Pressure sensors and thermistors -What do they do and how to calibrate them? E80 Feb 21, 2008 Agenda (1) Pressure sensors and calibration (2) Relating pressure to altitude (3) Thermistors and calibration (Steinhart-Hart constants) Pressure sensors Barometric pressure changes vs. altitude and temperature, so we can use pressure sensor data to indicate the altitude change in the rockets during their launch. Each sensor has slightly different characteristics, so we need to calibrate them individually. Analog voltage Computer LabVIEW Environment with varying pressures Pressure sensors on R-DAS or IMU Signal conditioning Analog 0-5V Raw data 0-1024 ADC on R-DAS Voltage Pressure sensors Barometric pressure changes vs. altitude and temperature, so we can use pressure sensor data to indicate the altitude change in the rockets during their launch. Each sensor has slightly different characteristics, so we need to calibrate them individually. Analog voltage Computer LabVIEW Environment with varying pressures Pressure sensors on R-DAS or IMU Signal conditioning Analog 0-5V Raw data 0-1024 ADC on R-DAS Voltage Pressure sensors-altimeter MPX4115A(IMU) / MPXA6115A (R-DAS) http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1 http://www.eng.hmc.edu/NewE80/PDFs/MPXA6115A.pdf Pressure sensors-MPX4115A http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1 Pressure units Pascal (Pa)=N/m2: standard atmosphere P0=101325 Pa=101.325kPa Bar: 1 bar=100 kPa Psi= (Force) pound per square inch: 1 Psi=6.89465 KPa MPX4115A measures pressure in the range: 15-115 kPa Sensitivity: 45.9mV/kPa (pressure range 100kPa voltage range 4.59V) Typical supply voltage 5.1V Output analog voltage Offset voltage (Voff) is the output voltage measured at minimum rated pressure (Typical@ 0.204V) Full scale output (Vfso) measured at maximum rated pressure (Typical@ 4.794 V) How does voltage correlate to pressure Nice its linear!!! http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1 0.204 V 4.794 V y=ax+b Calibration! Signal Conditioning Circuitry - 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 1k, 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 ADCMPXA4115APressureSensor1234+5V470uF0.01uF1uFbufferMeasure voltage and pressure in the lab After ADC, the digital readings (0-1024)(0-5V) analog voltage Pressure reading is in the units of Psi. Since everything is linearly scaled, you can choose your calibration curve or units freely. Pressure chamber Hand pump Precision pressure gauge R-DAS IMU Laptop LabView data Sensors & signal conditioning Calibration curve options Pressure (Psi) Digital reading kPa 89465 . 6 Psi 1sensor from voltage Analog 51024Digital== 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. http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1 Voltage Error=Pressure Error x Temperature Error Factor x0.009 x Vs Temperature Error Factor=1 (0oC-85oC), otherwise higher Pressure Error: +/- 1.5KPa Find a and b in calibration curve y=ax+b Collect data sets (x1,y1) (x2, y2)(xn, yn), n>2 Best fit (regression or least square) line Excel, Matlab or KlaidaGraph, of course LabView Excel Example Find a and b in calibration curve y=ax+b Believe it or not you can actually do it by hand: nx a ybx x ny x y x naniiniiniiniiniiniinii i|.|

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\|= = == == = =1 121 121 1 1 Intercept SlopeHow does pressure (P) relate to altitude (h)? Assume constant temperature gradient dT/dh, the altitude h is a function of pressure P given by: where h = altitude (above sea level) (Units in feet) P0 = standard atmosphere pressure= 101325Pa T0 = 288.15K (+15C) dT/dh=-0.0065 K/m: thermal gradient or standard temperature lapse rate R = for air 287.052 m2/s2/K g = (9.80665 m/s) ( ) ( )((((

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\| = gRdhdTPPdhdTTh001Reference: (1976 US standard atmosphere) How to relate pressure to altitude? Plug in all the constants ||.|

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\| =1902 . 05kPa 325 . 101kPa) (1 10 4544 . 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! Time (second) Voltage Time (second) Altitude Time (second) Pressure Calibration curve Equation (1) Thermistors Thermistors are widely used for temperature sensing purposes (sensitivity, accuracy, reliability) Thermistors are temperature dependent resistors Most common: Negative-Temperature Coefficient (NTC) thermistors NTC themistors have nonlinear R-T characteristics Steinhart-Hart equation is widely used to model the R-T relationship. More background: http://www.thermometrics.com/assets/images/ntcnotes.pdf Examples: thermistors in your car Air conditioning and seat temperature controls. Electronic fuel injection, in which air-inlet, air/fuel mixture and cooling water temperatures are monitored to help determine the fuel concentration for optimum injection. Warning indicators such as oil and fluid temperatures, oil level and turbo-charger switch off. Fan motor control, based on cooling water temperature Frost sensors, for outside temperature measurement Basic characteristics of thermistors (1) Operating temperature range (2) Zero power resistance of thermistor R=R0expB(1/T-1/T0), T, T0 are ambient temperatures, R, R0 are corresponding resistances and B is the B-constant (or constant ) of the thermistor Or B=ln(R/R0)/(1/T-1/T0) (3) Since thermistor is a resistor, power dissipation P=C(T2-T1), where C is the thermal dissipation constant (mW/C). This causes self-heating. (4) Thermal time constant R-T characteristics of thermistor A common 10kOhm NTC thermistor It is nonlinear!! Temperature goes up more charges in semiconductor resistance goes down! (NTC) Relating T to R: Steinhart-Hart (S-H) Equations 3 term form: 2 term form: T is measured in Kevin. Measure 3 resistances and 3 temperatures, you can solve three unknowns C1, C2 and C3. Matrix inversion (linear algebra) Minimize (least square) error in curve fitting Once C1, C2 and C3 are known, S-H equation (for your sensor) can be used to predict T based on R measurement. 33 2 1) ln( ) ln(1R C R C CT + + =2 2 1 12 1' , ' Note) ln( ' '1C C C CR C CT= = + =Solve C1, C2 and C3 33 2 1) ln( ) ln(1R C R C CT + + =( )( )( )( )( )( )X) solve known, are B (A, ln ln 1ln ln 1ln ln 1ln lnln lnln ln11132133 332 231 133 3 3 2 132 3 2 2 131 3 1 2 1321X B ACCCR RR RR RR C R C CR C R C CR C R C CTTT =((((

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Solve C1, C2 and C3 33 2 1) ln( ) ln(1R C R C CT + + =( )( )( )( )( )( )| | | |jiTij bBbBBX B B A BX B ACCCR RR RR RR C R C CR C R C CR C R C CTTT1 1 where X) solve known, are B (A, ln ln 1ln ln 1ln ln 1ln lnln lnln ln11111 132133 332 231 133 3 3 2 132 3 2 2 131 3 1 2 1321= = = =((((

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Matrix inversion Matrix determinant Matrix transpose Measure thermistor resistance with RT embedded? (1) Voltage divider circuit Relating Vout to RT (2) Wheatstone bridge circuit* Balancing the Bridge circuit Relating Vout to RT Embed a thermistor in voltage divider Design considerations: Vout voltage range (signal conditioning in order to interface with ADC) Vout sensitivity varies at different temperature range (R-T characteristics curve) +VsR1RTVout1R RRV VTTS out+=Recall BEM Lab #3: Where RT varies with T Bridge circuit to embed a thermistor* Design considerations: More sensitive to small changes Vout voltage range (to interface with ADC) Reference: http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317849058268369033Fsect2.PDF ||.|

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\|++=out Sout STToutTTS outV VV VR RR R R RVRRRRR RRR RRV V22 : Then& if0balanced) is (bridge if11 3 23213 2311+VsR1RTVoutR2R3+ -Thermistor signal conditioning circuits REF1951/4AD8606(AD8605)+-10kThermistorTo ADCbuffer+5 V referenceVoltage divider and a unity gain buffer is required! nominal at 10k Vout Thermistor on rocket! Voltage Reading Resistance RT Temperature on rocket S-H equation (with calibration constants C1, C2 and C3) Just a voltage divider In summary calibrate sensors in the lab ADC Analog voltage Computer LabVIEW Pressures chamber Signal conditioning Analog 0-5V Environment with different temperatures ADC Analog voltage Signal conditioning Analog 0-5V Measurement circuitry Thermistor on rocket Measurement circuitry Pressure sensor on rocket