CST – Computer Simulation Technology

Sensitivity Computation of an Inductive Proximity Sensor

Proximity sensors enable in a simple manner position, size and material of a metal target to be established. Such sensors are in the ability to obtain absolute analog signals proportional to proximity and are compact, robust and reliable constructions. Inductive sensors consist of a coil embedded in an open magnetic circuit.

The coil’s properties such as complex impedance depend on the magnetic resistance of the circuit. Metallic targets in the vicinity of the sensor affect the magnetic circuit and change the impedance and quality factor of the coil. These relatively small variations are detected by electronic circuitry and converted into desired length units.

Figure 1: Cut-Away snapshot section through the sensor

The geometry of the sensor was imported via the CST STUDIO SUITE™  STEP Interface (Figure 2). The coil, also imported, was simplified by a facetted representation. A target was added which was parameterised to allow a set of S-Parameters and subsequently the input impedance to be obtained as a function of distance to the sensor. ...

Figure 2: 3D Model of the inductive sensor imported through STEP

A second order tetra-based mesh was applied to the geometry (Figure 3) and the full wave frequency domain solver of CST MICROWAVE STUDIO® was used for solving the field problem.

Figure 3: Tetrahedral mesh representation of the 3D model

The field plots in Figures 4-6 show different configurations of sensor and target with respect to the magnetic flux and current densities.

Figure 4: Magnetic flux density including a 2.5 mm spaced metal target

Figure 5: Current density at a spaced target of 2.5 mm

Figure 6: Current density at the windings at 6 Mhz resonance

The complex impedance can be directly derived from the S-parameters shown in Figure 7 for R +jωL as a function of frequency, a resonance can be identified at 6 MHz.

Figure 7: Complex impedance as a function of frequency

The Q-Factor gives an indication of the effectiveness of the sensor in terms of the frequency (Figure 8). A measure of the sensitivity can be obtained by the following equations:

Figure 8: Q-Factor formulae

This Q- Sensitivity / Q-measure is shown in Figure 9. A good working point is in the area of 100kHz at which the Q-Sensitivity is maximum. A blind spot is also obtained at 300 kHz where the Q-factor remains constant and the target distance can not be  identified by the sensor.

Figure 9: Q-factor and Q-measure as a function of frequency

Finally, an equivalent of the sensor was derived for which the complex impedance was fitted over a wide range of frequencies.

Figure 10: Equivalent circuit representation and curve fitting of the impedance

This article has demonstrated how 3D EM field simulation in combination with S-Parameters and circuit optimisation can be applied to the design and analysis of inductive proximity sensors.

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