Pressure sensors and Pressure sensors and thermistorsthermistors

-What do they do and how to calibrate -What do they do and how to calibrate them?them?

E80E80Feb 21, 2008Feb 21, 2008

AgendaAgenda

(1)(1) Pressure sensors and Pressure sensors and calibrationcalibration

(2)(2) Relating pressure to altitudeRelating pressure to altitude

(3)(3) Thermistors and calibration Thermistors and calibration (Steinhart-Hart constants)(Steinhart-Hart constants)

Pressure sensorsPressure sensors Barometric pressure changes vs. Barometric pressure changes vs.

altitude and temperature, so we can altitude and temperature, so we can use pressure sensor data to indicate use pressure sensor data to indicate the altitude change in the rockets the altitude change in the rockets during their launch.during their launch.

Each sensor has slightly different Each sensor has slightly different characteristics, so we need to characteristics, so we need to calibrate them individually.calibrate them individually.

Analogvoltage

ComputerLabVIEW

Environment with varying pressures

Pressure sensorson R-DAS or IMU

Signalconditioning

Analog0-5V

Raw data0-1024

ADCon R-DAS

Voltage

Pressure sensorsPressure sensors Barometric pressure changes vs. Barometric pressure changes vs.

altitude and temperature, so we can altitude and temperature, so we can use pressure sensor data to indicate use pressure sensor data to indicate the altitude change in the rockets the altitude change in the rockets during their launch.during their launch.

Each sensor has slightly different Each sensor has slightly different characteristics, so we need to characteristics, so we need to calibrate them individually.calibrate them individually.

Analogvoltage

ComputerLabVIEW

Environment with varying pressures

Pressure sensorson R-DAS or IMU

Signalconditioning

Analog0-5V

Raw data0-1024

ADCon R-DAS

Voltage

Pressure sensors-altimeterPressure sensors-altimeterMPX4115A(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

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 MPX4115A measures pressure in the range: 15-115 kPakPa

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 ) is the output voltage measured at minimum rated pressure (minimum rated pressure (Typical@Typical@ 0.204V0.204V))

Full scale output (Vfso) measured at maximum rated Full scale output (Vfso) measured at maximum rated pressure (pressure (Typical@Typical@ 4.794 V4.794 V))

How does voltage correlate to pressureHow does voltage correlate to pressureNice it’s linear!!!Nice it’s linear!!!

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

0.204 V

4.794 V

y=ax+bCalibration!

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 no scaling/shifting circuitry is added for easy data processing.• The input impedance of R-DAS is 1kΩ, so a unity gain buffer is required for loading.• Low pass filter before ADC.• All power supplies should be bypassed to reduce noises.

1/4AD8606

(AD8605)

+

-To ADC

MPXA4115APressureSensor

1

2

3

4

+5V

470uF

0.01uF 1uF

buffer

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 can Since everything is linearly scaled, you can

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

Pressure chamber

Handpump

Precisionpressure gauge R-DAS

IMULaptop

LabView

data

Sensors &signal conditioning

Calibration curve options Calibration curve options

Pressure (Psi)

Dig

ital re

ad

ing kPa 89465.6Psi 1

sensor from voltageAnalog51024

Digital

If you want to compare with Manufacture specifications

If you want to use you calibration curve to find pressure in field test

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 x Voltage Error=Pressure Error x Temperature Error Factor x0.009 x VsTemperature Error Factor x0.009 x Vs

Temperature Error Factor=1 (0Temperature Error Factor=1 (0ooC-C-8585ooC), otherwise higherC), otherwise higher

Pressure Error: +/- 1.5KPaPressure Error: +/- 1.5KPa

Find Find aa and and bb in calibration curve in calibration curvey=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 course Excel, Matlab or KlaidaGraph, of course

LabView……LabView……

Excel Example

Find Find aa and and bb in calibration curve in calibration curvey=y=aax+x+bb

Believe it or not you can actually do it by Believe it or not you can actually do it by hand:hand:

n

xay

b

xxn

yxyxn

a

n

ii

n

ii

n

ii

n

ii

n

ii

n

ii

n

iii

11

2

11

2

111

Intercept

Slope

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

Assume constant temperature gradient Assume constant temperature gradient dT/dhdT/dh, the , the altitude altitude hh is a function of pressure is a function of pressure P P given by:given by:

wherewhere hh = altitude (above sea level) = altitude (above sea level) (Units in feet)(Units in feet) PP00 = standard atmosphere pressure= 101325Pa = standard atmosphere pressure= 101325Pa TT00 = 288.15K (+15 = 288.15K (+15ºC)ºC) dT/dh=-0.0065 KdT/dh=-0.0065 K/m: /m: thermal gradient or standard thermal gradient or standard

temperature lapse rate temperature lapse rate RR = for air 287.052 m = for air 287.052 m22/s/s22/K /K gg = (9.80665 m/s²) = (9.80665 m/s²)

g

RdhdT

P

P

dhdTT

h0

0 1

Reference: (1976 US standard atmosphere)Reference: (1976 US standard atmosphere)

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

Plug in all the constantsPlug in all the constants

1902.05

kPa325.101

kPa)(1104544.1

Ph

• h is measured in feet. • This equation is calibrated up to 36,090 feet (11,000m).• Reference: http://en.wikipedia.org/wiki/Atmospheric_pressure• A more general equation can be used to calculate the relationship for different layers of atmosphere

(1)

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

Time (second)

Voltage

Time (second)

Altitude

Time (second)

PressureCalibration curve

Equation (1)

ThermistorsThermistors Thermistors are widely used for Thermistors are widely used for

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

Thermistors are temperature dependent Thermistors are temperature dependent resistorsresistors

Most common: Negative-Temperature Most common: Negative-Temperature Coefficient (NTC) thermistors Coefficient (NTC) thermistors

NTC themistors have nonlinear R-T NTC themistors have nonlinear R-T characteristicscharacteristics

Steinhart-Hart equation is widely used to Steinhart-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.pdf

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

air/fuel mixture and cooling water temperatures air/fuel mixture and cooling water temperatures are monitored to help determine the fuel are monitored to help determine the fuel concentration for optimum injection. concentration for optimum injection.

Warning indicators such as oil and fluid Warning indicators such as oil and fluid temperatures, oil level and turbo-charger switch temperatures, oil level and turbo-charger switch off. off.

Fan motor control, based on cooling water Fan motor control, based on cooling water temperature temperature

Frost sensors, for outside temperature Frost sensors, for outside temperature measurement measurement

Basic characteristics of thermistorsBasic characteristics of thermistors(1) Operating temperature range(1) Operating temperature range(2) Zero power resistance of thermistor(2) Zero power resistance of thermistor

R=RR=R00expB(1/T-1/TexpB(1/T-1/T00), T, T), T, T00 are ambient are ambient temperatures, R, Rtemperatures, R, R00 are corresponding are corresponding resistances and B is the resistances and B is the B-constant (or B-constant (or ββ constant )constant ) of the thermistor of the thermistor

Or B=ln(R/ROr B=ln(R/R00)/(1/T-1/T)/(1/T-1/T00))(3) Since thermistor is a resistor, power (3) Since thermistor is a resistor, power

dissipationdissipation

P=C(TP=C(T22-T-T11), where ), where C is the thermal dissipation C is the thermal dissipation constantconstant (mW/ (mW/ººC). This causes self-heating.C). This causes self-heating.

(4) Thermal (4) Thermal time constanttime constant

R-T characteristics of thermistorR-T characteristics of thermistor

A common 10kOhm NTC thermistor

• It is nonlinear!!• Temperature goes up more charges in semiconductor resistance goes down! (NTC)

Relating Relating TT to to 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 Measure 3 resistances and 3 temperatures, you

can solve three unknowns Ccan solve three unknowns C11, C, C22 and C and 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 C and C3 3 are known, S-H equation (are known, S-H equation (for for your sensoryour sensor) can be used to predict ) can be used to predict TT based on based on RR measurement.measurement.

3321 )ln()ln(

1RCRCC

T

2211

21

',' Note

)ln(''1

CCCC

RCCT

Solve CSolve C11, C, C22 and C and C33

3321 )ln()ln(

1RCRCC

T

X) solve known, are B (A,

lnln1

lnln1

lnln1

lnln

lnln

lnln

1

1

1

3

2

1

333

322

311

333321

323221

313121

3

2

1

XBA

C

C

C

RR

RR

RR

RCRCC

RCRCC

RCRCC

T

T

T

Solve CSolve C11, C, C22 and C and C33

3321 )ln()ln(

1RCRCC

T

jiTij b

Bb

BB

XBBAB

XBA

C

C

C

RR

RR

RR

RCRCC

RCRCC

RCRCC

T

T

T

11 where

X) solve known, are B (A,

lnln1

lnln1

lnln1

lnln

lnln

lnln

1

1

1

1

11

3

2

1

333

322

311

333321

323221

313121

3

2

1

Matrix inversionMatrix determinantMatrix transpose

Measure thermistor resistance Measure thermistor resistance with R with RT T 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

Embed a thermistor in voltage dividerEmbed a thermistor in voltage divider

Design considerations:Design considerations: VVout out voltage range (voltage range (signal conditioning in signal conditioning in

order toorder to interface with ADCinterface with ADC)) VVoutout sensitivity varies at different temperature sensitivity varies at different temperature

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

Vs

R1

RT Vout 1RR

RVV

T

TSout

Recall BEM Lab #3:

Where RT varies with T

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 VVout out voltage range (voltage range (to interface with ADCto interface with ADC))Reference:Reference:

http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849058268369033Fsect2.PDF735317849058268369033Fsect2.PDF

outS

outST

T

out

T

TSout

VV

VVRR

RRRR

V

R

R

R

R

RR

R

RR

RVV

2

2 :Then

& if

0

balanced) is (bridge if

1

132

3

2

1

32

3

1

1

Vs

R1

RT

Vout

R2

R3

+ -

Thermistor signal conditioning circuits Thermistor signal conditioning circuits

REF195

1/4AD8606

(AD8605)

+

-10k

Thermistor

To ADC

buffer

+5 V reference

Voltage divider and a unity gain buffer is required!

nominal at 10k

Vout

Thermistor on rocket!Thermistor on rocket!

Voltage Reading

Resistance RT

Temperatureon rocket

S-H equation(with calibration constants C1, C2 and C3)

Just a voltage divider

In summaryIn summarycalibrate sensors in the lab calibrate sensors in the lab

ADCAnalogvoltage

ComputerLabVIEW

Pressures chamber

Signalconditioning

Analog0-5V

Environment with different temperatures

ADCAnalogvoltage

Signalconditioning

Analog0-5V

Measurementcircuitry

Thermistoron rocket

Measurementcircuitry

Pressure sensoron rocket