Investigation on Temperature Dependent Inductance (TDI) of a planar Multi-Layer Inductor (MLI) down to 4.2 K

This paper presents an investigation of the temperature dependence characteristics specific to cryogenic planar Multi-Layer Inductors (MLIs). This paper establishes that the inductance of a planar MLI at a specific frequency varies with temperature when the sensor is cooled down to 4.2 K while providing a detailed analysis of various possible factors that might contribute to the variation in the sensor performance, such as the thermal deformation and the variation in the properties of sensor materials, using a combination of experiments and simulations. By calculating the interlayer capacitance, we have attempted to adopt a novel approach in the investigation of the effects of thermal deformation on the sensor. In order to arrive at that, the relative permittivity of the base material (G10CR-FR4) at cryogenic temperatures was obtained through experiments. The ANSYS static structural package was used for modeling thermally induced deformations, after which the deformed capacitance and inductance were obtained using Ansoft MAXWELL. From the analysis, we have concluded that the variation in the inductance of the sensor has a direct correlation with the electrical resistivity (hence the residual resistivity ratio) of the coil material. The number of inductor layers and the area of the component layer will also determine the temperature dependence phenomenon. These conclusions are not obvious from the established inductance models.