cell and calibration-bench measurements are experimentally evaluated. The Monte Carlo numerical method is used to propagate the uncertainties of input quantities of the analytical model to the probe correction factor. The combined standard uncertainty of the magnitude of the correction factor has been estimated in the order of 10% at the frequencies of interest. For validation, a scalar calibration method based on power measurements is implemented, and the two approaches are compared using a normalized error criterion. The consistency between vector-based and scalar results confirms the validity of the proposed calibration method, establishing a traceable pathway for specific absorption rate measurements.