Pressure sensors and thermistors

1. Pressure sensors and thermistors -What do they do and how to calibrate them? E80 Feb 21, 2008

2. Agenda • Pressure sensors and calibration • Relating pressure to altitude • Thermistors and calibration (Steinhart-Hart constants)

3. 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 0-5V Computer LabVIEW Pressure sensors on R-DAS or IMU Voltage Signal conditioning ADC on R-DAS Analog voltage Raw data 0-1024 Environment with varying pressures

4. 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 0-5V Computer LabVIEW Pressure sensors on R-DAS or IMU Voltage Signal conditioning ADC on R-DAS Analog voltage Raw data 0-1024 Environment with varying pressures

5. Pressure sensors-altimeterMPX4115A(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

6. Pressure sensors-MPX4115A • 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) http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1

7. How does voltage correlate to pressureNice it’s linear!!! 4.794 V y=ax+b Calibration! 0.204 V http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1

8. 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 1kΩ, so a unity gain buffer is required for loading. • Low pass filter before ADC. • All power supplies should be bypassed to reduce noises.

9. Measure voltage and pressure in the lab Sensors & signal conditioning • 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. Precision pressure gauge Pressure chamber data R-DAS IMU Laptop LabView Hand pump

10. Calibration curve options If you want to compare with Manufacture specifications Digital reading If you want to use you calibration curve to find pressure in field test Pressure (Psi)

11. In case you care about error. • Voltage Error=Pressure Error x Temperature Error Factor x0.009 x Vs • Temperature Error Factor=1 (0oC-85oC), otherwise higher • Pressure Error: +/- 1.5KPa http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll=1

12. Find a and b in calibration curvey=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

13. Find a and b in calibration curvey=ax+b Believe it or not you can actually do it by hand:

14. How 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 (+15ºC) • 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/s²) Reference: (1976 US standard atmosphere)

15. How to relate pressure to altitude? Plug in all the constants (1) • 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

16. It is finally rocket time! Pressure Voltage Calibration curve Time (second) Time (second) Altitude Equation (1) Time (second)

17. 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

18. 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

19. 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 β 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/ºC). This causes self-heating. (4) Thermal time constant

20. R-T characteristics of thermistor A common 10kOhm NTC thermistor • It is nonlinear!! • Temperature goes up more charges in semiconductor resistance goes down! (NTC)

21. 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.

22. Solve C1, C2 and C3

23. Solve C1, C2 and C3 Matrix inversion Matrix determinant Matrix transpose

24. 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

25. Embed a thermistor in voltage divider Recall BEM Lab #3: Design considerations: • Vout voltage range (signal conditioning in order tointerface with ADC) • Vout sensitivity varies at different temperature range (R-T characteristics curve) Where RT varies with T

26. 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

27. Thermistor signal conditioning circuits Vout nominal at 10k Voltage divider and a unity gain buffer is required!

28. Thermistor on rocket! Voltage Reading Resistance RT Just a voltage divider S-H equation (with calibration constants C1, C2 and C3) Temperature on rocket

29. In summarycalibrate sensors in the lab Measurement circuitry Pressure sensor on rocket Signal conditioning ADC Analog voltage Analog 0-5V Pressures chamber Computer LabVIEW Measurement circuitry Thermistor on rocket Signal conditioning ADC Analog voltage Analog 0-5V Environment with different temperatures