Cap 0020 Cap Theory

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Lion Precision 563 Shoreview Park Rd. St. Paul, MN 55126 651-484-6544 www.lionprecision.com [email protected] All Rights Reserved

Contents

Capacitance and Distance2

Focusing the Electric Field3

Effects of Target Size3

Range of Measurement3

Multiple Channel Sensing3

Effects of Target Material4

Measuring Non-Conductors4

Maximizing Accuracy5

Target Size5

Target Shape5

Surface Finish5

Parallelism6

Environment6

Factory Calibration7

Denitions8

Sensitivity8

Sensitivity Error8

Offset Error8

Linearity Error8

Error Band9

Bandwidth9Resolution9

TechNoteLIONPRECISION

Capacitive Sensor Operation and Optimization

LT03-0020 February, 2009

Applicable Equipment:Capacitive displacement measurement systems.

Applications: All capacitive measurements.

Summary:This TechNote reviews concepts and theory of capacitive sensing to help inoptimizing capacitive sensor performance. It also denes capacitive sensingterms as used throughout Lion Precision literature and manuals.


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Lion Precision 563 Shoreview Park Rd. St. Paul, MN 55126 651-484-6544 www.lionprecision.com [email protected] All Rights Reserved 2

Capacitance and Distance

Noncontact capacitive sensors work by measuring changes in an electrical erty called capacitance. Capacitance describes how two conductive objectsa space between them respond to a voltage difference applied to them. Wha voltage is applied to the conductors, an electric eld is created between tcausing positive and negative charges to collect on each object (Fig. 1). If polarity of the voltage is reversed, the charges will also reverse.

Capacitive sensors use an alternating voltage which causes the charges to ctinually reverse their positions. Te moving of the charges creates an alternaelectric current which is detected by the sensor (Fig. 2). Te amount of curreow is determined by the capacitance, and the capacitance is determined barea and proximity of the conductive objects. Larger and closer objects caugreater current than smaller and more distant objects. Te capacitance is alsoaffected by the type of nonconductive material in the gap between the obje

echnically speaking, the capacitance is directly propotional to the surfaceof the objects and the dielectric constant of the material between them, andinversely proportional to the distance between them (Fig. 3).

In typical capacitive sensing applications, the probe or sensor is one of the ductive objects; the target object is the other. (Using capacitive sensors to splastics and other insulators is discussed in the nonconductive targets sectiTe sizes of the sensor and the target are assumed to be constant as is the marial between them. Terefore, any change in capacitance is a result of a chanin the distance between the probe and the target. Te electronics are calibratto generate specic voltage changes for corresponding changes in capacitaTese voltages are scaled to represent specic changes in distance. Te amouof voltage change for a given amount of distance change is called the sensi A common sensitivity setting is 1.0V/100m. Tat means that for every 100change in distance, the output voltage changes exactly 1.0V. With this calibtion, a +2V change in the output means that the target has moved 200m cto the probe.The Farad

Capacitance is measured in Farads,named after Michael Faraday who didpioneering experiments in electricityand magnetism in the middle 1800s.

A Farad is a rather large unit. Most

capacitors in electronic circuitry aremeasured in microfarads (F, 10 -6).The capacitance changes sensedby a capacitive sensor are around 1femtofarad (fF, 10-15).

Figure 3

Capacitance is determined by Area, Distance, and Dielectric (the material between the conductors).

Capacitance increases when Area or Dielectric increase, and capacitance decreases when the Distance increases.

Figure 1

Applying a voltage to conductive objects causes posi-tive and negative charges to collect on each object.This creates an electric eld in the space between

the objects.

Figure 2

Applying an alternating voltage causes the charges to move back and forth between the objects, creating an

alternating current which is detected by the sensor.

Area x DielectricDistance

+


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Focusing the Electric Field

When a voltage is applied to a conductor, the electric eld eminates from esurface. In a capacitive sensor, the sensing voltage is applied to the Sensingof the probe (Figs. 4, 5). For accurate measurements, the electric eld fromsensing area needs to be contained within the space between the probe andtarget. If the electric eld is allowed to spread to other items or other areasthe target then a change in the position of the other item will be measured achange in the position of the target. A technique called guarding is used tovent this from happening. o create a guard, the back and sides of the sensiarea are surrounded by another conductor that is kept at the same voltage asensing area itself (Fig. 4, 6). When the voltage is applied to the sensing aseparate circuit applies the exact same voltage to the guard. Because there difference in voltage between the sensing area and the guard, there is no eleld between them. Any other conductors beside or behind the probe formelectric eld with the guard instead of the sensing area. Only the unguardefront of the sensing area is allowed to form an electric eld with the target.

Effects of Target SizeTe target size is a primary consideration when selecting a probe for a speciapplication. When the sensing electric eld is focused by guarding, it creatslightly conical eld that is a projection of the sensing area. Te minimum tdiameter for standard calibration is 30% of the diameter of the sensing areafurther the probe is from the target, the larger the minimum target size.

Range of Measurement

Te range in which a probe is useful is a function of the size of the sensing a

Te greater the area, the larger the range. Te driver electronics are designed a certain amount of capacitance at the probe. Terefore, a smaller probe musconsiderably closer to the target to achieve the desired amount of capacitanTe electronics are adjustable during calibration but there is a limit to the raof adjustment.

In general, the maximum gap at which a probe is useful is approximately 4of the sensing area diameter. Standard calibrations usually keep the gap conerably less than that.

Multiple Channel Sensing

Frequently, a target is measured simultaneously by multiple probes. Becausystem measures a changing electric eld, the excitation voltage for each pmust be synchronized or the probes would interfere with each other. If they were not synchronized, one probe would be trying to increase the electric while another was trying to decrease it thereby giving a false reading.

Driver electronics can be congured as masters or slaves. Te master sets th

Figure 4

Capacitive sensor probe components

Figure 5

Cutaway view showing an unguarded sensing areaelectric eld

Figure 6

Cutaway showing the guard eld shaping the sensing area electric eld

SensingArea

Body

Guard

SensingArea

Guard

The sensing electric eld covers an areaabout 30% larger than the sensing areaof the probe.

In general, the maximum gap at which aprobe is useful is approximately 40% ofthe sensor diameter. Standard calibra-tions usually keep the gap considerablyless than that.

Using multiple probes on the same tar-get requires that the excitation voltagesbe synchronized. This is accomplishedby conguring one driver as a masterand others as slaves.


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synchronization for the slaves in multiple channel systems.

Effects of Target Material

Te sensing electric eld is seeking a conductive surface. Provided that the is a conductor, capacitive sensors are not aeffected by the specic target mBecause the sensing electric eld stops at the surface of the conductor, targthickness does not affect the measurement.

Measuring Non-ConductorsCapacitive sensors are most often used to measure the change in position oa conductive target. But capacitive sensors can be very effective in measurpresence, density, thickness, and location of non-conductors as well. Non-cductive materials like plastic have a different dielectric constant than air. Telectric constant determines how a non-conductive material affects capacitbetween two conductors. When a non-conductor is inserted between the prand a stationary reference target, the sensing eld passes through the materto the grounded target (Fig. 7). Te preseence of the non-conductive materia

changes the dielectric and therefore changes the capacitance. Te capacitanc will change in relationship to the thickness or density of the material.

It is not always feasible to have a reference target in front of the probe. Oftmeasurements can still be made by a technique called fringing. If there is nconductive reference directly in front of the probe, the sensing electric eld will wrap back to the body of the probe itself. Tis is called a fringe eld. Ifnon-conductive material is brought in proximity to the probe, its dielectric change the fringe eld; this can be used to sense the non-conductive mater

Te sensitivity of the sensor to the non-conductive target is directly proporti

al to the dielectric constant of the material. Te table below lists the dielectrconstant of some common non-conductive materials.

Capacitive sensors measure all conduc-tors: brass, steel, aluminum, or even

salt-water, as the same.

Figure 7

Non-conductors can be measured by passing theelectric eld through them to a stationary conductive

target behind

Figure 8

Without a conductive target behind, a fringe eld can form through a nearby non-conductor allowing the

non-conductor to be sensed

Material Dielectric ConstantRelative ( r)

Vacuum 1.0

Air 1.0006

Epoxy 2.5-6.0

PVC 2.8-3.1

Glass 3.7-10.0

Water 80.0


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symmetry of the surface irregularities.

Parallelism

During calibration the surface of the sensor is parallel to the target surfacethe probe or target is tilted any signicant amount, the shape of the spot whthe eld hits the target elongates and changes the interaction of the eld withe target (Fig. 12). Because of the different behavior of the electric eld, m

surement errors will be introduced. At very high resolutions, even a few decan introduce error. Parallelism must be considered when designing a xtuthe measurement.

Environment

Lion Precision capacitive sensors are compensated to minimize drift due totemperature from 22C - 35C (72F - 95F). In this temperature range erroare less than 0.5% of full scale.

A more troublesome problem is that virtually all target and xture materialhibit a signicant expansion and contraction over this temperature range. W

this happens, the changes in the measurement are not gauge error. Tey are rchanges in the gap between the target and the probe. Careful xture designa long way toward maximizing accuracy.

Te dielectric constant of air is affected by humidity. As humidity increasesdielectric increases. Humidity can also interact with probe construction maals. Experimental data shows that changes from 50%RH to 80%RH can caerrors up to 0.5% of full scale.

While Lion Precision probe materials are selected to minimize these errorsapplications requiring utmost precision, control of temperature and humidi

is standard practice. International standards specify that measurements shadone at 20C or corrected to true length at 20C.

More temperature related errors aredue to expansion and contraction ofthe measurement xture than probe orelectronics drift.

Figure 12

Lack of parallelism will introduce errors


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Factory Calibration

Lion Precisions calibration system was designed in cooperation with Profeal Instruments, a world leader in air bearing spindle and slide design. Its stthe art design is driven by precision motion control electronics with positioaccuracies of less than 0.012m uncertainty.

Te calibration system is certied on a regular basis with a NIS traceable l

interferometer. Te measurement equipment used during calibration (digitalmeters and signal generators) are also calibrated to NIS traceable standarTe calibration information for each of these pieces of equipment is kept onfor verication of traceability.

echnicians use the calibration system to precisely position a calibration taat known gaps to the probe. Te measurements at these points are collected the sensitivity and linearity are analyzed by the calibration system. Te analof the data is used to adjust the system being calibrated to meet order spections.

After sensitivity and linearity are calibrated, the systems are placed in an enronmental chamber where the temperature compensation circuitry is calibrto minimize drift over the temperature range of 22C to 35C. Measuremenare also taken of bandwidth and output noise which effect resolution.

When calibration is complete, a calibration certicate is generated. Tis certcate is shipped with the ordered system and archived. Calibration certicatconform to section 4.8 of ISO 10012-1.

ProbeModel: C13-M

ProbeSerial: 040131-17

Channel: 0

DriverModel: DMT20

DriverSerial: 040086-01

Bandwidth(-3dB): 1000HzSensitivity Switch: NA

Output Sensitivity:

CalibrationNumber:2574

CustomerID: 1066 OrderID: 46939B

Calibration Report

CalibrationDate: 2/19/04 CalibrationDue Date:2/18/05

0.025

Range:

Standoff(range center):

800

1100

10 to -10 VDC

m

Output Voltage:

V/ m

Target:

SystemComponents CalibrationParameters

See definition of terms on the back of this sheet

TARGET

Standoff

RangeCenter

RangeTARGET m

m

G ap to St and of f O ut pu t O utp ut co nve rt ed to

-350.000

Error

mVolts

9.970

-349.577

1.195

-300.000

-250.000

8.739

6.253

-300.002

-250.117

-0.002

-0.117

-400.000 -398.805

0.423

7.500

-200.000 5.000 -199.999 0.001

3.747 -149.889 0.111

2.499 -99.962 0.038

1.250 -50.001 -0.001

0.0 0.000 0.000 0.000

-1.250 49.984 -0.016

-2.500 100.006 0.006

-3.753 150.105 0.105

-5.000 199.990 -0.010

-6.240 249.616 -0.384

-7.498 299.940 -0.060

-8.761 350.438 0.438

400.000 -9.998 399.914 -0.086

Meter ID:128 MechanicalCalibrator ID:88 FunctionGenerator ID:129Thermometer ID: 140 Barometer ID: 145 Hydrometer ID: 140

Temperature: 22.1 C Pressure: 729.7 mmHg Humidity: 13.9% RHCombineduncertainty ofcalibration:Environmental Conditions:Environmental Conditions Measurement IDs:Calibration Equipment IDs:

T014-6360

0 .1 1% ( Sp ec : 1% )Error Band: (Spec: 0.3%)

Peak to Peak Resolution: (Spec: 190 nm)RMSResolution:

Linearity Error:0.15%

nmnm

GaptoTarget

700.000

750.000

800.000

850.000

900.000

950.000

1000.000

1050.000

1100.000

1150.000

1200.000

1250.000

1300.000

1350.000

1400.000

1450.000

1500.000

m m

700.00 -400.00

750.00

800.00

850.00

900.00

950.00

1000.00

1050.00

1100.00

1150.00

1200.00

1250.00

1300.00

1350.00

1400.00

1450.00

1500.00

-50.000

-100.000

-150.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

-350.00

-300.00

-250.00

-200.00

-150.00

-100.00

-50.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

denotes out of spec condition*

12.9 in plus 0.5 in/in of range

Bandwid th: ( -3dB) : 1110Hz

72.03.2

Calibration Procedure ID:

(Spec: 30 nm)

AllLionPrecisioncalibrationsareNIST traceable.

Detailedtraceabilityinformationavailableupon request.LionPrecision 563ShoreviewParkRoad Shoreview,MN 55126 USAPhone:(651)484-6544 Fax:(651)484-6824 [email protected]

Thiscertificateconformsto ISO10012-1,Section 4.8

Technician: Skip Buckmiller

NIST traceable calibration certicate


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Denitions

Sensitivity

Sensitivity indicates how much the output voltage changes as a result of achange in the gap between the target and the probe. A common sensitivity 1V/0.1mm. Tis means that for every 0.1mm of change in the gap, the outpuvoltage will change 1V. When the output voltage is plotted against the gap

the slope of the line is the sensitivity.Sensitivity Error

A systems sensitivity is set during calibration. When sensitivity deviates frthe ideal value this is called sensitivity error, gain error, or scaling error. Sisensitivity is the slope of a line, sensitivity error is usually presented as a page of slope; comparing the ideal slope with the actual slope.

Offset Error

Offset error occurs when a constant value is added to the output voltage of

system. Capacitive gauging systems are usually zeroed during setup, eliming any offset deviations from the original calibration. However, should theoffset error change after the system is zeroed, error will be introduced into measurement. emperature change is the primary factor in offset error. LioPrecision systems are compensated for temperature related offset errors to them less than 0.04%F.S./C.

Linearity Error

Sensitivity can vary slightly between any two points of data. Te accumulateffect of this variation is called linearity error. Te linearity specication is t

measurement of how far the output varies from a straight line.o calculate the linearity error, calibration data is compared to the straight

that would best t the points. Tis straight reference line is calculated from calibration data using a technique called least squares tting. Te amount oferror at the point on the calibration line that is furthest away from this ideais the linearity error. Linearity error is usually expressed in terms of percenfull scale. If the error at the worst point was 0.001mm and the full scale ranthe calibration was 1mm, the linearity error would be 0.1%.

Note that linearity error does not account for errors in sensitivity. It is only

measure of the straightness of the line and not the slope of the line. A syste with gross sensitivity errors can be very linear.

0.50 0.75 1.00

Ideal

Actual

1.25 1.50-10

-5

0

5

10

Gap in mm

O u t p u t

V o

l t a g e

Sensitivity - The slope of the line is thesensitivity; in this case 1V/0.05mm.

Ideal

Actual

-10

-5

0

5

10

O u t p u t

V o

l t a g e

0.50 0.75 1.00 1.25 1.50

Gap in mm

Sensitivity Error - The slope of the actualmeasurements deviates from the idealslope.

Ideal

Actual

-10

-5

0

5

10

O u t p u t

V o

l t a g e

0.50 0.75 1.00 1.25 1.50

Gap in mm

Offset Error - A constant value is added toall measurements.

Ideal

Actual

-10

-5

0

5

10

O u t p u t

V o

l t a g e

0.50 0.75 1.00 1.25 1.50

Gap in mm

Linearity Error - Measurement data is noton a straight line.


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Error Band

Error band accounts for the combination of linearity and sensitivity errors.is the measurement of the worst case absolute error in the calibrated range.error band is calculated by comparing the output voltages at specic gaps ttheir expected value. Te worst case error from this comparison is listed as tsystems error band (Fig. 13).

BandwidthBandwidth is dened as the frequency at which the output falls to -3dB. Tifrequency is also called the cutoff frequency. A -3dB drop in the signal levequates to approximately 70% drop in actual output voltage. With a 15kHzbandwidth, a change of 1V at low frequency will only produce a 0.7V cat 15kHz.

In addition to sensing high-frequency motion, fast responding outputs maxmize phase margin when used in servo-control feedback systems. Some drprovide selectable bandwidth for maximizing either resolution or response

Resolution

Resolution is dened as the smallest reliable measurement that a system camake. Te resolution of a measurement system must be better than the nalaccuracy the measurement requires. If you need to know a measurement w0.02m, then the resolution of the measurement system must be better than0.02m.

Te primary determining factor of resolution is electrical noise. Electrical noappears in the output voltage causing small instantaneous errors in the outpEven when the probe/target gap is perfectly constant, the output voltage ofdriver has some small but measurable amount of noise that would seem to dicate that the gap is changing. Tis noise is inherent in electronic componeand can only be minimized, but never eliminated.

If a driver has an output noise of 0.002V with a sensitivity of 10V/1mm, thit has an output noise of 0.000,2mm (0.2m). Tis means that at any instanttime, the output could have an error of 0.2m.

Te amount of noise in the output is directly related to bandwidth. Generallyspeaking, noise is distributed uniformly over a wide range of frequencies. Ithe higher frequencies are ltered before the output, the result is less noise better resolution (Figs. 14, 15). When examining resolution specications, critical to know at what bandwidth the specications apply.

Gap(mm)

ExpectedValue(VDC)

ActualValue(VDC)

Error(mm)

0.50 -10.000 -9.800 -0.010

0.75 -5.000 -4.900 -0.005

1.00 0.000 0.000 0.000

1.25 5.000 5.000 0.000

1.50 10.000 10.100 0.005

Fast responding outputs maximizephase margin when used in servo-control feedback systems.

Figure 13

Error band is the worst case error in the calibrated range. In this case, the Error Band is 0.01.

Figure 14

Noise from a 15kHz sensor

Figure 15

Noise from a 100Hz sensor

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Cap 0020 Cap Theory