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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=18/8/2019 Lecture Pressure Sensor Therm is Tors
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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=18/8/2019 Lecture Pressure Sensor Therm is Tors
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How does voltage correlate to pressureHow does voltage correlate to pressure
Nice its linear!!!Nice its linear!!!
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1
0.204 V
4.794 V
y=ax+bCalibration!
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=18/8/2019 Lecture Pressure Sensor Therm is Tors
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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
1/4
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.
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1
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
http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=18/8/2019 Lecture Pressure Sensor Therm is Tors
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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_pressure8/8/2019 Lecture Pressure Sensor Therm is Tors
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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.pdf8/8/2019 Lecture Pressure Sensor Therm is Tors
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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.PDF8/8/2019 Lecture Pressure Sensor Therm is Tors
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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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