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MARCH & APRIL 2001 VOL. 18 NO. 3 & 4

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T H E J O U R N A L O F A P P L I E D S E N S I N G T E C H N O L O G Y

PUBLICATIONAN

The Next Generationof Position Sensing

Parts 1 and 2

The Next Generationof Position Sensing

Parts 1 and 2

www.sensorsmag.com

Position SensingTechnologyPart 1: Theory and Design

The Next Generation of

Position SensingTechnology

To meet the stringent reliability, cost, and size requirements of the automotive,industrial, and aerospace industries, modern position sensors for motion controlapplications must be based on a noncontact design that minimizes wear and tearon the internal components. There are many different ways to measure position,

and each of the most common has certain drawbacks that can be severe enough to precludeits use for some applications. Among the better-known technologies are:

• Wirewound potentiometric [2]• Resistive ink potentiometric [3]• Capacitive [4]• Inductive LVDT/RVDT [5,6,7]• Planar coil inductive [8]• Hall effect [9,10]• Magnetoresistive [11]• Magnetostrictive [12]• Optical [13]

With the exception of the first two, all ofthese sensors can be described as noncon-tact in terms of the relationship betweenthe stationary and the moving parts of thesensor. Some of the salient features of eachsensor type are listed in Table 1 (page 4).

The Genesis of NCAPSThe basic design parameters for the devel-

opment of a new noncontact position sen-sor were:

• Low-cost components and materials• Simple electronics with no onboard

microprocessor• Full 360° measuring range

Asad M. Madni, Jim B. Vuong, andRoger F. Wells, BEI Technologies, Inc.

NCAPS is a new noncontact angular position sensor [1] featuring an inductive

attenuating coupler that measures phase shift rather than the magnitude of

the coupling signal. The original implementations were for a 360° rotary

sensor, but the basic concept has also evolved into a linear version.

RECEIVER

COUPLER

TRANSMITTER

HOUSING

COVER

Figure 1. NCAPS consists of a transmit-ter, a receiver (= transceiver), a coupler,the housing, and the cover.

The Next Generation of

Position Sensing TechnologyPart 1: Theory and DesignPosition Sensing Technology

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• Absolute linearity better than 1% overfull range

• Minimal radiated signals• Accommodation of significantly large

misalignments between the rotary and staticcomponents in radial, axial, and tilted rotorconditions

• Simple analog output for drop-inreplacement of potentiometric sensors

• Good manufacturability• Operating temperature of –40°C to

>125°C• High EMI and RFI immunity

The resulting NCAPS sensor meets all ofthese requirements, and also has someunique and desirable features that add to itsperformance:

• The sensor’s internal operating fre-quency can be selected as any desired valuefrom a few kilohertz to many megahertz,

whichever is least likely to interfere with anyadjacent device such as a radio receiver.

• The sensor’s primary output is a pulse-width-modulated (PWM) signal with a volt-age analog as a second alternative.

• The cross-talk immunity between twoadjacent NCAPS with respectively differentoperating frequencies allows two or moresensors to be closely stacked in a very thinpackage.

• The basic sensor element size canrange from 25 mm dia. to as large as theapplication requires. It can also be pro-duced to measure linear motion with thesame degree of size flexibility. For any spe-cific application and sensor size, the elec-tronics portion is common; only the rotor(or slider for the linear sensor) and the sta-tor design and size are changed to accom-modate specific packaging and installationrequirements.

Applications for NCAPSBecause NCAPS is a true 360° rotational

sensor, any application requiring one ormore full turns can be accommodated. Thesensor’s frequency response will also allowits use on rotating machinery with shaftspeeds up to 16,000 rpm, and will provide asignal ramping from minimum to maxi-mum that will snap back to minimum at the0°/360° transition point. NCAPS will alsomeet applications with less than a full turn,thus providing a viable alternative to rotarymagnetic sensors such as those based on theHall effect.

One ideal application for NCAPS is inautomotive steering angle measurements.Such a sensor must satisfy certain require-ments, among them:

• Very low acoustical noise• Extremely limited installation space that

necessitates a very thin profile• Very low frictional torque• Ability to accommodate steering column

runout• Versatile mechanical configuration

Another requirement for steering positionsensors is to measure absolute position from“lock-to-lock,” i.e., over several turns of thesteering wheel. A supplement to this is thatthe sensor should have instant recognitionof absolute position at “key-on.” TheNCAPS’s very low profile permits otherdevices and mechanisms to be added to thepackage. Commonly used methods for turnscounting include:

• “Geneva” turns-counting mechanisms• Simple optical devices• Reduction gears• Vernier counting devices using twin,

geared sensors but with different gear ratiosfor each sensor rotor

Theory of OperationAn earlier paper, “A Non-Contact Angular

Position Sensor (NCAPS) for MotionControl Applications,” by Madni et al. [1]was published in the proceedings of theUKACC International Conference onControl 2000, and copyrighted by theInstitution of Electrical Engineers (IEE).

The NCAPS is based on a transceiver con-cept. A loop antenna on the transmittertransmits a signal that is picked up by a cor-

Competing Technologies

Technology Features Advantages Disadvantages

Wirewound Single or multiturn High-temperature use Uses contactsPotentiometric output Temp. compensated Axially largeLinear and nonlinear High accuracy Noisy output

>360° Eventually wearsNo electronics

Resistive ink Single turn High-temperature use Perceived short lifePotentiometric output Temp. compensated Moderately noisy outputHigh linearity (tailored) Inexpensive

Low profile

Capacitive Generally linear Noncontact <360° rotationInexpensive for rotary sensors

Very gap sensitive

Inductive Planar coil rotary DT very precise Very susceptible toLVDT linear misalignment errorsRVDT rotary DT very expensive

Hall effect Rotary to 120° Mature technology Uses magnetsNeeds several Hall elements

to exceed 360° rotation

Magnetoresistive Rotary to 120° Uses magnetsNeeds temp.

compensation for specifictemp. ranges

Magnetostrictive Linear applications Very accurate Expensivepredominate Small package size

Optical Rotary Low cost for low- Temp. limitationLinear resolution incremental High cost for high-Absolute resolution absoluteIncremental Non-analog

Needs compensationfor LED deterioration

TABLE 1

5

responding loop antenna in the receiver.When there is no interfering (attenuating)object in this path, the amplitude of thereceived signal will be maximum. However,if a variably attenuating object is used tocause interference in this path, the receivedamplitude will attenuate in a proportionatemanner. This variable attenuation charac-teristic of the received signal is proportionalto the position of the varying object with ref-erence to the transceiver. Theoretically, asingle channel should be adequate to detectand provide the position and/or angular dis-placement information. However, since thedetected amplitude will also be affected bythe separation between the transmitter andthe receiver, as well as by the power level ofthe transmitted signal, errors resulting fromthis uncertainty will not provide perform-ance acceptable for critical automotive,industrial, and aerospace applications. Toovercome this problem, a multichannel sys-tem with an amplitude-to-phase conversiontechnique is used to convert the amplitudeinformation into phase information.

The phase separation in degrees betweenadjacent channels is determined by theequation:

∆θ = 2π/N (1)

where:

N = number of channels

The sum of the received signals is con-verted into a single sinusoidal waveformthrough a summing amplifier such that thephase shift changes of the signal are propor-tional to the degree of interference (angularposition). Since the signals received by thechannels are ratiometric with respect to oneanother, variations in the transmitted signalamplitude will have no effect on the resul-tant phase information.

System DescriptionThe NCAPS consists of a transmitter, cou-

pler, and receiver (see Figure 1, page 3).The transmitter disk consists of N spiralloop antenna patterns connected in series;in this case N = 6, as shown in Figure 2.The receiver disk consists of the same spiralloop antenna patterns as the transmitter

disk, except that each receiver is connectedseparately to a downconverter circuit. Thecoils are positioned every 60° on a constantradius that is dictated by the application.Both the disks are stationary with respect tothe housing.

The coupler, or rotating middle disk, con-sists of a tapered pattern. It has a positive-image crescent shape etched from copper,whose centerline coincides with the center-line of the elements. The cross section grad-uates from very little blockage of the signaldown to completely blocking the signalfrom reaching the receiver element (seeFigure 3). The main signal source of thesystem, Fc, is fed to the transmitter disk, andis also divided to generate N local oscillator

(LO) signals. These signals are separated by∆θ in phase, and downconverted to N inter-mediate frequency signals, IFN. A block dia-gram demonstrating the digital signal pro-cessing of the NCAPS is shown in Figure 4.

Theoretically, the transceiver designapproach can operate over a wide range offrequencies, but on a practical basis therange is limited by the material and struc-ture of the loop antenna, i.e., epoxy glassG10 PC board is usable up to RF range,and Teflon glass duroid material is good upto gigahertz range. For the developmentunits, a 1 MHz operating frequency waschosen due to the low-cost PC board etch-ing process and the availability of standardoff-the-shelf electronic components.

Figure 2. The transceiver pattern is composed ofmultiple loop antennas.

Figure 3. The coupler is a tapered trace in a circularconfiguration.

Figure 4. The digital signal processing is illustrated by this functional block diagram of NCAPS.

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Circuit DescriptionWhen the signal Fc is sent from the trans-

mitter disk to the receiver disk, the trans-mitted signal reaching each receiver coil iscontrolled by the coupler’s rotational posi-tion. The coupler is configured such that itcauses the energy to be distributed over thearray of N (in this case, 6) receivers in asinusoidal manner. If coil #1 is receivingmaximum signal, then coil #4 (180° apart)is receiving minimum signal and the oth-ers in between are receiving an amountthat is attenuated in a sinusoidal or bell-shaped manner. Each signal is then mixedagainst an LO that is derived by dividingthe transmit oscillator, Fc. This maintainsthe phase coherency of the resulting IF sig-nals. Each signal is then shifted in phase inaccordance with its physical position onthe circuit board (i.e., the element posi-tioned at 60° will be given a phase shift of60°, the element positioned at 120° will begiven a phase shift of 120°, and so on forthe 180°, 240°, and 300° elements). Thus,N different amplitude signals are gener-ated at any one position of the couplerwith a ∆θ phase separation via the digitalsignal generator as shown in Figure 4, andsummed by amplifier A1.

The output signal of amplifier A1 is a sinu-soidal waveform whose phase shift varies withrespect to the rotation of the coupler pattern.The signal is then filtered and amplified bylow-pass filter/limiting amplifier circuit A2and converted to a 50% duty cycle squarewave signal through comparator A3. Figure 5demonstrates the combined waveform at theoutput of A2 relative to four different couplerpositions. The output of A3 is fed into a phasecomparator circuit that compares its phasedifference to the IF reference signal that wasgenerated by the digital signal generator (seeFigure 6). The result is a PWM signal thatwill vary from <5% to >95% duty cycle in apulse repetition frequency based on the refer-ence IF, and which will track the rotation ofthe coupler from 0° to 360°. A PWM-to-ana-log converter, A4, is placed at one of the twooutputs of the PWM circuit to provide ananalog output voltage range from 0.05 to 4.9VDC.

Amplitude-to-Phase ConversionAs noted above, a single-channel trans-

ceiver based on amplitude level detection atthe receiver is, in theory, adequate to pro-vide the coupler’s angular position. Thisassumes, however, that the distance be-tween and alignment of the three disks, andthe power level of the transmitter remainconstant. To achieve this requires both arelatively complex signal conditioner circuitwith automatic gain control and a precisemechanical alignment, which would limitthe sensor’s suitability for low-cost, high-vol-ume production.

To circumvent these problems, a multi-channel transceiver with an amplitude-to-phase conversion technique was used in thedesign of the NCAPS. The signal amplitudeat each receiver, RI, is defined by:

Ri(t) = Ai cos ωct (2)

Ai = A cos [θ + 2π (i/N)] (3)

where:

N = number of channelsi = 1 to NA = magnitude of the transmitted signalAi = magnitude of attenuated signal

received at channel icos [θ + 2π (i/N)] = attenuation factor

related to each receiver based on the angu-lar position, θ

Each of the LO outputs may be repre-sented by:

cos ωct – cos [ωot + 2π (i/N)] (4)

where:

cos ωct = transmitted signal frequencycos ωot = predetermined IF frequency

Based on the mixer downconversion proc-ess, the relationship between LO, IF, andRF (transmitted frequency) is defined by:

IF = RF – LO (5)

Assuming a lossless mixer, each of the IFsignals may be represented by:

IFi = Ai cos [ωot + 2π (i/N)] (6)

The signal at the output of amplifier A1 isgiven by:

N NΣ IFi = Σ Ai cos [ωot + 2π (i/N)]i=l i=l

N= Σ A cos [θ + 2π (i/N)]

i=lcos [ωot + 2π (i/N)]

Figure 6. A pulse width modulated waveform isgenerated as a result of the signal processing.

Figure 5. The combined waveform of the A1 outputshows change in the phase vs. coupler position.

7

N= Σ 1/2 A {cos [ωot + 2π (i/N)

i=l

+θ + 2π (i/N)]+cos [ωot + 2π (i/N)– θ – 2π (i/N)]}

N= Σ 1/2A {cos [ωot + θ + 4π (i/N)]

i=l+ cos (ωot – θ)}

= 1/2A cos (ωot – θ)N

+ Σ 1/2A cos [(ωot + θ) i=l

+ 4π (i/N)] (7)

N Σ 1/2A cos [(ωot + θ) + 4π (i/N)]i=l

N=Σ1/2A{cos (ωot + θ) cos 4π (i/N)

i=l–sin (ωot + θ) sin 4π (i/N)}

when N=6

6Σ cos 4π (i/N)i=l

= cos 120° + cos 240° + cos 360°+ cos 480° + cos 600° + cos 720°= – 0.5 – 0.5 + 1–0.5 – 0.5+1= 0

and6Σ sin 4π (i/N)i=l

= sin 120° + sin 240° + sin 360°+ sin 480° + sin 600° + sin 720°

= 0.866–0.866 + 0+ 0.866 – 0.866 +0= 0

thenNΣ 1/2A cos [(ωot + θ) i=l+ 4π (i/N)] =0

and equation 7 may be rewritten as:

IF = 1/2A cos (ωot – θ) (8)

From Equation 8, it can be seen that theoutput signal of amplifier A1 is a phase rela-tionship representing the angular position ofthe coupler and is not dependent on thetransmitted signal amplitude variation. Thevarying composite waveform for a six-chan-nel transceiver design, representing Equa-tion 8, is shown in Figure 5.

Mechanical DesignThe mechanical design of all three disks is

based on mature PCB technology. The onlyrequirement is that the thickness be ade-quate to keep the boards reasonably flat.Because the sensor is operated in the RFrange, the transmitter and receiver antennasare based on a loop antenna design, which istypically a multiturn coil that can be printedon a multilayer PCB using standard manu-facturing techniques. The number of turnsof the coil determines the number of layersin the board. In general, this can be verycostly because the inductance of the coil isinversely proportional to the operating fre-quency; i.e., the lower the frequency, thehigher the required inductance. To achievelow cost and ease in manufacturing, anetched spiral inductor on a multilayer PCBwas chosen for this application, as shown inFigure 2. Computation of the spiral inductordesign is based on the planar rectangularmicroelectronic inductor method [14]:

LT = L0 + M+–M– (9)

L0 = L1 + L2 + ..... +LX (10)

LX = 2lx {ln[2lX/(w+t)]+0.500049 (11)+(w+t)/3lx]}

where:

LT = total inductanceL0 = sum of the self-inductances of all

straight segmentsM+ = sum of the positive mutual

inductancesM– = sum of the negative mutual

inductances

Lx = segment inductance (nanohenries)lx = segment lengthw = segment widtht = segment thickness (all

measurements are in centimeters)The number of channels on each disk

directly affects the sensor’s linearity andaccuracy. Initial tests indicated that a three-channel unit provides a linearity of betterthan ±2.0%, and a six-channel unit betterthan ±1.0%. The greater the number ofchannels, the better the linearity. However,the tradeoffs are increased cost and com-plexity. More channels require an increasednumber of modulators and digital mixers(demodulators) that end up driving the costper unit higher.

The coupler disk, as previously described,is a tapered trace in a circular layout. Thegeometric symmetry of the pattern is veryimportant because it has a direct effect onthe linearity error. The coupler’s linear rota-tion is designed to cause the received signalof each element, RI, to vary in a sinusoidalmanner. Circular patterns, arranged asshown in Figure 7, provide this functionand are easy to construct. Figure 8 illus-trates the sinusoidal characteristic of thecoupler by plotting the width of the patternvs. rotational angle. Also shown is the squarearea of the inductor that is covered, which,as would be expected, closely tracks. Theinitial design of the single tapered pattern is

Figure 7. The geometric symmetry of the couplerdesign causes the signal of each element to vary ina sinusoidal manner.

Figure 8. Plotting the width of the coupler’s physi-cal pattern against the rotational angle shows thecoupler’s sinusoidal characteristic.

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based on:

d3 = 1/4(3 d1 + d2) (12)d4 = 1/4(d1 +3 d2) (13)

where:d1 = outer diameterd2 = inner diameterd3 = outer diameter of patternd4 = inner diameter of pattern

The surface area of the tapered couplerpattern is equal to exactly half the area ofthe disk between the d1 and d2:

A3 – A4 = 1/2 (A1 – A2) (14)

where:

A1 = area with outer diameter d1A2 = area with inner diameter d2A3 = area with tapered outer diameter d3A4 = area with tapered inner diameter d4

Figure 9 shows the mechanical assemblyof the six major components. The receiver

PCB, which consists of the six inductivecoil sections and the associated electronics,is attached to the front housing by heat-staked pins. The output of the six receiverchannels is connected to the signal process-ing electronics. The receiver PCB providesthe excitation signal to the transmitter viatwo pins that snap into receptacles on thetransmitter PCB. It also provides intercon-nection for the voltage input and the PWMand analog outputs.

The transmitter PCB, consisting of the sixinductive coil sections connected in series,is attached to the rear housing by means ofan epoxy preform. It has two receptacles forelectrical connection. As stated above, thetransmitter and receiver are fixed in positionand the moving component, the coupler, ismounted on a hub with adhesive. The hubis connected to the shaft. The air gapsbetween the coupler and the transmitter-receiver pair can be as small as 0.1 mm, but to accommodate misalignmentand runout, 1–2 mm can be used. Since theangular position is determined by the cou-

pler position relative to the receivers (ratherthan the amplitude of the transmitted sig-nal), the air gap between the transmitter andthe receiver is not very critical.

Injection-molded, glass-filled plastics areused for the rotor hub, housing, and cover.If the sensor will be immersed or the elec-tronic circuits or components will beexposed to corrosive or otherwise harmfulambient gases, vapor, or liquids, additionalshaft seals will be necessary.

PerformanceTo test the linearity characteristics and per-

centage full-scale error of the NCAPS, thetest setup in Figure 10 was used. The sensorwas compared against a reference 12-bitabsolute optical encoder with a linearity bet-ter than 0.023%/step. The 360° of mechani-cal rotation is represented as 4096 codes(steps) of the 12-bit encoder and plottedagainst the analog output of the NCAPS,monitored by a digital voltmeter.

From the test results shown in Figures 11and 12, a linearity of ±1.0% (compared to astraight line drawn through the two extremeposition end points) is easily achievablewithout any fine tuning. The unit is also rel-atively forgiving with reference to the align-ment of the three disks. Since the NCAPStechnique is based on the transceiver con-cept, with <1/8 in. physical separationbetween the transmitter and receiver disks,most of the transmitted energy will bereceived by the receiver.

It should also be kept in mind that signalprocessing is based on a single down-conver-sion process. This is expressed in Equation5, whereby a mixer is used to downconvertthe transmitted signal, Fc, at the receiver toIF signals. Unless there is a strong fieldapplied to the NCAPS at or very close to Fc,or a strong field that saturates all receiverchannels and no phase relationship is avail-able, electromagnetic interference (EMI)and electromagnetic susceptibility will havea relatively minor effect on the performance.

AcknowledgementThe authors wish to thank Linet Aghassi for

her help in the preparation of thismanuscript, and Robert K. Hansen, MitchellLondon, and Philip Vuong for their support.

Figure 9. The key components of NCAPS areshown in this exploded view.

Figure 11. The full-scale linearity error is plottedat 25°C.

Figure 12. Here, the linearity error is plottedagainst temperature.

Figure 10. The test setup for linearity measure-ment uses a 12-bit optical encoder.

9

References1. A.M. Madni et al. 2000. “A Non-Contact

Angular Position Sensor (NCAPS) for MotionControl Applications,” Proc UK-ACC Inter-national Conference on Control 2000, Universityof Cambridge, U.K., 2-7 Sept.

2. C.D. Todd, P.E. 1975. The PotentiometerHandbook, McGraw Hill.

3. R.E. Riley. 1989. “High Performance ResistivePosition Sensors,” SAE Technical Paper 890302.

4. R.D. Peters. 1989. “Linear Rotary Dif-ferential Capacitance Transducer,” Rev SciInstru, Vol. 60:2789-2793.

5. J.V. Byrne et al. April 1987. “The ScreenedInductance Sensor: A New Position and SpeedMeasurement System,” Proc Motorcon, Han-nover, Vol. 10:220-237.

6. J.V. Byrne et al. June 1987. “Linear-MotionScreened Inductance Sensors,” Proc Conf onApplied Motion Control, Minneapolis,MN:221-230.

7. E.E. Herceg. May 1986. Handbook ofMeasurement and Control: An AutoritativeTreatise on the Theory and Application ofLVDTs, Schaevitz Engineering, LCCC #76-24971.

8. J.H. Francis. “PIPS, a New Technology inInductive Position Sensing,” Positek Ltd.,Gloucestershire, U.K. (May be found atwww.positek.co.uk.)

9. E.H. Putlye. 1960. “The Hall Effect andRelated Phenomena,” Semiconductor Mono-graphs, Hogarth, ed., Butterwort, London.

10. “Sprague Hall Effect and OptoelectronicSensors.” 1987. Data Book SN-500.

11. W. Kwiatkowski and S. Tumanski. 1986.“The Permalloy Magnetoresistive Sensors—Properties and Applications,” J Phy E:S. Intrum,Vol. 19:502-515.

12. P. Pecorari et al. 2000. “Magnetostrictionin Automotive Position Measurement,” SAETechnical paper 2000-01-1374.

13. J. Fraden. 1993. AIP Handbook of ModernSensors, American Institute of Physics:296-299.

14. H.M. Greenhouse. 1974. “Design of PlanarRectangular Microelectronic Inductors,” IEEETrans on Parts, Hybrids, and Packaging, Vol.PHP-10, No. 2:101-109. ■

Dr. Asad M. Madni is President and ChiefOperating Officer, BEI Technologies, Inc.,13100 Telfair Ave., Sylmar, CA 91342; 818-364-7215, fax 818-362-1836, bei1madni@aol.com.Jim B. Vuong is Senior Staff Engineer, BEITechnologies, Inc., 13100 Telfair Ave.,Sylmar, CA 91342; 818-364-7210, fax 818-362-1836, jvuong@bei-tech.com.Roger F. Wells is Vice President and GeneralManager, Duncan Electronics (a division ofBEI Technologies, Inc.), 15771 Red Hill Ave.,Tustin, CA 92780; 714-247-2531, fax 714-258-8120, roger.wells@beiduncan.com.

©Reprinted from SENSORS, March 2001 AN ADVANSTAR ★ PUBLICATION Printed in U.S.A.

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Position SensingTechnologyPosition SensingTechnologyPart 2: D i f f e r e n t i a lD i s p l a c e m e n t a n dL i n e a r C a p a b i l i t i e s

The Next Generation of

11

Part 1 of this article, which appeared in the March 2001 issueof Sensors, examined the underlying theory of NCAPS tech-nology and explored the details of rotary sensors based on it.The figures, equations, and references in Part 2 are num-

bered consecutively from those in Part 1.

NCAPS as a Differential Displacement SensorThe never-ending demand for higher efficiency and greater reliabil-

ity in automobiles, and the introduction of the modern electric vehi-cle, have collectively doomed power-hungry devices such as the powersteering hydraulic pump and the air conditioning compressor. Thebest replacement for the pump is at present an electric motor thatdirectly assists the steering. The problem now lies with reliably sensingthe driver-applied torque so as to know how much assist to add. Thiscould be accomplished with potentiometers, but the limited life of thewipers is unacceptable in this critical application. Optical encodersare another option. While these would work, they are prohibitivelyexpensive (especially absolute encoders), and reliability concerns dis-courage the use of a light source. NCAPS technology can determineangular displacement and at the same time comply with the very strin-gent demands of the automotive and heavy equipment industries.

An NCAPS is placed at each end of a torsion bar, one mounted onthe upper rotor, T, and the other mounted on the lower rotor, P, (seeFigure 13). By electronically taking the difference between the twoanalog outputs or by comparing the phase shift of the two PWM sig-nals and applying the transfer coefficient of torque to degrees, it is pos-sible to obtain both torque and directional information. Referring toFigure 13 and the functional block diagram of Figure 14 (page 12),assume that the first NCAPS has an angular position θa and the sec-ond an angular position θb,with reference to 0°.

Asad M. Madni, Jim B. Vuong, andRoger F. Wells, BEI Technologies, Inc.

The NCAPS noncontact angular position sensor, originally

developed to measure 360° rotary motion, is capable of

determining linear motion as well.

The Next Generation of

Position Sensing TechnologyPart 2: Differential Displacement and Linear Capabilities

Figure 13. NCAPS can be configured as a noncontact differ-ential angular displacement and absolute position sensor.

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The Next Generation of

Position Sensing TechnologyPart 2: Differential Displacement and Linear CapabilitiesPosition Sensing Technology

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Then, in accordance with Equation 8, theoutput of the first NCAPS is given by:

IF1 = 1/2A cos (ωot – θa) (15)

and the output of the second by:

IF2 = 1/2A cos (ωot – θb) (16)

Taking the difference between these twooutputs yields:

IF = IF1 – IF2 = 1/2A [cos (ωot – θa)– cos (ωot – θb)] (17)

IF = 1/2A (cos ωot cos θa + sin ωot sin θa– cos ωot cos θb– sin ωot sin θb)= 1/2A [cos ωot (cos θa – cos θb) + sin ωot (sin θa – sin θb)] (18)

Let

sin � = sin θa – sin θb

and

cos � = cos θa – cos θb

Then (18) becomes:

IF = 1/2A (cos ωot cos �+ sin ωot sin �) (19)

= 1/2A cos (ωot – �) (20)

where:A cos ωot = received signal� = tan-1 [(sin θa – sin θb)/( cos θa – cos θb)]

= torque component

A typical automotive torque sensing appli-cation specifies a nominal 2.5 V output ±2 V at ±8°. A typical NCAPS provides 11 mV/° to satisfy the 360° requirement. Toachieve the required 250 mV/°, a simplebuffer with a gain of ~23 would be neededfor the NCAPS output. This applicationalso requires absolute position informationover ±2.25 turns of the steering wheel. Thiscan be satisfied with a third NCAPS, P2,with a gear reduction mechanism. Referringto T, P1, and P2 in Figure 13, T is thetorque sensor when compared to P1; P1 isthe fine 0° to ±180° sensor; and P2 is thegear-reduced 0° to ±810° coarse absoluteposition sensor.

A potential obstacle presents itself withthis method of torque sensing. It should benoted that the T and P sensors are set nom-inally at 2.5 V and are therefore step free for±180°. The difference between their out-puts is used to measure torque. As the steer-ing wheel turns and the sensor approaches180°, however, the T sensor will transitionfirst, so the output torque signal goes fromseeing a difference of a couple of degrees toseeing a difference of hundreds, and tendsto rail in the direction opposite to the onethat needs assist. A few degrees later, theother sensor transitions and the measure-ment is back to normal accurate determina-tion. This is, of course, totally unacceptable.To overcome this limitation, the followingdesign approach was implemented.

Since each NCAPS generates a 50% dutycycle signal at the output of its respectivesumming amplifier/comparator circuit, witha phase shift proportional to the respectivecoupler position, precise differential angularinformation can be generated without thecrossover point concern by comparing thesetwo signals via a phase comparator (EXLU-SIVE OR circuit), when the output of T isphase shifted by 90° as shown in Figure 14.

Under this condition, when the two sig-nals are in phase (no torque), the output ofthe phase comparator is a 50% duty cyclesignal due to one signal’s being shifted 90°(in this case, T). When a torque is appliedto the shaft, the duty cycle of the signal will

vary in a manner proportionate to the leador lag of the two couplers (see Figure 15).

The differential angular displacement rangeof a typical drive shaft is ±8° to ±12°, whichimplies that signals P and T will never crossover the 0° ±180° point with respect to eachother. The output can be converted to a full-scale digital output by using the edge triggercounting method, or it can provide a full-scaleanalog output (in this case, 0–5 VDC) byusing the gain and offset method in an ampli-fier circuit. Since the two NCAPS share atransmitter frequency, Fc, a common trans-mitter can be used for both couplers andreceivers when the rotor gap is <0.1 in. Withthis approach, where the transmitters andreceivers are mounted on a solid platform andthe couplers are on the rotating shaft, a truenoncontact differential angular displacement(torque) measurement can be made.

Figure 14. This functional block diagram of a noncontact torque and absolute position sensor illustratesthe signal processing technique.

Figure 15. In the presence of an applied torque,the signal’s duty cycle varies in a manner propor-tionate to the lead or lag of the two couplers.

D I S P L A C E M E N T

13

Mechanical Design of a Differential Displacement Sensor

To measure steering effort in a torsionallycompliant steering system, several mechani-cal construction and space considerationsmust be addressed. The first is related to thephysical location of the sensor. There aretwo main candidate locations. The first isinside the passenger compartment and justunder the steering wheel, a position that iscomparatively benign in terms of environ-ment. Operating temperatures are low andsealing is necessary only for protection fromdust and occasional liquid spills. Salt sprayand hot fluids found in under-hood applica-tions need not be considered. Acousticalnoise is an issue, particularly with electri-cally contacting sensors, but the NCAPS isnoncontact and generates negligible noise.

The second candidate location, in theengine compartment as part of the steeringrack mechanism, subjects the sensor toambient temperatures often >150°C.Physical size, particularly the outside diam-eter of the sensor, is usually tightly con-strained. Sealing is also crucial because thesensor must survive the full range of enginecompartment fluids as well as salt spray andicy fluids from the roadway.

Sensors in either location also have verylow torque-to-turn limitations. At first itmight appear that sensor torque is relativelyunimportant because the large-diametersteering wheel will easily magnify small

steering efforts and overcome any seal fric-tion in the sensor. But this is not the case.Steering systems are designed to self-center,i.e., when the steering wheel is released andthe car is in motion, the driver expects thewheel to automatically return to thestraight-ahead position. Because of the step-down gear ratio between the steering gearsand the steering wheel shaft, the self-center-ing torque necessary to overcome the sensorseal friction will be multiplied by the steer-ing gear ratio and added to all the gear trainand steering joint friction plus tire-to-roadresistance. The caster angle of the frontwheels can be increased to accommodatethis resistance but at the expense of increas-ing the steering effort necessary to maneu-

ver the car. The maximum allowable torqueresistance for the sensor is typically 70 mN•m (10 ozf•in).

This article details a design for the firstcase, but given the versatility of NCAPS,similar mechanical components can beassembled for a sensor to meet the require-ments of the second case.

Using limits of torsional compliance similarto those currently in hydraulic power-assistedsteering systems, an operating range of ±8º isavailable for the torque-measuring position ofthe sensor. The configuration in Figure 13requires three sensor elements and a reduc-tion gear assembly to be packaged in a singlehousing with a maximum thickness of 21mm. Figures 16 and 17 illustrate the arrange-

Figure 16. Assembly details of the torque and position sensor can be seen in this exploded view. Figure 17. A sectional view of the sensor’s key ele-ments provides additional information.

Figure 18. A noncontact linear position sensor can be built based on NCAPS technology.

D I S P L A C E M E N T

ment of all the necessary elements.As can be seen, the steering column is

split and connected by a flexible torsion bar.Hard stops are included to limit the allow-able twist that prevents the torsional wind-up from exceeding the elastic limit of thetorsion bar. Other components are:

NCAPS Elements. These consist of threecoupler discs and three transmitter-receiverpairs. Because the torque element of thesensor uses a common transmitter, there is atotal of eight sensor discs.

Reduction Gears. To provide the absoluteanalog position from lock to lock, themotion of the position coupler is reduced bya 5:1 ratio gear train.

Self-Centering Coupling. This compo-nent is included to accommodate radialrunout of the steering shaft.

Linear Version of NCAPSA linear version of the NCAPS technology

(see Figure 18) was developed for use withlinear voice coil actuators to provide built-infeedback control for motion control applica-tions. Its basic design and theory of opera-tion is the same as NCAPS—the transmitterand the receiver section each contains sixidentical loop antenna coils. The totallength of the six antenna coils, La, deter-mines the maximum measurable displace-ment. The slider section consists of atapered pattern (equivalent to the crescent

shape in the NCAPS coupler) equivalent toLa, except that the pattern is repeated on theslider so that the transmitter and receiverare exposed to 360° of the pattern at alltimes. The total length of the slider is equalto the measured displacement, Lc, plus La,with the limitation that Lc ≤ La. For a multi-section tapered pattern (for long displace-ment measurement), a cycle counter mustbe used to identify the revolutions.

The voice coil actuators are direct-drive,limited-motion devices that use a perma-nent magnet field and a coil winding (con-ductor) to produce a force proportional tothe current applied to the coil [15]. Theelectromechanical conversion mechanismof a voice coil actuator is governed by theLorentz principle, which states that if a cur-rent-carrying conductor is placed in a mag-netic field, a force will act upon it. Themagnitude of this force is determined by themagnetic flux density, B, the current, I, andthe orientation of the field and current vec-tors. Furthermore, if a total of N conductors(in series) of length L are placed in the mag-netic field, the force acting upon the con-ductors is given by:

F= KBLIN (23)

where:

K = a constant

Figure 19 is a simplified illustration of thisphysical law.

In its simplest form, a linear voice coilactuator is a tubular coil of wire situatedwithin a radially oriented magnetic field(see Figure 20). The field is produced bypermanent magnets embedded on theinside diameter of a ferromagnetic cylinder,arranged such that the magnets facing thecoil all have the same polarity. An innercore of ferromagnetic material set along theaxial centerline of the coil, joined at oneend to the permanent magnet assembly,completes the magnetic circuit. The forcegenerated axially on the coil when currentflows through will produce relative motionbetween the field assembly and the coil,provided the force is large enough to over-come friction, inertia, and any other forces

from loads attached to the coil. The linearposition sensor is embedded in the actuatoras shown in Figure 20. The slider board isattached to the coil holder and moves inaccordance with the actuation level,thereby providing the same function as thecoupler in the angular version. For thisapplication the maximum measured dis-tance, Lc, was equal to 1/3 La. The electron-ics for processing the data from the linearsensor are identical to the functional blockdiagram in Figure 4. Figure 21 is a rearview of the actuator with the built-in sen-sor. This linear position sensor can also beused to detect differential linear position inaccordance with the equations governingthe angular position measurement. The sig-nal processing circuitry would be the sameas that in Figure 14.

Future WorkThe next phase of development will focus

on advancing the sensor functions, such asreducing the signal processing electronics toa mixed signal ASIC as well as incorporatingseveral interface options. Serial and paralleldata bus interfaces and an RS-232 optionwill be provided for most application inter-faces, and a Controller Area Network (CAN)interface will be provided for automotiveapplications. Additionally, further enhance-ments to EMI and RFI susceptibility will beincorporated.

SummaryA noncontact angular position sensor with

an inductive attenuating coupler has beendeveloped for use in motion control appli-cations. The sensor features a linearity ofbetter than ±0.5% over 360° of rotation.The measurement of phase shift, ratherthan the magnitude of the coupling signal,to determine the angular position gives thedesign a very high tolerance to mechanicalmisalignment of the rotating componentsand makes it conducive to mass production.The analog and digital signal processingelectronics can be readily converted to anASIC. The sensor, which does not use anypermanent magnets, LEDs, or photodetec-tors, lends itself to the high-volume, low-cost, and high-reliability requirements ofthe automotive, industrial, robotics, medical

14

Figure 19. The Lorentz force il lustrated heredescribes the force on a charged particle moving inelectrical and magnetic fields as being equal tothe particle’s charge times the sum of the electricfield and the cross product of the particle’s veloc-ity with the magnetic flux density.

D I S P L A C E M E N T

Copyright Notice Copyright by Advanstar Communications Inc. Advanstar Communications Inc. retains all rights to this article. This article may only be viewed or printed (1) for personal use. User may not activelysave any text or graphics/photos to local hard drives or duplicate this article in whole or in part, in any medium. Advanstar Communications Inc. home page is located at http://www.advanstar.com.

15

D I S P L A C E M E N T

instrumentation, and aerospace and defenseindustries. A linear version of this sensor hasbeen developed for use with voice coil actu-ators, resulting in smart actuators with built-in feedback control.

AcknowledgementThe authors wish to thank Linet Aghassi for

her help in the preparation of thismanuscript, and Robert K. Hansen, MitchellLondon, and Philip Vuong for their support.

Reference15. A.M. Madni et al. 1998. “Adaptive Fuzzy Logic

Based Control System For Rifle Stabilization,” ProcWorld Automation Congress (WAC ’98), Anchorage,AK, 10-14 May, TSI Press, PO Box 14126, Albu-querque, NM 87191:103-112. ■

Dr. Asad M. Madni is President and ChiefOperating Officer, BEI Technologies, Inc.,

13100 Telfair Ave., Sylmar, CA 91342; 818-364-7215, fax 818-362-1836, bei1madni@aol.com.Jim B. Vuong is Senior Staff Engineer, BEITechnologies, Inc., 13100 Telfair Avenue,Sylmar, CA 91342; 818-364-7210, fax 818-362-1836, jvuong@bei-tech.com.Roger F. Wells is Vice President and GeneralManager, Duncan Electronics (a division ofBEI Technologies, Inc.), 15771 Red Hill Ave.,Tustin, CA 92780; 714-247-2531, fax 714-258-8120, roger.wells@beiduncan.com.

©Reprinted from SENSORS, April 2001 AN ADVANSTAR ★ PUBLICATION Printed in U.S.A.

Figure 21. This is a rear view of the smart actuator shown in Figure 20.Figure 20. A linear voice coil actuator with a built-in noncontact displacementsensor provides a smart actuator.

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