Vol.108 (1) March 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS4

DESIGN AND OPTIMISATION OF A PCB EDDY CURRENTDISPLACEMENT SENSOR

A.J. Grobler∗ , G. van Schoor† and E.O. Ranft∗

∗ School of Electrical, Electronic and Computer Engineering, North-West University, Potchefstroom,South Africa, e-mail: andre.grobler@nwu.ac.za† Unit for Energy and Technology Systems, North-West University, Potchefstroom, South Africa.

Abstract: Position sensing is one of the crucial parts of many systems, specifically in an active magneticbearing. The position is used to control the magnetic forces within an active magnetic bearing to keep arotor levitated. Sensors used in these systems must be very sensitive and are usually very expensive. Inthis paper a low cost printed circuit board position sensor is analysed. The sensor uses an excitation coilto establish a magnetic field. Four sensing coils are then used to measure the influence a conductingtarget has on the magnetic field to enable position sensing. The sensor’s magnetic operation is analysedusing finite element methods and very good correlation is found with measured results. The effects ofthe target material and the number of PCB layers are analysed. It is shown that a two layer sensor canproduce acceptable sensitivity and linearity.

Key words: eddy current, displacement sensor, multiple layer PCB

1. INTRODUCTION

IN active magnetic bearings (AMB) systems accurateposition sensing of the levitated object, mostly a

rotating rotor, is essential. Due to its impact both interms of cost and reliability, position sensing in AMBsystems is an important research topic. Two currentlyprominent approaches to determining the rotor positionare self-sensing and dedicated non-contact sensors. Inself sensing, the rotor position is approximated using thechange in actuator inductance, caused by rotor movement[1, 2]. Dedicated position sensor technologies usedin AMBs, include; optical, inductive, eddy current,Hall-effect and capacitive types [3]. AMB systems havevery small airgaps between the rotor and stator, usuallyaround 0.5 mm. The rotor can thus only move 0.25 mm inthe radial direction before making contact with the backupbearings.

Eddy current sensors induce eddy currents in a conductingtarget and uses the change in magnetic field due to theeddy currents to measure various physical parameters. Asingle coil can be used as the excitation and measuringcoil in which case the change in inductance is usuallydetected through the change in oscillation frequency ofthe excitation circuit. Sensing coils are not connected tothe excitation coil and a change in induced voltage can bemeasured using analog to digital converters. These sensorsare commonly used to measure lateral displacement [4],rotation [5] and axial displacement [6]. It is also usedto detect defects in materials like PCBs [7] and is highlydependent on material properties [8]. These sensorshave also been used in condition monitoring, for examplemeasuring turbine rotor vibrations [9], [10]. Variousapplications require that flexible PCBs be used to reachin small spaces [11]. Vyroubal has developed transformerequivalent circuits for the probes [12] as well as improvingthe driving circuitry [13].

Philipp Buhler registered a patent in 2002 [14] for a deviceto measure a rotor position in multiple directions. In2004, Larsonneur and Buhler presented a printed circuitboard (PCB) sensor, based on the aforementioned patent,for measuring radial movement of the rotor in an AMBsystem [15]. This concept was also used to developa sensor for high temperature AMBs, using thick-filmmanufacturing techniques [16]. Larsonneur and Buhlerreported that modelling of the sensor should be exploredfurther as “model predictions do not yet satisfyingly agreewith measurement results” [15]. The contribution of thisarticle is showing a two-dimensional finite element method(FEM) model can accurately predict the sensor’s output formovement perpendicular to the sensing coil.

The probe of this sensor comprises an excitation coiland four sensing coils; all planar coils formed usingPCB tracks. Figure 1(a) and (b) illustrate the sensorarrangement through a side and top view respectively. Ahigh frequency sinusoidal current (1-10 MHz) is appliedto the excitation coil, thus establishing a varying magneticfield around it. The four sensing coils are placed aroundthe excitation coil, each covering about a quarter of thecircumference of the target. Placing a conductive targetinside the excitation coil causes eddy currents to flowin the target. When the target is moved relative to theprobe, magnetic field coupling to the sensing coils willbe influenced by the eddy currents flowing in the target.When the target is close to a sensing coil, the magneticfield coupling with the sensing coil will be decreasedby the eddy currents. Similarly a larger magnetic fieldcoupling with the sensing coil located far from the targetwill prevail.

As explained above, the target should be electricallyconductive for an eddy current sensing principle to be used.The penetration depth (δ) of the magnetic fields can becalculated using

Vol.108 (1) March 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 5

Figure 1: PCB eddy current displacement sensor: (a) Side viewand (b) top view [15].

δ =√

22π f µσ (1)

where f is the frequency of the excitation current, µ isthe permeability and σ is the conductivity of the target.Aluminium is commonly used as target for eddy currentsensors and has a calculated penetration depth of 58.5 µmif a 2 MHz signal is used. Stainless steel, for exampleSAE 304, is also widely used in AMB rotors since it hasa high yield strength and does not influence the AMB’smagnetic field as it is non-magnetic. The penetrationdepth of SAE 304 at 2 MHz is calculated as 302 µm. Ifa magnetic material is used as the target the penetrationdepth will be significantly smaller. Mild steel has acalculated penetration depth of less than 10 µm. In theAMB environment the position sensing is usaually doneon a non-magnetic surface. As the position sensor’s targeton the rotor is placed very close to the AMB, a magnetictarget will introduce hytesteresis losses if a heteropolarradial AMB is used.

This article presents a FEM model for a PCB sensor inSection 2. The model is verified using a purpose built testplatform as discussed in Section 3. In Section 4 the optimal

sensor configuration is analysed to deterimine the impactsome paramenters has on performance.

2. MODELLING

Deriving an accurate model for the PCB sensor can helpthe designer understand the influence a certain parameterhas on the operation and performance of the sensor. Amodel can be used to ensure specifications are met whendesigning a sensor. A model can perdict the behavior ofthe sensor in various conditions and operating modes.

The computational resources needed to solve a FEM modelare influenced by the number of nodes in the model.If the three-dimensional reality has a symmetry axis,a two-dimensional approximation can be made withoutdecreasing the accuracy of the model. Figure 2 showsthe two-dimensional approximation of the PCB sensor.The excitation and sensing coils will be realised withtracks on a PCB as shown in the lower part of the figure.In an approximation in the upper part of Figure 2, theexcitation coils are modeled as a rectangle with the samedimensions of the tracks and half the current density, thusincorperating the voids between the tracks. The sensingcoil is approximated with a line, since only the magneticflux passing through this line will be used further tocalculate the induced voltage. This model is implementedin COMSOL MultiphysicsR© using the axial symmetryQuasi-Statics Azimuthal Currents application mode.

The sensing coils’ voltages are the main model output. Acoil voltage (e) can be determined using Faraday’s law,shown in (2), if the change in magnetic flux (∆Φ) throughthe sensing coil, number of turns on the coil (N) and periodof the excitation current (∆t), are known.

e = N dΦdt � N ∆Φ

∆t (2)

The magnetic flux can be determined using (3), where B isthe magnetic field density and A the sensing coil area.

Φ =∫

BdA (3)

Figure 2: FEM model assumptions

Vol.108 (1) March 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS6

Sensitivity and linearity are two of the performanceparameters used when optimising the sensor. Sensitivity(S) is the ratio of voltage change (∆V ) and displacement(∆x), see (4). Linearity gives an indication of how closethe calibration curve fits a straight line. The maximumdeviation above and below the straight line, VMT and VMB,and the total displacement (∆x), are used to determinelinearity, as given by (5).

S(V/m) =∆V∆x

(4)

Linearity (%) =VMT −VMB

∆x×100 (5)

Figure 3 shows the magnetic fields established by theexcitation coil and passing through the sensing coils. Themagnetic fields passing through the target induces eddycurrents in the target. Figure 4 shows the modelledpeak voltage induced in a sensing coil when a target ismoved between 0.25 mm and 0.75 mm from the PCB.The results for three different materials (SAE 304 stainlesssteel, copper and aluminium) are shown. The conductance(σ) and permeability (µ) of the target influences the eddycurrents flowing in the target and thus the amplitude ofthe voltage induced in the sensing coil. Copper is themost conductive, thus a smaller voltage is induced whencompared to stainless steel that is less conductive.

Figure 3: Simulated magnetic fields established by the excitationcoil

The simulation results shown in Figure 4 support thesensor operation described previously. There is a sufficientchange in voltage to warrant manufacturing a prototypesensor. This prototype will be used to verify the modelpresented in this section.

3. MODEL VERIFICATION

3.1 Evaluation platform

To verify the FEM model, a sensor was designedusing the model and constructed using standard PCBmanufacturing techniques. An evaluation platform wasalso developed as is shown in Figure 5. The referenceposition was measured by two eddyNCDT 3701 sensors

2 3 4 5 6 7 8

x 10−4

0.18

0.185

0.19

0.195

0.2

0.205

0.21

0.215

Airgap between target and sensor coils [m]

Vo

ltag

e [V

]

Copper target

Stainless steel target

Aluminium target

Figure 4: Simulated sensing coil voltage for different materialswhen changing the airgap.

from MICRO-EPSILONR© on an aluminium target. Thesesensors can measure on any conductive material but werecalibrated on aluminium. These sensors have a measuringrange of 1 mm, linearity of 6 % full scale output (FSO),< 0.001 % FSO repeatability, < 0.000033 % FSO staticresolution and < 0.00016 % FSO dynamic resolution. Inthe test setup, movement is always parallel with a coil pair(e.g. coils 1 and 3) and perpendicular with the other coilpair (e.g. coils 2 and 4).

Figure 5: Evaluation platform.

3.2 Comparing simulation and measured results

This section compares the simulation results to themeasured results. The voltage on a sensing coil wasrecoded for 10 µs (or 20 cycles), sampled at 2.5 GHz usingthe LeCroyR© WaveRunnerR© 6030A digital oscilloscope.Ten data sets were recorded and the amplitude of thefundamental frequency determined using fast Fouriertransform in MATLAB. The median of these 10 valuesrepresents a data point, referred to as measured voltage.

Figures 6 and 7 show the voltage measured on the foursensing coils of the single layer sensor when moving the

Vol.108 (1) March 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 7

aluminium target from sensing coil 4 towards sensing coil2 as well as moving from sensing coil 1 towards sensingcoil 3. This movement causes an increase in the airgapbetween sensing coil 4 (1) and the target. As a result thevoltage measured on sensing coil 4 (1) and 2 (3) decreasesand increases, respectively. Due to the symmetry in themodel, the model results for sensing coil 2 (3) have thesame but negative gradient and the values but will decreaseas the airgap increase, labled “Simulation decrease” inFigure 6. The sensing coils are numbered 1 - 4 in aclockwise rotation, starting at the coil just right of theconnector.

There is a dc offset in all measurements compared to themodel results. This can be attributed to voltage induced inthe connection track of the sensing coils by the excitationcoil magnetic field. The voltages measured across sensingcoils remain constant when the target does not moverelative to these coils. Again there is some dc offset andthe voltages measured on sensing coils 3 and 2 are largeras these have longer connection tracks.

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

x 10−4

0.3

0.31

0.32

0.33

0.34

0.35

0.36

Airgap [m]

Vo

ltag

e [V

]

Sensing coil 1

Sensing coil 2

Sensing coil 3

Sensing coil 4

Simulation increase

Simulation decrease

Figure 6: Induced voltage on sensing coils 1 to 4 includingsimulation results when moving in the direction of the coils (1

layer sensor).

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

x 10−4

0.315

0.32

0.325

0.33

0.335

0.34

0.345

Airgap [m]

Vo

ltag

e [V

]

Sensing coil 1

Sensing coil 2

Sensing coil 3

Sensing coil 4

Simulation

Figure 7: Induced voltage on sensing coils 1 to 4 includingsimulation results when moving perpendicular to the coils (1

layer sensor).

Differential measurements of opposite coils will be usedwhen implementing the sensor as this will reduce theinfluence of common mode effects like temperature and

magnetic interference. The sensitivity is also doubled.Differential measurements were taken for the 2-layersensor, moving an aluminium target between sensing coil1 and 3. Figure 8 shows the differential results. Sensingcoils 1 and 3 results closely agree with that predicted bythe model.

Table 1 compares the sensitivity results for 2 differenttarget materials when the single-layer sensor is used. Theresults when using aluminium (Al) and stainless steel(Ss) targets show good correlation between modelled andmeasured results.

Table 1: Sensitivity comparisonTarget Sensing Model Measured Differencematerial coil no. [V/m] [V/m] [%]Al 1 158 155.41 1.63Al 2 158 140.12 11.31Al 3 158 151.49 4.12Al 4 158 147.85 6.42Ss 2 148.62 138.35 6.91Ss 4 148.62 148.37 0.17

Table 2 shows the results for the double-layer sensor whenan aluminium target is used. The results of the two sensingcoil pairs (1&3, 2&4) are not the same. Sensing coils 1 and3 measured results correlate well with the modelled results.Sensing coils 2 and 4 results do not show good correlationwith the model. The next section will discuss a possiblecause for the difference in results.

Table 2: Sensitivity comparison: Double-layer withAluminium target.

Sensing Model Measured Deviationcoil no. [V/m] [V/m] [%]1 335.25 338.50 0.962 335.25 253.85 24.283 335.25 335.73 0.144 335.25 264.16 21.2

2 3 4 5 6 7 8

x 10-4

-0.1

-0.05

0

0.05

0.1

Airgap [m]

Vol

tage

[V]

Simulation differential 1.6mmSimulation differential 2.2mmS3 - S1 με A movementS4 - S2 με A movementS3 - S1 με B movementS4 - S2 με B movement

Figure 8: 2-layer sensor: differential results for an aluminiumtarget.

Vol.108 (1) March 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS8

3.3 Oscillator circuit drift

The excitation current was created using avoltage-to-current circuit and a bench signal generator(EZR© Digital FG7020A), together called the oscillatorcircuit. In this section the change of the measured sensingcoil voltage over time is investigated. Figure 9 showsthe rms voltage measured on a sensing coil against anumber of measurements. The target is not moved andno changes are made to the test setup. The voltage wasmeasured using a LeCroyR© WaveRunnerR© 6030A digitaloscilloscope. Measurements 1 to 24 are taken after theoscillator circuit operated for a long time (> 7 hours),measurements 25 to 53 were taken 10 minutes afterswitching on the oscillator circuit and measurements 54to 78 are taken 1 hour after switching on the oscillatorcircuit. At the start of each measuring series the oscillatorvoltage is adjusted to ensure a 100 mA rms current isflowing in the excitation coil. Each of the measurementseries is taken over a 6 minute time frame in 15 secondintervals.

0 10 20 30 40 50 60 70 80

0.242

0.244

0.246

0.248

0.25

0.252

X: 3Y: 0.2458

Measurements

RM

S v

olta

ge [V

]

X: 22Y: 0.2472

X: 28Y: 0.2466

X: 50Y: 0.2505

X: 63Y: 0.2433

X: 78Y: 0.2459

Figure 9: Sensing coil 2 voltage showing oscillator drift.

When the circuit was active for a long time (measurements1 to 24) there is not a significant change in the voltage. Butwhen considering the large change when just switching onthe circuit and when adjusting as at measurement 54, it isclear that the oscillator circuit has a significant influenceon the measurements. Considering the small change involtage (around 40 mV for the single layer) when movingthe target through the whole range, the measurementsshown in Figure 9 could easily cause a 10 % error as seenin Table 1. The large deviation in sensing coils 2 and 4seen in Table 2 when moving in the sensing coil 2 directioncould thus be caused by oscillator circuit drift.

Note that there are also other differences when comparingthe experimental setup to the simulation results. Sensingcoils 2 and 3 have longer tracks from the connecter tothe coil that sensing coils 1 and 4. It was found that thedifference can be as big as 100 mV, thus accounting for thedc offsets seen in Figures 6 and 7. But these differencesremained the same, regardless of the target movement andwould thus not influence the sensor’s sensitivity.

4. OPTIMISATION CONSIDERATIONS

This section presents some of the considerations to designan optimal sensor using the model presented in theprevious section. Table 3 lists the optimisation criteriaand variables that can be modified to optimise the sensorperformance as well as some of the paramenters assumedto be constant.

Linearity is the least crucial performance parameter sincethe position signal can be linearised by applying a functionfit to the calibration curve. Figure 10 shows the modelledlinearity (in percentage of full scale output (FSO) of asingle sensor when varying the number of excitation coilwindings (nexc) and the number of sensing coil windings(nsens). An exponential decrease in linearity can be seenwhen increasing either variables. All of the combinationswhere nexc > 5 and nsens > 5 have a linearity smaller than0.3 % FSO, an acceptable value for the sensor.

The modelled sensitivity for different combinations of nexcand nsens are shown in Figure 11. Increasing nsens causesan increase in sensitivity. When increasing nexc, sensitivityalso increases but reaches a turning point, clearly seenwhen nsens = 15 and nexc = 1 → 15. According to thisfigure, nsens should be as large as possible and nexc shouldbe chosen on a turning point, when designing an optimalsensor. More insight can be gained by considering thegradient of the sensitivity when varying nsens and nexc, asshown in Figure 12. From this figure it is clear that fora certain nsens, a maximum gradient of sensitivity can befound by varying nexc.

The number of layers the PCB sensor is implementedon can also be varied to optimise the sensor’s sensitivityand signal level. A high signal level is beneficial whenthe noise effects between the sensor and demodulationcircuitry must be minimised. The conductors connectingthe sensing coils and the demodulation circuitry will, insome cases, be long and routed in noisy environments.Figure 13 shows the voltage induced on a sensing coil

0

5

10

15

0

5

10

15

0

0.5

1

1.5

nsensn

exc

Lin

eari

ty [

% F

SO

]

Figure 10: Modelled linearity for excitation coil windings(nexc = 1 → 15) and sensing coil windings (nsens = 1 → 15).

Vol.108 (1) March 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 9

Table 3: Optimisation criteria and variablesOptimisation criteriaLinearity, Sensitivity, Signal level, CostVariablesNumber of sensing coil windings nsensNumber of excitation coil windings nexcNumber of PCB copper layersTrack width and spacingInsulating material thicknessTarget materialConstants ValuesExcitation frequency 2 MHzExcitation current 100 mAExcitation voltage ±15VdcTarget size diameter 50 mmMinimum airgap 0.25 mmMovement range 0.5 mmTrack height 0.035 mm

05

1015

0

5

10

150

50

100

150

200

nsens

nexc

Sen

siti

vit

y [

V/

m]

Figure 11: Modelled sensitivity for no. of excitation coilwindings (nexc = 1 → 15) and no. of sensing coil windings

(nsens = 1 → 15).

05

1015

0

5

10

150

2

4

6

8

10

12

nsensnexc

Gra

dien

t of s

ensi

tivity

[V/m

/turn

]

Figure 12: Modelled gradient of sensitivity for excitation coilwindings (nexc = 1 → 15) and sensing coil windings

(nsens = 1 → 15).

when varying the airgap, for a single-, double- andfive-layer sensor configuration. The signal level andsensitivity increase with an increase in number of PCBlayers. Unfortunately, the cost of manufacturing the PCBalso increases when the number of PCB layers increase.A five-layer sensor costs ten times more to manufacturethan a single-layer sensor. It was found that a double-layersensor is the best option when considering cost andsensitivity.

The conductive layers of a PCB are placed on an insulatingmaterial (fr4). The effect of varying this thickness mustalso be investigated. Figure 14 shows the induced voltagevs. airgap for four fr4 thicknesses: 0.1, 0.5, 1.6 and2.2 mm. The standard fr4 thickness is 1.6 mm, thus thisfigure represents the whole range of commonly found fr4thicknesses. A small improvement in sensitivity and signallevel is found when using a thinner insulation layer. Thiscan be attributed to an increase in the magnetic couplingbetween the excitation and sensing coils located on thedifferent layers. A thinner insulation material is morefragile and expensive to manufacture, and the performanceimprovement is not significant when compared to othervariables.

The influence of changing the copper track width andspacing is the final variables explored in this article. Figure15 shows the induced sensing coil voltage when adjustingthe airgap, for different combinations of excitation andsensing coil’s track spacing and width. The signal levelis significantly higher when a narrower excitation coiltrack width and spacing is used. In this situation, thesame magnetic flux is generated by a physical smallercoil thus more of the magnetic flux couples to the sensingcoil, inducing an larger voltage in it. The sensing coil’strack spacing and width does not significantly influence thesignal level.

Sensitivity is increased when using a narrower excitationcoil track and spacing. In this situation, the sensing coilsare located close to the target, thus more sensitive for targetmovement. The sensitivity is marginally increased whenincreasing the sensor coil’s track width and spacing.

Figure 13: Induced sensing coil voltage vs. displacement for 1, 2and 5 layer sensors.

Vol.108 (1) March 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS10

Figure 14: Modelled induced sensing coil voltage vs.displacement for different insulation material thicknesses.

Figure 15: Modelled induced sensing coil voltage vs.displacement for different track spacing and track width.

5. CONCLUSION

This article presented a low cost, eddy current displace-ment sensor. The sensor unit can be produced verycheaply by using PCBs to realise the sensor coils. Thesensor is designed to use in AMBs and was testedon a representative rotor diameter. The number ofexcitation and sensing coil turns that will result in anoptimal sensitivity and linearity have been identified usingFEM simulations. The FEM model was verified usingan evaluation platform where MICRO-EPSILONR© eddycurrent sensors were used as reference. Aluminium,stainless steel and mild steel targets were used and goodcorrelation achieved for the first two.

The use of multi-layer PCBs was also investigated.Increasing the number of layers led to a significant increasein sensitivity. This came at a significant increase inmanufacturing cost. It is thus proposed that a standardthickness FR4, double layer PCB be used with 0.2 mmtracks and spacing be used. The sensor can then bemanufactured for less than 2 % of the cost of eddy currentsensors usually used in AMB systems. Note that the driveelectronics, amplification and signal processing required togive an position output have not been included in the costas these components are still being developed.

Future work will include futher modelling and characteri-sation to assess the viability of the concept. This includes3D FEM modelling to establish the linearity of the finalsensing results in the 2 principal directions. This will alsoinvolve signal processing using all four sensing signals.Finally the electromagnetic compatibility of the sensor inan actual AMB system with all possible electromagneticdisturbances should be investigated.

REFERENCES

[1] E. O. Ranft, G. van Schoor, and C. P. du Rand, “Anintegrated self-sensing approach for active magneticbearings,” SAIEE African Research Journal, vol. 4,pp. 90 – 97, 2011.

[2] G. van Schoor, A. Niemann, and C. du Rand,“Evaluation of demodulation algorithms for robustself-sensing active magnetic bearings,” Sensors andActuators A: Physical, vol. 189, no. 0, pp. 441 – 450,2013.

[3] G. Schweitzer, H. Bleuler, and A. Traxler, Activemagnetic bearings : Basics, Properties andApplications of Active magnetic bearings. Zurich:Authors Working Group, 2003.

[4] L. Weiwen, Z. Hui, and Q. Hongli, “Researchon novel grating eddy-current absolute-positionsensor,” Instrumentation and Measurement, IEEETransactions on, vol. 58, no. 10, pp. 3678–3683, Oct2009.

[5] A. Wogersien, S. Samson, J. Guttler, S. Beiftner,and S. Biittgenbach, “Novel inductive eddy currentsensor for angle measurement,” in Sensors, 2003.Proceedings of IEEE, vol. 1, Oct 2003, pp. 236–241Vol.1.

[6] P. Wang, Z. Fu, and T. Ding, “A framelesseddy current sensor for cryogenic displacementmeasurement,” Sensors and Actuators A: Physical,vol. 159, no. 1, pp. 7 – 11, 2010.

[7] K. Chomsuwan, S. Yamada, and M. Iwahara,“Bare PCB inspection system with SV-GMR sensoreddy-current testing probe,” Sensors Journal, IEEE,vol. 7, no. 5, pp. 890–896, May 2007.

[8] G. Y. Tian, Z. X. Zhao, and R. W. Baines, “Theresearch of inhomogeneity in eddy current sensor,”Sensors and Actuators, vol. A 69, pp. 148–151, 1998.

[9] J. Wilde and Y. Lai, “Design optimization of an eddycurrent sensor using the finite-elements method,”Microelectronics Reliability, vol. 43, no. 3, pp. 345– 349, 2003.

[10] M. Tsutomu, G. Sho, D. Kenta, K. Yoshinori,A. Yuichi, E. Shigemi, and S. Hiroki, “Methodfor identifying type of eddy-current displacementsensor,” Magnetics, IEEE Transactions on, vol. 47,no. 10, pp. 3554–3557, Oct 2011.

Vol.108 (1) March 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 11

[11] X. Chen and T. Ding, “Flexible eddy current sensorarray for proximity sensing,” Sensors and ActuatorsA: Physical, vol. 135, no. 1, pp. 126 – 130, 2007.

[12] D. Vyroubal, “Impedance of the eddy-currentdisplacement probe: The transformer model,” IEEETransactions on instrumentation and measurement,vol. 53, no. 2, pp. 384–391, April 2004.

[13] ——, “Eddy-current displacement transducer withextended linear range and automatic tuning,” Instru-mentation and Measurement, IEEE Transactions on,vol. 58, no. 9, pp. 3221–3231, Sept 2009.

[14] P. Buhler, “Device for cantact-less measurementof distances in multiple directions,” Europe Patent1 422 492, May 26, 2004.

[15] R. Larsonneur and P. Buhler, “New radial sensorfor active magnetic bearings,” in InternationalSymposium on Magnetic Bearings, no. 9, Lexington,Kentucky, USA, August 2004.

[16] L. Burdet, T. Maeder, R. Siegwart, P. Buhler, andB. Aeschlimann, “Thick-film radial position sensorfor high temperature active magnetic bearings,” inSymposium on Magnetic Bearings, no. 10, Marigny,Switzerland, August 2006.