Mathematical model of a double-coil inductive transducer for measuring electrical conductivity

Abstract

A technique for the contactless measurement of the electrical conductivity of conducting materials using a double-coil inductive transducer is presented. A mathematical model of the transducer has been created and it consists of two cylindrical coils and a tested sample in the form of a cylinder coaxial with the coils. A processing function of the transducer is defined as the ratio of voltages between terminals of the measurement coil with and without the test sample. This processing function depends on the conductivity of the test sample, the dimensions of the sample and of both coils of the transducer (the measurement coil and the excitation coil), and the frequency of the current supplied to the excitation coil. An analytical formula for the processing function is derived; analysis of graphs of this function in different formats enables us to evaluate the influence of all the essential parameters of the transducer. This is a necessary step for both transducer optimization and carrying out of the conductivity measurement of the investigated materials. In order to verify the theoretical predictions, experimental investigations have been performed using a computerized data acquisition system. First, an experimental validation of the obtained analytical formula has been completed using an aluminum sample of known conductivity. Then, the conductivity measurements of a sample made of brass have been carried out. The obtained experimental results confirm the high accuracy of the theoretical analysis.