Refined Calculation of the Influence Coefficient from the Changes difference in Dielectric Constant from the Operating Conditions of the Electromagnetic Field Sensors

Abstract

This is never exactly known where a developed instrument will be used. The developer must take into account the operating conditions during the design and determine the influencing factors on the measurement result to obtain the most reliable result. The article describes the mathematical calculation of the correction coefficient of the electromagnetic field sensors by the difference in dielectric constant in the external conditions. The calculation is evaluated, as well as its influence on the metrological characteristics of the sensor making it possible to estimate the error of use. A new mathematical model consisting of a system of integral equations is constructed. The basis of these equations is the functional dependence of the error on the angular dimensions of the sensitive elements and the dielectric constant of the sensor housing and the environment. The basis of the mathematical model is a coefficient $\alpha$ that takes into account the difference dielectric permittivity of the sensor housing and the environment. Using constructed mathematical model, data and plots are obtained depending both on normalized energy value in unit volume of sensor from angular sizes $\theta_{0\mathrm{I}}$ and $\theta_{02}$ of its sensitive electrodes, and from different ratios of dielectric constants of sensor base and environment. In the plots of these dependencies, maxima are observed. These maxima correspond to the maximum energy per unit volume of the sensor for specific angular sizes of its spherical segments ($\theta_{0\mathrm{I}}$ and $\theta_{02}$) and for constant values of the parameter $\alpha$.