Analysis on the Characteristics of Coil Impedance Change Induced by Nonferromagnetic and Ferromagnetic Cylinders

What's the difference between the coil impedance changes induced by the ferromagnetic and nonferromagnetic cylinders? What's the difference between the coil impedance changes induced by the cylinders with different conductivity? It is important to make them clear theoretically. According to the second order vector potential theory, the coil impedance change can be expressed as the function of the coil coefficient and the reflection coefficient when the normal direction of the circular solenoid coil is perpendicular to the axis of the conductive cylinder. It is also a function of lift-off (or cover depth, the least distance to the surface of the concreate), diameter, conductivity of the cylinder and the exciting frequency. Theoretical and experimental results show that the coil reactance change is negative, the coil resistance change is positive, and the magnitude of them increases as the exciting frequency increases if the cylinder is made of nonferromagnetic materials. If the cylinder is made of ferromagnetic materials, the coil reactance change is positive in the lower frequency band, it increases as the frequency increases, and reaches to its maximum at the frequency fx_max. After that, it decreases as the frequency increases continuously. At a special frequency fx₀, the reactance change decreases to zero. When the frequency is higher than fx₀, the reactance change decreases as the frequency increases continuously, in the other words, the magnitude of the reactance change increases as the frequency increases in the upper frequency band. The coil resistance change induced by ferromagnetic cylinder increases as the frequency increases in the whole frequency band we studied. In the upper frequency band, the impedance changes, which are induced by ferromagnetic and nonferromagnetic cylinders with same conductivity and diameter at the same liftoff, have little difference. The influence of the conductivity of the cylinder on the coil impedance change, and the physical interpretation of the impedance change induced by ferromagnetic cylinders are also studied. These characteristics of the coil impedance change can help to design the nondestructive testing instruments such as the cover meter to locate and evaluate the diameter of the rebar embedded in concreate, and the conductivity testing meter, etc. They can also help the designer to choose exciting frequency and optimize the performance of these nondestructive instruments.