The Next Generation

of Position Sensing

Parts 1 and 2




The Next Generation of

Position Sensing


Part 1: Theory and Design


The Next Generation of

Position Sensing Technology

Part 1: Theory and Design

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.

To meet the stringent reliability, cost, and size requirements of the automotive,

industrial, and aerospace industries, modern position sensors for motion control

applications must be based on a noncontact design that minimizes wear and tear

on 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 preclude

its 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]

Asad M. Madni,

Jim B. Vuong, and

Roger F. Wells,

BEI Technologies, Inc.


With the exception of the first two, all of

these sensors can be described as noncontact

in terms of the relationship between

the stationary and the moving parts of the

sensor. Some of the salient features of each

sensor type are listed in Table 1 (page 4).

The Genesis of NCAPS

The basic design parameters for the development

of a new noncontact position sensor


• Low-cost components and materials

• Simple electronics with no onboard


• Full 360° measuring range




Figure 1. NCAPS consists of a transmitter,

a receiver (= transceiver), a coupler,

the housing, and the cover.




• Absolute linearity better than 1% over

full range

• Minimal radiated signals

• Accommodation of significantly large

misalignments between the rotary and static

components in radial, axial, and tilted rotor


• Simple analog output for drop-in

replacement of potentiometric sensors

• Good manufacturability

• Operating temperature of –40°C to


• High EMI and RFI immunity

The resulting NCAPS sensor meets all of

these requirements, and also has some

unique and desirable features that add to its


• The sensor’s internal operating frequency

can be selected as any desired value

from a few kilohertz to many megahertz,

Competing Technologies

Technology Features Advantages Disadvantages

Wirewound Single or multiturn High-temperature use Uses contacts

Potentiometric output Temp. compensated Axially large

Linear and nonlinear High accuracy Noisy output

>360° Eventually wears

No electronics

Resistive ink Single turn High-temperature use Perceived short life

Potentiometric output Temp. compensated Moderately noisy output

High linearity (tailored)


Low profile

Capacitive Generally linear Noncontact


responding loop antenna in the receiver.

When there is no interfering (attenuating)

object in this path, the amplitude of the

received signal will be maximum. However,

if a variably attenuating object is used to

cause interference in this path, the received

amplitude will attenuate in a proportionate

manner. This variable attenuation characteristic

of the received signal is proportional

to the position of the varying object with reference

to the transceiver. Theoretically, a

single channel should be adequate to detect

and provide the position and/or angular displacement

information. However, since the

detected amplitude will also be affected by

the separation between the transmitter and

the receiver, as well as by the power level of

the transmitted signal, errors resulting from

this uncertainty will not provide performance

acceptable for critical automotive,

industrial, and aerospace applications. To

overcome this problem, a multichannel system

with an amplitude-to-phase conversion

technique is used to convert the amplitude

information into phase information.

The phase separation in degrees between

adjacent channels is determined by the



∆θ = 2π/N (1)

Figure 2. The transceiver pattern is composed of

multiple loop antennas.

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


N = number of channels

The sum of the received signals is converted

into a single sinusoidal waveform

through a summing amplifier such that the

phase shift changes of the signal are proportional

to the degree of interference (angular

position). Since the signals received by the

channels are ratiometric with respect to one

another, variations in the transmitted signal

amplitude will have no effect on the resultant

phase information.

System Description

The NCAPS consists of a transmitter, coupler,

and receiver (see Figure 1, page 3).

The transmitter disk consists of N spiral

loop antenna patterns connected in series;

in this case N = 6, as shown in Figure 2.

The receiver disk consists of the same spiral

loop antenna patterns as the transmitter

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

disk, except that each receiver is connected

separately to a downconverter circuit. The

coils are positioned every 60° on a constant

radius that is dictated by the application.

Both the disks are stationary with respect to

the housing.

The coupler, or rotating middle disk, consists

of a tapered pattern. It has a positiveimage

crescent shape etched from copper,

whose centerline coincides with the centerline

of the elements. The cross section graduates

from very little blockage of the signal

down to completely blocking the signal

from reaching the receiver element (see

Figure 3). The main signal source of the

system, F c , is fed to the transmitter disk, and

is also divided to generate N local oscillator

(LO) signals. These signals are separated by

∆θ in phase, and downconverted to N intermediate

frequency signals, IF N . A block diagram

demonstrating the digital signal processing

of the NCAPS is shown in Figure 4.

Theoretically, the transceiver design

approach can operate over a wide range of

frequencies, but on a practical basis the

range is limited by the material and structure

of the loop antenna, i.e., epoxy glass

G10 PC board is usable up to RF range,

and Teflon glass duroid material is good up

to gigahertz range. For the development

units, a 1 MHz operating frequency was

chosen due to the low-cost PC board etching

process and the availability of standard

off-the-shelf electronic components.



Circuit Description

When the signal F c is sent from the transmitter

disk to the receiver disk, the transmitted

signal reaching each receiver coil is

controlled by the coupler’s rotational position.

The coupler is configured such that it

causes the energy to be distributed over the

array of N (in this case, 6) receivers in a

sinusoidal manner. If coil #1 is receiving

maximum signal, then coil #4 (180° apart)

is receiving minimum signal and the others

in between are receiving an amount

that is attenuated in a sinusoidal or bellshaped

manner. Each signal is then mixed

against an LO that is derived by dividing

the transmit oscillator, F c . This maintains

the phase coherency of the resulting IF signals.

Each signal is then shifted in phase in

accordance with its physical position on

the circuit board (i.e., the element positioned

at 60° will be given a phase shift of

60°, the element positioned at 120° will be

given a phase shift of 120°, and so on for

the 180°, 240°, and 300° elements). Thus,

N different amplitude signals are generated

at any one position of the coupler

with a ∆θ phase separation via the digital

signal generator as shown in Figure 4, and

summed by amplifier A1.

The output signal of amplifier A1 is a sinusoidal

waveform whose phase shift varies with

respect to the rotation of the coupler pattern.

The signal is then filtered and amplified by

low-pass filter/limiting amplifier circuit A2

and converted to a 50% duty cycle square

wave signal through comparator A3. Figure 5

demonstrates the combined waveform at the

output of A2 relative to four different coupler

positions. The output of A3 is fed into a phase

comparator circuit that compares its phase

difference to the IF reference signal that was

generated by the digital signal generator (see

Figure 6). The result is a PWM signal that

will vary from 95% duty cycle in a

pulse repetition frequency based on the reference

IF, and which will track the rotation of

the coupler from 0° to 360°. A PWM-to-analog

converter, A4, is placed at one of the two

outputs of the PWM circuit to provide an

analog output voltage range from 0.05 to 4.9


Amplitude-to-Phase Conversion

As noted above, a single-channel transceiver

based on amplitude level detection at

the receiver is, in theory, adequate to provide

the coupler’s angular position. This

assumes, however, that the distance between

and alignment of the three disks, and

the power level of the transmitter remain

constant. To achieve this requires both a

relatively complex signal conditioner circuit

with automatic gain control and a precise

mechanical alignment, which would limit

the sensor’s suitability for low-cost, high-volume


To circumvent these problems, a multichannel

transceiver with an amplitude-tophase

conversion technique was used in the

design of the NCAPS. The signal amplitude

at each receiver, RI, is defined by:


R i (t) = A i cos ω c t (2)

A i = A cos [θ + 2π (i/N)] (3)

N = number of channels

i = 1 to N

A = magnitude of the transmitted signal

A i = magnitude of attenuated signal

received at channel i

cos [θ + 2π (i/N)] = attenuation factor

related to each receiver based on the angular

position, θ

Each of the LO outputs may be represented



cos ω c t – cos [ω o t + 2π (i/N)] (4)

cos ω c t = transmitted signal frequency

cos ω o t = predetermined IF frequency

Based on the mixer downconversion process,

the relationship between LO, IF, and

RF (transmitted frequency) is defined by:

IF = RF – LO (5)

Assuming a lossless mixer, each of the IF

signals may be represented by:

IF i = A i cos [ω o t + 2π (i/N)] (6)

Figure 5. The combined waveform of the A1 output

shows change in the phase vs. coupler position.

Figure 6. A pulse width modulated waveform is

generated as a result of the signal processing.

The signal at the output of amplifier A1 is

given by:



Σ IFi = Σ A i cos [ω o t + 2π (i/N)]

i=l i=l


= Σ A cos [θ + 2π (i/N)]


cos [ω o t + 2π (i/N)]




= Σ 1 / 2 A {cos [ω o t + 2π (i/N)


+θ + 2π (i/N)]

+cos [ω o t + 2π (i/N)

– θ – 2π (i/N)]}


= Σ 1 / 2 A {cos [ω o t + θ + 4π (i/N)]


+ cos (ω o t – θ)}

= 1 / 2 A cos (ω o t – θ)


+ Σ 1 / 2 A cos [(ω o t + θ)


+ 4π (i/N)] (7)


Σ 1 / 2 A cos [(ω o t + θ) + 4π (i/N)]



=Σ 1 / 2 A{cos (ω o t + θ) cos 4π (i/N)


–sin (ω o t + θ) sin 4π (i/N)}

when N=6




Σ cos 4π (i/N)


= cos 120° + cos 240° + cos 360°

+ cos 480° + cos 600° + cos 720°

= – 0.5 – 0.5 + 1–0.5 – 0.5+1

= 0


Σ sin 4π (i/N)


= sin 120° + sin 240° + sin 360°

+ sin 480° + sin 600° + sin 720°

= 0.866–0.866 + 0

+ 0.866 – 0.866 +0

= 0


Σ 1 / 2 A cos [(ω o t + θ)


+ 4π (i/N)] =0

and equation 7 may be rewritten as:

IF = 1 / 2 A cos (ω o t – θ) (8)

From Equation 8, it can be seen that the

output signal of amplifier A1 is a phase relationship

representing the angular position of

the coupler and is not dependent on the

transmitted signal amplitude variation. The

varying composite waveform for a six-channel

transceiver design, representing Equation

8, is shown in Figure 5.

Figure 7. The geometric symmetry of the coupler

design causes the signal of each element to vary in

a sinusoidal manner.

Mechanical Design

The mechanical design of all three disks is

based on mature PCB technology. The only

requirement is that the thickness be adequate

to keep the boards reasonably flat.

Because the sensor is operated in the RF

range, the transmitter and receiver antennas

are based on a loop antenna design, which is

typically a multiturn coil that can be printed

on a multilayer PCB using standard manufacturing

techniques. The number of turns

of the coil determines the number of layers

in the board. In general, this can be very

costly because the inductance of the coil is

inversely proportional to the operating frequency;

i.e., the lower the frequency, the

higher the required inductance. To achieve

low cost and ease in manufacturing, an

etched spiral inductor on a multilayer PCB

was chosen for this application, as shown in

Figure 2. Computation of the spiral inductor

design is based on the planar rectangular

microelectronic inductor method [14]:

L T = L 0 + M + –M – (9)

L 0 = L 1 + L 2 + ..... +L X (10)

L X = 2lx {ln[2l X /(w+t)]+0.500049 (11)

+(w+t)/3l x ]}



L 0

= total inductance

= sum of the self-inductances of all

straight segments

M + = sum of the positive mutual


M – = sum of the negative mutual


Figure 8. Plotting the width of the coupler’s physical

pattern against the rotational angle shows the

coupler’s sinusoidal characteristic.

L x

l x



= segment inductance (nanohenries)

= segment length

= segment width

= segment thickness (all

measurements are in centimeters)

The number of channels on each disk

directly affects the sensor’s linearity and

accuracy. Initial tests indicated that a threechannel

unit provides a linearity of better

than ±2.0%, and a six-channel unit better

than ±1.0%. The greater the number of

channels, the better the linearity. However,

the tradeoffs are increased cost and complexity.

More channels require an increased

number of modulators and digital mixers

(demodulators) that end up driving the cost

per unit higher.

The coupler disk, as previously described,

is a tapered trace in a circular layout. The

geometric symmetry of the pattern is very

important because it has a direct effect on

the linearity error. The coupler’s linear rotation

is designed to cause the received signal

of each element, R I , to vary in a sinusoidal

manner. Circular patterns, arranged as

shown in Figure 7, provide this function

and are easy to construct. Figure 8 illustrates

the sinusoidal characteristic of the

coupler by plotting the width of the pattern

vs. rotational angle. Also shown is the square

area of the inductor that is covered, which,

as would be expected, closely tracks. The

initial design of the single tapered pattern is



Figure 9. The key components of NCAPS are

shown in this exploded view.

Figure 10. The test setup for linearity measurement

uses a 12-bit optical encoder.

based on:

d 3 = 1 / 4 (3 d 1 + d 2 ) (12)

d 4 = 1 / 4 (d 1 +3 d 2 ) (13)


d 1 = outer diameter

d 2 = inner diameter

d 3 = outer diameter of pattern

d 4 = inner diameter of pattern

The surface area of the tapered coupler

pattern is equal to exactly half the area of

the disk between the d1 and d2:

A 3 – A 4 = 1 / 2 (A 1 – A 2 ) (14)


A 1 = area with outer diameter d 1

A 2 = area with inner diameter d 2

A 3 = area with tapered outer diameter d 3

A 4 = area with tapered inner diameter d 4

Figure 9 shows the mechanical assembly

of the six major components. The receiver

Figure 11. The full-scale linearity error is plotted

at 25°C.

Figure 12. Here, the linearity error is plotted

against temperature.

PCB, which consists of the six inductive

coil sections and the associated electronics,

is attached to the front housing by heatstaked

pins. The output of the six receiver

channels is connected to the signal processing

electronics. The receiver PCB provides

the excitation signal to the transmitter via

two pins that snap into receptacles on the

transmitter PCB. It also provides interconnection

for the voltage input and the PWM

and analog outputs.

The transmitter PCB, consisting of the six

inductive coil sections connected in series,

is attached to the rear housing by means of

an epoxy preform. It has two receptacles for

electrical connection. As stated above, the

transmitter and receiver are fixed in position

and the moving component, the coupler, is

mounted on a hub with adhesive. The hub

is connected to the shaft. The air gaps

between the coupler and the transmitterreceiver

pair can be as small as

0.1 mm, but to accommodate misalignment

and runout, 1–2 mm can be used. Since the

angular position is determined by the coupler

position relative to the receivers (rather

than the amplitude of the transmitted signal),

the air gap between the transmitter and

the receiver is not very critical.

Injection-molded, glass-filled plastics are

used for the rotor hub, housing, and cover.

If the sensor will be immersed or the electronic

circuits or components will be

exposed to corrosive or otherwise harmful

ambient gases, vapor, or liquids, additional

shaft seals will be necessary.


To test the linearity characteristics and percentage

full-scale error of the NCAPS, the

test setup in Figure 10 was used. The sensor

was compared against a reference 12-bit

absolute optical encoder with a linearity better

than 0.023%/step. The 360° of mechanical

rotation is represented as 4096 codes

(steps) of the 12-bit encoder and plotted

against the analog output of the NCAPS,

monitored by a digital voltmeter.

From the test results shown in Figures 11

and 12, a linearity of ±1.0% (compared to a

straight line drawn through the two extreme

position end points) is easily achievable

without any fine tuning. The unit is also relatively

forgiving with reference to the alignment

of the three disks. Since the NCAPS

technique is based on the transceiver concept,

with < 1 / 8 in. physical separation

between the transmitter and receiver disks,

most of the transmitted energy will be

received by the receiver.

It should also be kept in mind that signal

processing is based on a single down-conversion

process. This is expressed in Equation

5, whereby a mixer is used to downconvert

the transmitted signal, F c , at the receiver to

IF signals. Unless there is a strong field

applied to the NCAPS at or very close to F c ,

or a strong field that saturates all receiver

channels and no phase relationship is available,

electromagnetic interference (EMI)

and electromagnetic susceptibility will have

a relatively minor effect on the performance.


The authors wish to thank Linet Aghassi for

her help in the preparation of this

manuscript, and Robert K. Hansen, Mitchell

London, and Philip Vuong for their support.




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

Angular Position Sensor (NCAPS) for Motion

Control Applications,” Proc UK-ACC International

Conference on Control 2000, University

of Cambridge, U.K., 2-7 Sept.

7. E.E. Herceg. May 1986. Handbook of

Measurement and Control: An Autoritative

Treatise on the Theory and Application of

LVDTs, Schaevitz Engineering, LCCC #76-


8. J.H. Francis. “PIPS, a New Technology in

13. J. Fraden. 1993. AIP Handbook of Modern

Sensors, American Institute of Physics:296-299.

14. H.M. Greenhouse. 1974. “Design of Planar

Rectangular Microelectronic Inductors,” IEEE

Trans on Parts, Hybrids, and Packaging, Vol.

PHP-10, No. 2:101-109. ■

2. C.D. Todd, P.E. 1975. The Potentiometer

Handbook, McGraw Hill.

3. R.E. Riley. 1989. “High Performance Resistive

Inductive Position Sensing,” Positek Ltd.,

Gloucestershire, U.K. (May be found at

Position Sensors,” SAE Technical Paper 890302. 9. E.H. Putlye. 1960. “The Hall Effect and Dr. Asad M. Madni is President and Chief

Operating Officer, BEI Technologies, Inc.,

4. R.D. Peters. 1989. “Linear Rotary Differential

Capacitance Transducer,” Rev Sci graphs, Hogarth, ed., Butterwort, London. 364-7215, fax 818-362-1836, bei1madni

Related Phenomena,” Semiconductor Mono-

13100 Telfair Ave., Sylmar, CA 91342; 818-

Instru, Vol. 60:2789-2793.

5. J.V. Byrne et al. April 1987. “The Screened

10. “Sprague Hall Effect and Optoelectronic

Sensors.” 1987. Data Book SN-500.

Jim B. Vuong is Senior Staff Engineer, BEI

Inductance Sensor: A New Position and Speed 11. W. Kwiatkowski and S. Tumanski. 1986. Technologies, Inc., 13100 Telfair Ave.,

Sylmar, CA 91342; 818-364-7210, fax 818-

Measurement System,” Proc Motorcon, Hannover,

Vol. 10:220-237.

Properties and Applications,” J Phy E:S. Intrum, Roger F. Wells is Vice President and General

“The Permalloy Magnetoresistive Sensors—


6. J.V. Byrne et al. June 1987. “Linear-Motion

Screened Inductance Sensors,” Proc Conf on

Vol. 19:502-515.

12. P. Pecorari et al. 2000. “Magnetostriction

Manager, Duncan Electronics (a division of

BEI Technologies, Inc.), 15771 Red Hill Ave.,

Applied Motion Control, Minneapolis, in Automotive Position Measurement,” SAE Tustin, CA 92780; 714-247-2531, fax 714-



Technical paper 2000-01-1374.


The Next Generation of

Position Sensing


Part 2: Differential

Displacement and

Linear Capabilities



The Next Generation of

Position Sensing Technology

Part 2: Differential Displacement and Linear Capabilities

The NCAPS noncontact angular position sensor, originally

developed to measure 360° rotary motion, is capable of

determining linear motion as well.

Part 1 of this article, which appeared in the March 2001 issue

of Sensors, examined the underlying theory of NCAPS technology

and explored the details of rotary sensors based on it.

The figures, equations, and references in Part 2 are numbered

consecutively from those in Part 1.

NCAPS as a Differential Displacement Sensor

The never-ending demand for higher efficiency and greater reliability

in automobiles, and the introduction of the modern electric vehicle,

have collectively doomed power-hungry devices such as the power

steering hydraulic pump and the air conditioning compressor. The

best replacement for the pump is at present an electric motor that

directly assists the steering. The problem now lies with reliably sensing

the driver-applied torque so as to know how much assist to add. This

could be accomplished with potentiometers, but the limited life of the

wipers is unacceptable in this critical application. Optical encoders

are another option. While these would work, they are prohibitively

expensive (especially absolute encoders), and reliability concerns discourage

the use of a light source. NCAPS technology can determine

angular displacement and at the same time comply with the very stringent

demands of the automotive and heavy equipment industries.

An NCAPS is placed at each end of a torsion bar, one mounted on

the upper rotor, T, and the other mounted on the lower rotor, P, (see

Figure 13). By electronically taking the difference between the two

analog outputs or by comparing the phase shift of the two PWM signals

and applying the transfer coefficient of torque to degrees, it is possible

to obtain both torque and directional information. Referring to

Figure 13 and the functional block diagram of Figure 14 (page 12),

assume that the first NCAPS has an angular position θ a and the second

an angular position θ b ,with reference to 0°.

Asad M. Madni,

Jim B. Vuong, and

Roger F. Wells,

BEI Technologies, Inc.

Figure 13. NCAPS can be configured as a noncontact differential

angular displacement and absolute position sensor.




Then, in accordance with Equation 8, the

output of the first NCAPS is given by:

IF 1 = 1 / 2 A cos (ω o t – θ a ) (15)

and the output of the second by:

IF 2 = 1 / 2 A cos (ω o t – θ b ) (16)

Taking the difference between these two

outputs yields:

IF = IF 1 – IF 2 = 1 / 2 A [cos (ω o t – θ a )

– cos (ω o t – θ b )] (17)

IF = 1 / 2 A (cos ω o t cos θ a + sin ω o t sin θ a

– cos ω o t cos θ b – sin ω o t sin θ b )

= 1 / 2 A [cos ω o t (cos θ a – cos θ b )

+ sin ω o t (sin θ a – sin θ b )] (18)

Figure 14. This functional block diagram of a noncontact torque and absolute position sensor illustrates

the signal processing technique.


sin = sin θ a – sin θ b


cos = cos θ a – cos θ b

Then (18) becomes:

IF = 1 / 2 A (cos ω o t cos

+ sin ω o t sin ) (19)

= 1 / 2 A cos (ω o t – ) (20)


A cos ω o t = received signal

= tan -1 [(sin θ a – sin θ b )/( cos θ a – cos θ b )]

= torque component

A typical automotive torque sensing application

specifies a nominal 2.5 V output

±2 V at ±8°. A typical NCAPS provides

11 mV/° to satisfy the 360° requirement. To

achieve the required 250 mV/°, a simple

buffer with a gain of ~23 would be needed

for the NCAPS output. This application

also requires absolute position information

over ±2.25 turns of the steering wheel. This

can be satisfied with a third NCAPS, P2,

with a gear reduction mechanism. Referring

to T, P1, and P2 in Figure 13, T is the

torque sensor when compared to P1; P1 is

the fine 0° to ±180° sensor; and P2 is the

gear-reduced 0° to ±810° coarse absolute

position sensor.

A potential obstacle presents itself with

this method of torque sensing. It should be

noted that the T and P sensors are set nominally

at 2.5 V and are therefore step free for

±180°. The difference between their outputs

is used to measure torque. As the steering

wheel turns and the sensor approaches

180°, however, the T sensor will transition

first, so the output torque signal goes from

seeing a difference of a couple of degrees to

seeing a difference of hundreds, and tends

to rail in the direction opposite to the one

that needs assist. A few degrees later, the

other sensor transitions and the measurement

is back to normal accurate determination.

This is, of course, totally unacceptable.

To overcome this limitation, the following

design approach was implemented.

Since each NCAPS generates a 50% duty

cycle signal at the output of its respective

summing amplifier/comparator circuit, with

a phase shift proportional to the respective

coupler position, precise differential angular

information can be generated without the

crossover point concern by comparing these

two signals via a phase comparator (EXLU-

SIVE OR circuit), when the output of T is

phase shifted by 90° as shown in Figure 14.

Under this condition, when the two signals

are in phase (no torque), the output of

the phase comparator is a 50% duty cycle

signal due to one signal’s being shifted 90°

(in this case, T). When a torque is applied

to the shaft, the duty cycle of the signal will

Figure 15. In the presence of an applied torque,

the signal’s duty cycle varies in a manner proportionate

to the lead or lag of the two couplers.

vary in a manner proportionate to the lead

or lag of the two couplers (see Figure 15).

The differential angular displacement range

of a typical drive shaft is ±8° to ±12°, which

implies that signals P and T will never cross

over the 0° ±180° point with respect to each

other. The output can be converted to a fullscale

digital output by using the edge trigger

counting method, or it can provide a full-scale

analog output (in this case, 0–5 VDC) by

using the gain and offset method in an amplifier

circuit. Since the two NCAPS share a

transmitter frequency, F c , a common transmitter

can be used for both couplers and

receivers when the rotor gap is


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 elements

provides additional information.

Mechanical Design of a

Differential Displacement Sensor

To measure steering effort in a torsionally

compliant steering system, several mechanical

construction and space considerations

must be addressed. The first is related to the

physical location of the sensor. There are

two main candidate locations. The first is

inside the passenger compartment and just

under the steering wheel, a position that is

comparatively benign in terms of environment.

Operating temperatures are low and

sealing is necessary only for protection from

dust and occasional liquid spills. Salt spray

and hot fluids found in under-hood applications

need not be considered. Acoustical

noise is an issue, particularly with electrically

contacting sensors, but the NCAPS is

noncontact and generates negligible noise.

The second candidate location, in the

engine compartment as part of the steering

rack mechanism, subjects the sensor to

ambient temperatures often >150°C.

Physical size, particularly the outside diameter

of the sensor, is usually tightly constrained.

Sealing is also crucial because the

sensor must survive the full range of engine

compartment fluids as well as salt spray and

icy fluids from the roadway.

Sensors in either location also have very

low torque-to-turn limitations. At first it

might appear that sensor torque is relatively

unimportant because the large-diameter

steering wheel will easily magnify small

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

steering efforts and overcome any seal friction

in the sensor. But this is not the case.

Steering systems are designed to self-center,

i.e., when the steering wheel is released and

the car is in motion, the driver expects the

wheel to automatically return to the

straight-ahead position. Because of the stepdown

gear ratio between the steering gears

and the steering wheel shaft, the self-centering

torque necessary to overcome the sensor

seal friction will be multiplied by the steering

gear ratio and added to all the gear train

and steering joint friction plus tire-to-road

resistance. The caster angle of the front

wheels can be increased to accommodate

this resistance but at the expense of increasing

the steering effort necessary to maneuver

the car. The maximum allowable torque

resistance for the sensor is typically

70 mN•m (10 ozf•in).

This article details a design for the first

case, but given the versatility of NCAPS,

similar mechanical components can be

assembled for a sensor to meet the requirements

of the second case.

Using limits of torsional compliance similar

to those currently in hydraulic power-assisted

steering systems, an operating range of ±8º is

available for the torque-measuring position of

the sensor. The configuration in Figure 13

requires three sensor elements and a reduction

gear assembly to be packaged in a single

housing with a maximum thickness of 21

mm. Figures 16 and 17 illustrate the arrange-



Figure 19. The Lorentz force illustrated here

describes the force on a charged particle moving in

electrical and magnetic fields as being equal to

the particle’s charge times the sum of the electric

field and the cross product of the particle’s velocity

with the magnetic flux density.

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 allowable

twist that prevents the torsional windup

from exceeding the elastic limit of the

torsion bar. Other components are:

NCAPS Elements. These consist of three

coupler discs and three transmitter-receiver

pairs. Because the torque element of the

sensor uses a common transmitter, there is a

total of eight sensor discs.

Reduction Gears. To provide the absolute

analog position from lock to lock, the

motion of the position coupler is reduced by

a 5:1 ratio gear train.

Self-Centering Coupling. This component

is included to accommodate radial

runout of the steering shaft.

Linear Version of NCAPS

A linear version of the NCAPS technology

(see Figure 18) was developed for use with

linear voice coil actuators to provide built-in

feedback control for motion control applications.

Its basic design and theory of operation

is the same as NCAPS—the transmitter

and the receiver section each contains six

identical loop antenna coils. The total

length of the six antenna coils, L a , determines

the maximum measurable displacement.

The slider section consists of a

tapered pattern (equivalent to the crescent

shape in the NCAPS coupler) equivalent to

L a , except that the pattern is repeated on the

slider so that the transmitter and receiver

are exposed to 360° of the pattern at all

times. The total length of the slider is equal

to the measured displacement, L c , plus L a ,

with the limitation that L c ≤ L a . For a multisection

tapered pattern (for long displacement

measurement), a cycle counter must

be used to identify the revolutions.

The voice coil actuators are direct-drive,

limited-motion devices that use a permanent

magnet field and a coil winding (conductor)

to produce a force proportional to

the current applied to the coil [15]. The

electromechanical conversion mechanism

of a voice coil actuator is governed by the

Lorentz principle, which states that if a current-carrying

conductor is placed in a magnetic

field, a force will act upon it. The

magnitude of this force is determined by the

magnetic flux density, B, the current, I, and

the orientation of the field and current vectors.

Furthermore, if a total of N conductors

(in series) of length L are placed in the magnetic

field, the force acting upon the conductors

is given by:

F= KBLIN (23)


K = a constant

Figure 19 is a simplified illustration of this

physical law.

In its simplest form, a linear voice coil

actuator is a tubular coil of wire situated

within a radially oriented magnetic field

(see Figure 20). The field is produced by

permanent magnets embedded on the

inside diameter of a ferromagnetic cylinder,

arranged such that the magnets facing the

coil all have the same polarity. An inner

core of ferromagnetic material set along the

axial centerline of the coil, joined at one

end to the permanent magnet assembly,

completes the magnetic circuit. The force

generated axially on the coil when current

flows through will produce relative motion

between the field assembly and the coil,

provided the force is large enough to overcome

friction, inertia, and any other forces

from loads attached to the coil. The linear

position sensor is embedded in the actuator

as shown in Figure 20. The slider board is

attached to the coil holder and moves in

accordance with the actuation level,

thereby providing the same function as the

coupler in the angular version. For this

application the maximum measured distance,

L c, was equal to 1 / 3 L a . The electronics

for processing the data from the linear

sensor are identical to the functional block

diagram in Figure 4. Figure 21 is a rear

view of the actuator with the built-in sensor.

This linear position sensor can also be

used to detect differential linear position in

accordance with the equations governing

the angular position measurement. The signal

processing circuitry would be the same

as that in Figure 14.

Future Work

The next phase of development will focus

on advancing the sensor functions, such as

reducing the signal processing electronics to

a mixed signal ASIC as well as incorporating

several interface options. Serial and parallel

data bus interfaces and an RS-232 option

will be provided for most application interfaces,

and a Controller Area Network (CAN)

interface will be provided for automotive

applications. Additionally, further enhancements

to EMI and RFI susceptibility will be



A noncontact angular position sensor with

an inductive attenuating coupler has been

developed for use in motion control applications.

The sensor features a linearity of

better than ±0.5% over 360° of rotation.

The measurement of phase shift, rather

than the magnitude of the coupling signal,

to determine the angular position gives the

design a very high tolerance to mechanical

misalignment of the rotating components

and makes it conducive to mass production.

The analog and digital signal processing

electronics can be readily converted to an

ASIC. The sensor, which does not use any

permanent magnets, LEDs, or photodetectors,

lends itself to the high-volume, lowcost,

and high-reliability requirements of

the automotive, industrial, robotics, medical



Figure 20. A linear voice coil actuator with a built-in noncontact displacement

sensor provides a smart actuator.

Figure 21. This is a rear view of the smart actuator shown in Figure 20.

instrumentation, and aerospace and defense

industries. A linear version of this sensor has

been developed for use with voice coil actuators,

resulting in smart actuators with builtin

feedback control.


The authors wish to thank Linet Aghassi for

her help in the preparation of this

manuscript, and Robert K. Hansen, Mitchell

London, and Philip Vuong for their support.


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

Based Control System For Rifle Stabilization,” Proc

World Automation Congress (WAC ’98), Anchorage,

AK, 10-14 May, TSI Press, PO Box 14126, Albuquerque,

NM 87191:103-112. ■

Dr. Asad M. Madni is President and Chief

Operating Officer, BEI Technologies, Inc.,

13100 Telfair Ave., Sylmar, CA 91342; 818-

364-7215, fax 818-362-1836, bei1madni

Jim B. Vuong is Senior Staff Engineer, BEI

Technologies, Inc., 13100 Telfair Avenue,

Sylmar, CA 91342; 818-364-7210, fax 818-


Roger F. Wells is Vice President and General

Manager, Duncan Electronics (a division of

BEI Technologies, Inc.), 15771 Red Hill Ave.,

Tustin, CA 92780; 714-247-2531, fax 714-


©Reprinted from SENSORS, April 2001 AN ADVANSTAR ★ PUBLICATION

Printed in U.S.A.

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MEMS-Based Optical Mirrors

BEI’s OpticNet Subsidiary is

developing Micro Electro

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optical mirrors that will serve as

the heart of new fiber optic

telecommunications components,

offering new silicon-based solutions

for a host of new products.

Microgryro: A New


Designed as a rate of rotation sensor

utilizing core proprietary processes

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etch, these new chip-based technologies

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on a vibrating mass.

Uniquely Focused. Uniquely Positioned.

When it comes to position sensing and motion control, BEI Technologies has the definitive

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Miniature Integrated GPS/INS System

The C-MIGITS II combines BEI’s

proprietery solid-state Digital

Quartz Inertial Measure- ment

Unit (DQI) with a Global

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receiver. Micromachined

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with a coarse/acquisition (C/A)

Code GPS engine, providing

digital latitude, longitude,

velocity, angle and rate output.

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High Performance Encoder

With A Smart Future

Widely acknowledged as the

standard for industrial encoders,

the Model H25 is used

wherever reliability and

repeatability are critical. High

efficiency optics, EMI shielding,

CE and IP66 ratings are featured in

a standard 2.5" package. Available in

incremental, absolute and serial interface

versions, the H25 is ideal for machine and

process control, web printing, motor

feedback and robotics.

BEI Industrial Encoder Division

Fiber Optic Displacement Sensor Immune


Using noncontact reflective

technology, BEI’s

Linear Gap


Transducer (LGDT)

measures displacements

up to 12mm,

provides accuracy and resolutions to 100nm,

immunity to EMI/RFI, and ratiometric

signals resulting in immunity to variations in input, power and temperature,

target reflectivity and light source intensity.

Scale factors, offset and polarity are adjustable over a wide range.

BEI Precision Systems & Space Division

Applying Intelligence To Sensor And Motion Control Products.

(714) 258-7500

BEI Duncan Electronics


15771 Red Hill Avenue

Tustin, CA 92780

(805) 968-0782

BEI Industrial

Encoder Division

7230 Hollister Avenue

Goleta, CA 93117

(760) 744-5671

BEI Kimco Magnetics


804-A Rancheros Drive

San Marcos, CA 92069

NCAPS : Next Generation

Noncontact Position Sensors

Featuring an inductive attenuating

coupler that measures phase shift, BEI’s

NCAPS offers simple electronics and

absolute position feedback with no

microprocessor on board. Capable of

compact packaging in both angular and

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withstands elevated temperatures

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flexible alignment tolerances.

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Electronics Division

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Pressure Sensors Assure Stability

Designed in a NEMA 4 & 4X all-welded, 316

construction unit for high reliability and high

performance pressure measurements, these

micromachined silicon pressure sensors provide

exceptional stability (long term ±0.15% FSO/year)

and very low noise. Models 6-07 (13mm) and

6-08 (19mm) feature a media isolated diaphragm,

ideal for instrumentation and process controls.

Accuracy is rated at ±0.20% of FSO @ 21°C

(BFSL). Operating temperature range is -40° to

+121°C, with pressure ranges from 5 to 5,000 psi.

BEI Edcliff Instruments Division

(501) 851-4000

BEI Precision

Systems & Space


P.O. Box 3838

Little Rock, AR 72203

Intelligence-Based Controller Optimizes

Direct Drive Actuators

Optimized position, velocity and torque control are

achieved with BEI’s VCA-100 Controller featuring 16-bit

microprocessor architecture, when used with a BEI directdrive

Actuator. The unit offers intelligent control and

amplifier in a slim 1.23" thick case, easy-to-use Windows

compatible set up and program editor. Features include

RS-232/RS-485 serial interface, 10 Amp peak rating, 5 Amp

continuous current at 50VDC, and PWM

output frequency of 18kHz. Sixteen

TTL general

purpose, user

programmable I/Os

enable preemptive



BEI Kimco

Magnetics Division

(818) 362-0300

BEI Edcliff Instruments


13100 Telfair Avenue

Sylmar, CA 91342

(925) 671-6400

BEI Systron Donner

Inertial Division

2700 Systron Drive

Concord, CA 94518

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