Lecture Pressure Sensor Therm is Tors

8/8/2019 Lecture Pressure Sensor Therm is Tors

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Pressure sensors andPressure sensors and

thermistorsthermistors-What do they do and how to calibrate-What do they do and how to calibrate

them?them?

E80E80

Feb 21, 2008Feb 21, 2008


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AgendaAgenda

(1)(1) Pressure sensors andPressure sensors andcalibrationcalibration

(2)(2) Relating pressure to altitudeRelating pressure to altitude(3)(3)Thermistors and calibrationThermistors and calibration

(Steinhart-Hart constants)(Steinhart-Hart constants)


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Pressure sensorsPressure sensors Barometric pressure changes vs. altitude andBarometric pressure changes vs. altitude and

temperature, so we can use pressure sensortemperature, so we can use pressure sensordata to indicate the altitude change in thedata to indicate the altitude change in therockets during their launch.rockets during their launch.

Each sensor has slightly differentEach sensor has slightly different

characteristics, so we need to calibrate themcharacteristics, so we need to calibrate themindividually.individually.

Analogvoltage

ComputerLabVIEW

Environment with

varying pressures

Pressure sensorson R-DAS or IMU

Signalconditioning

Analog0-5V

Rawdata0-

1024

ADCon R-DAS

Voltage


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Pressure sensorsPressure sensors Barometric pressure changes vs. altitude andBarometric pressure changes vs. altitude and

temperature, so we can use pressure sensortemperature, so we can use pressure sensordata to indicate the altitude change in thedata to indicate the altitude change in therockets during their launch.rockets during their launch.

Each sensor has slightly differentEach sensor has slightly different

characteristics, so we need to calibrate themcharacteristics, so we need to calibrate themindividually.individually.

Analogvoltage

ComputerLabVIEW

Environment with

varying pressures

Pressure sensorson R-DAS or IMU

Signalconditioning

Analog0-5V

Rawdata0-

1024

ADCon R-DAS

Voltage


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Pressure sensors-altimeterPressure sensors-altimeter

MPX4115A(IMU) / MPXA6115A (R-DAS)MPX4115A(IMU) / MPXA6115A (R-DAS)

http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1http://www.eng.hmc.edu/NewE80/PDFs/MPXA6115A.pdf
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1http://www.eng.hmc.edu/NewE80/PDFs/MPXA6115A.pdfhttp://www.eng.hmc.edu/NewE80/PDFs/MPXA6115A.pdfhttp://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1


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Pressure sensors-Pressure sensors-MPX4115AMPX4115A

http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1

Pressure unitsPressure units Pascal (Pa)=N/m2: standard atmosphere P0=101325 Pa=101.325kPa

Bar: 1 bar=100 kPaBar: 1 bar=100 kPa

Psi= (Force) pound per square inch:Psi= (Force) pound per square inch: 1 Psi=6.89465 KPa1 Psi=6.89465 KPa

MPX4115A measures pressure in the range: 15-115 kPaMPX4115A measures pressure in the range: 15-115 kPa Sensitivity: 45.9mV/kPa (Sensitivity: 45.9mV/kPa (pressure range 100kPapressure range 100kPa

voltage range 4.59Vvoltage range 4.59V)) Typical supply voltage 5.1VTypical supply voltage 5.1V Output analog voltageOutput analog voltage

Offset voltage (VOffset voltage (Voffoff) is the output voltage measured at minimum) is the output voltage measured at minimum

rated pressure (rated pressure (Typical@[email protected])) Full scale output (Vfso) measured at maximum rated pressureFull scale output (Vfso) measured at maximum rated pressure

((Typical@[email protected] V4.794 V))
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1


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How does voltage correlate to pressureHow does voltage correlate to pressure

Nice its linear!!!Nice its linear!!!


0.204 V

4.794 V

y=ax+bCalibration!


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Signal Conditioning CircuitrySignal Conditioning Circuitry

- From sensor voltage to ADC on R-DAS- From sensor voltage to ADC on R-DAS

0.2-4.8V (close to 0-5V in ADC), so noscaling/shifting circuitry is added for easy dataprocessing. The input impedance of R-DAS is 1k, so a unitygain buffer is required for loading.

Low pass filter before ADC. All ower su lies should be b assed to reduce

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AD8606

(AD8605)

+

- To ADC

MPXA4115A

Pressure

Sensor

1

2

3

4

+5V

470uF

0.01uF 1uF

buffer


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Measure voltage and pressure in the labMeasure voltage and pressure in the lab

After ADC, the digital readings (0-1024)After ADC, the digital readings (0-1024)(0-(0-5V) analog voltage5V) analog voltage

Pressure reading is in the units of Psi.Pressure reading is in the units of Psi. Since everything is linearly scaled, you canSince everything is linearly scaled, you can

choose your calibration curve or units freely.choose your calibration curve or units freely.

Pressurechamber

Handpump

Precisionpressuregauge R-DAS

IMULaptop

LabView

data

Sensors &

signalconditioning


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Calibration curve optionsCalibration curve options

Pressure (Psi)Digital

rea

ding kPa89465.6Psi1

sensorfromvoltageAnalog51024

Digital

=

=

If you want to compare withManufacture specifications

If you want to use you calibrationcurve to find pressure in field test


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In case you care about error.In case you care about error.


Voltage Error=Pressure Error xVoltage Error=Pressure Error xTemperature Error Factor x0.009 x VsTemperature Error Factor x0.009 x Vs

Temperature Error Factor=1 (0Temperature Error Factor=1 (0ooC-85C-85ooC),C),

otherwise higherotherwise higher Pressure Error: +/- 1.5KPaPressure Error: +/- 1.5KPa


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FindFind aa andand bb in calibration curvein calibration curve

y=y=aax+x+bb Collect data sets (xCollect data sets (x11,y,y11) (x) (x22, y, y22)(x)(xnn, y, ynn), n>2), n>2 Best fit (regression or least square) lineBest fit (regression or least square) line Excel, Matlab or KlaidaGraph, of courseExcel, Matlab or KlaidaGraph, of course

LabViewLabView

Excel Example


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FindFind aa andand bb in calibration curvein calibration curve

y=y=aax+x+bb

Believe it or not you can actually do it byBelieve it or not you can actually do it byhand:hand:

n

xay

b

xxn

yxyxna

n

i

i

n

i

i

n

i

i

n

i

i

n

ii

n

ii

n

iii

=

=

==

==

===

11

2

11

2

111

Intercept

Slope


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How does pressure (P) relate to altitude (h)?How does pressure (P) relate to altitude (h)?

Assume constant temperature gradientAssume constant temperature gradient dT/dhdT/dh, the, the

altitudealtitude hh is a function of pressureis a function of pressure PP given by:given by:

wherewhere hh = altitude (above sea level)= altitude (above sea level) (Units in feet)(Units in feet) PP

00= standard atmosphere pressure= 101325Pa= standard atmosphere pressure= 101325Pa

TT00 = 288.15K (+15= 288.15K (+15C)C) dT/dh=-0.0065 KdT/dh=-0.0065 K/m:/m: thermal gradient or standardthermal gradient or standard

temperature lapse ratetemperature lapse rate RR = for air 287.052 m= for air 287.052 m22/s/s22/K/K gg = (9.80665 m/s)= (9.80665 m/s)

( )

( )

=

g

Rdh

dT

P

P

dhdT

Th

0

0 1

Reference: (1976 US standard atmospherReference: (1976 US standard atmospher


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How to relate pressure to altitude?How to relate pressure to altitude?

Plug in all the constantsPlug in all the constants

=

1902.0

5

kPa325.101

kPa)(

1104544.1

P

h

h is measured in feet.

This equation is calibrated up to 36,090 feet (11,000m).Reference: http://en.wikipedia.org/wiki/Atmospheric_pressureA more general equation can be used to calculate thelationship for different layers of atmosphere

(1)
http://en.wikipedia.org/wiki/Atmospheric_pressurehttp://en.wikipedia.org/wiki/Atmospheric_pressure


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It is finally rocket time!It is finally rocket time!

Time (second)

Voltage

Time (second)

Altitude

Time (second)

PressureCalibration curve

Equation (1)


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ThermistorsThermistors

Thermistors are widely used forThermistors are widely used for

temperature sensing purposes (sensitivity,temperature sensing purposes (sensitivity,accuracy, reliability)accuracy, reliability)

Thermistors are temperature dependentThermistors are temperature dependent

resistorsresistors

Most common: Negative-TemperatureMost common: Negative-Temperature

Coefficient (NTC) thermistorsCoefficient (NTC) thermistors

NTC themistors have nonlinear R-TNTC themistors have nonlinear R-T

characteristicscharacteristics Steinhart-Hart equation is widely used toSteinhart-Hart equation is widely used to

model the R-T relationship.model the R-T relationship.

More background: http://www.thermometrics.com/assets/images/ntcnotes.
http://www.thermometrics.com/assets/images/ntcnotes.pdfhttp://www.thermometrics.com/assets/images/ntcnotes.pdf


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Examples: thermistors in your carExamples: thermistors in your car Air conditioning and seat temperature controls.Air conditioning and seat temperature controls. Electronic fuel injection, in which air-inlet, air/fuelElectronic fuel injection, in which air-inlet, air/fuel

mixture and cooling water temperatures aremixture and cooling water temperatures aremonitored to help determine the fuel concentrationmonitored to help determine the fuel concentrationfor optimum injection.for optimum injection.

Warning indicators such as oil and fluidWarning indicators such as oil and fluidtemperatures, oil level and turbo-charger switch off.temperatures, oil level and turbo-charger switch off. Fan motor control, based on cooling waterFan motor control, based on cooling water

temperaturetemperature Frost sensors, for outside temperature measurementFrost sensors, for outside temperature measurement


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R-T characteristics of thermistorR-T characteristics of thermistor

A common 10kOhm NTC thermistor

It is nonlinear!! Temperature goes up

more charges insemiconductor resistancegoes down! (NTC)


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RelatingRelating TT toto RR::

Steinhart-Hart (S-H) EquationsSteinhart-Hart (S-H) Equations

3 term form:3 term form:

2 term form:2 term form:

T is measured in Kevin.T is measured in Kevin. Measure 3 resistances and 3 temperatures, you canMeasure 3 resistances and 3 temperatures, you can

solve three unknowns Csolve three unknowns C11, C, C22 and Cand C3.3. Matrix inversion (linear algebra)Matrix inversion (linear algebra) Minimize (least square) error in curve fittingMinimize (least square) error in curve fitting

Once COnce C11, C, C22 and Cand C33 are known, S-H equation (are known, S-H equation (for yourfor your

sensorsensor) can be used to predict) can be used to predictTT based onbased on RRmeasurement.measurement.

3

321 )ln()ln(1

RCRCCT ++=

2211

21

','Note

)ln(''1

CCCC

RCCT

+=


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Solve CSolve C11, C, C22 and Cand C33

3

321 )ln()ln(1

RCRCCT ++=

( )

( )( )

( )

( )( )

X)solveknown,areB(A,

lnln1

lnln1

lnln1

lnln

lnln

lnln

1

1

1

3

2

1

3

33

322

3

11

3

33321

323221

3

13121

3

2

1

XBA

C

C

C

RR

RR

RR

RCRCC

RCRCC

RCRCC

T

T

T

=

=

++++

++

=


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Measure thermistor resistanceMeasure thermistor resistance

with Rwith RTT embedded?embedded?

(1) Voltage divider circuit(1) Voltage divider circuit

Relating Vout to RRelating Vout to RTT

(2) Wheatstone bridge circuit*(2) Wheatstone bridge circuit* Balancing the Bridge circuitBalancing the Bridge circuit

Relating Vout to RRelating Vout to RTT


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Embed a thermistor in voltage dividerEmbed a thermistor in voltage divider

Design considerations:Design considerations:

VVoutout voltage range (voltage range (signal conditioning in order tosignal conditioning in order tointerface with ADCinterface with ADC))

VVoutout sensitivity varies at different temperaturesensitivity varies at different temperature

range (R-T characteristics curve)range (R-T characteristics curve)

+Vs

R1

RTVout 1

RR

RVV

T

TSout

+=

Recall BEM Lab #3:

Where RT varies with T


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Bridge circuit to embed a thermistor*Bridge circuit to embed a thermistor*

Design considerations:Design considerations: More sensitive to small changesMore sensitive to small changes VVoutout voltage range (voltage range (to interface with ADCto interface with ADC))

Reference:Reference:http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849

+

==

=

=

+

+

=

outS

outST

T

out

T

T

Sout

VV

VVRR

RRRR

V

R

R

R

RRR

R

RR

RVV

2

2:Then

&if

0

balanced)is(bridgeif

1

132

3

2

1

32

3

1

1

+Vs

R1

RT

Vout

R2

R3

+ -
http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849058268369033Fsect2.PDFhttp://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849058268369033Fsect2.PDFhttp://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849058268369033Fsect2.PDF


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Thermistor on rocket!Thermistor on rocket!

VoltageReading

ResistanceRT

Temperature

on rocket

S-H equation(with calibration constantsC1, C2 and C3)

Just a voltage divider


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Lecture Pressure Sensor Therm is Tors