There are several types of position sensors based on different concepts. This article intends to show the workflow and some features in CST EM STUDIO® (CST EMS) which can be applied to the efficient electromagnetic field simulation of a eddy current sensor, namely a shaded ring sensor for automotive applications such as the position sensing of a regulating rod in inline injection pumps. More advanced designs have superceeded this, but the workflow and features remain the same.
A typical goal in such a sensor simulation is the linear impedance-position characteristic which is influenced by the geometry of the yoke limbs.
The geometry of the shaded ring sensor is shown in figure 1 based on data in . The sensor consists of a laminated E-shaped iron yoke, a fixed shaded ring coil and a conducting aluminium ring....
The model was entirely created in CST EMS but the process may also involve more complicated geometries, again, either created in the software or imported via a wide range CAD formats such as DXF, STEP and Pro/E® etc.
The fixed coil, excited with a 10 kHz current, has been modeled as a stranded coil which assumes a constant current distribution i.e. eddy currents / proximity effects are not taken into account. The operation of the sensor is based on the induction of eddy currents in the shaded ring. This ring basically short circuits the magnetic circuit formed by the core. The position of the ring affects the degree of short circuiting of the flux and hence the inductance in the sensor.
The laminations in the yoke suppress the eddy currents and therefore a zero conductivity has been applied. A constant permeability, 1500, has been assumed. With these assumptions, the CST EMS low frequency time-harmonic solver can be applied.
Critical to the device behavior is the formation of eddy currents in the shaded ring. This entails the modeling of the skin depth in the ring. Two possibilities exist in the CST EMS low frequency solver. A surface impedance approximation may be applied which avoids the need to resolve the mesh in the skin depth. Alternatively, the mesh can be either automatically refined with mesh adaption or user-refinement. Although the surface impedance technique can be easily applied, the latter offers the ability to visualize the eddy currents which are shown in Figure 2. The phase of the eddy currents has been animated with the field values logarithmically scaled.
The flux line plot (logarithmic) in Figure 3 shows the short circuiting effect of the shaded ring on the flux in the sensor.
Once the feasibility of the model has been established, a parametric analysis can be performed using the integrated parametric module in CST EMS. The position of the shaded ring has been shifted by the use of a transform operation in the axial direction. A parameter, in this case, x, is attributed to the displacement. Automatic extraction of the secondary quantities is performed at each parametric step. In this case, the impedance versus displacement has been extracted as shown in Figure 4.
The workflow for simulating such a sensor is extremely straightforward in CST EMS. Other possibilities include the ability to optimize the linearity of the sensor, also using the inbuilt optimization module.
 M. Clemens and T. Weiland, "Numerical algorithms for the FDiTD and FDFD simulation of slowly varying electromagnetic electromagnetic fields", INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Int. J. Numer. Model. 12, 3-22 (1999)