Analysis of Uncertainties in Inductance of Multi-Layered Printed-Circuit Spiral Coils

Eddy-current sensors are widely used for precise displacement sensing and non-destructive testing. Application of printed-circuit board (PCB) technology for manufacturing sensor coils may reduce the cost of the sensor and enhance the performance by ensuring consistency. However, these prospects depend on the uniformness of the sensor coil. Inductance measurements of sample coils reveal rather considerable variations. In this paper, we investigate the sources of these variations. Through image analysis of cut-away cross-sections of sensor coils, four factors that contribute to the inductance variations are identified: the distance between layers, the distance between tracings, cross-sectional areas, and misalignment among layers. By using and extending existing method of calculating inductance of spiral coils, the inductance distributions are obtained when these factors are randomly varied. A sensitivity analysis shows that the inductance uncertainty is most affected by the uniformness of the spacings between coil traces and the distances between layers. Improvements in PCB manufacturing process can help to reduce the uncertainty in inductance.