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Pressure sensors and thermistors -What do they do and how to calibrate them? E80 Feb 21, 2008 Agenda (1) (2) (3) Pressure sensors and calibration Relating pressure to altitude 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. Pressure sensors on R-DAS or IMU Voltage Analog Signal conditioning voltage Environment with varying pressures Analog 0-5V ADC on R-DAS Raw data 0-1024 Computer LabVIEW 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. Pressure sensors on R-DAS or IMU Voltage Analog Signal conditioning voltage Environment with varying pressures Analog 0-5V ADC on R-DAS Raw data 0-1024 Computer LabVIEW Pressure sensors-altimeter MPX4115A(IMU) / MPXA6115A (R-DAS) http://www.freescale.com/files/sensors/doc/data_sheet/MPX4115A.pdf?pspll= 1 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 How does voltage correlate to pressure Nice 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= Signal Conditioning Circuitry - From sensor voltage to ADC on R-DAS +5V 0.01uF 1 1uF buffer 2 MPXA4115A Pressure Sensor 3 4 - To ADC + 470uF 1/4 AD8606 (AD8605) • 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. Measure voltage and pressure in the lab Sensors & signal conditioning Precision pressure gauge Hand pump R-DAS IMU data Laptop LabView Pressure chamber 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. Calibration curve options If you want to compare with Manufacture specifications Digital reading Digital 5 Analog voltage from sensor 1024 1 Psi 6.89465 kPa If you want to use you calibration curve to find pressure in field test Pressure (Psi) 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 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: n n n n xi yi xi yi i 1 i 1 Slope a i 1 2 n n 2 n xi xi i 1 i 1 n yi a xi i 1 Intercept b i 1 n n 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: dT R dh P g T0 h 1 dT P dh 0 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) How to relate pressure to altitude? Plug in all the constants 0.1902 P ( kPa) 5 h 1.4544 10 1 101.325kPa • 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! Pressure Voltage Calibration curve Time (second) Altitude Time (second) Equation (1) Time (second) 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 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 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: 1 C1 'C2 ' ln( R) T Note C1 ' C1 , C2 ' C2 T is measured in Kevin. Measure 3 resistances and 3 temperatures, you can solve three unknowns C1, C2 and C3. 1 C1 C2 ln( R) C3 ln( R)3 T 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. Solve C1, C2 and C3 1 C1 C2 ln( R) C3 ln( R)3 T 1 3 T1 C1 C2 ln R1 C3 ln R1 1 ln R1 1 C C ln R C ln R 3 1 ln R 2 2 3 2 2 T2 1 3 1 C1 C2 ln R3 C3 ln R3 1 ln R3 T3 ln R1 3 C1 ln R2 3 C2 ln R3 3 C3 A B X (A, B are known, solve X) Solve C1, C2 and C3 1 C1 C2 ln( R) C3 ln( R)3 T 1 3 T1 C1 C2 ln R1 C3 ln R1 1 ln R1 1 C C ln R C ln R 3 1 ln R 2 2 3 2 2 T2 1 3 1 C1 C2 ln R3 C3 ln R3 1 ln R3 T3 ln R1 3 C1 3 ln R2 C2 ln R3 3 C3 A B X (A, B are known, solve X) B 1 A B 1 B X 1 where B 1 bij B T 1 b ji B 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 Recall BEM Lab #3: Vs R1 Vout RT Vout RT VS RT R1 Where RT varies with T Design considerations: Vout voltage range (signal conditioning in order to interface with ADC) Vout sensitivity varies at different temperature range (R-T characteristics curve) Bridge circuit to embed a thermistor* Vs RT + R1 Vout R2 R3 R1 R3 Vout VS RT R1 R2 R3 R R if T 2 (bridge is balanced) R1 R3 Vout 0 if R2 R3 & R1 RT V 2Vout Then : RT R1 S VS 2Vout Design considerations: More sensitive to small changes Vout voltage range (to interface with ADC) Reference: http://www.analog.com/UploadedFiles/Associated_Docs/324555617048500532024843352497435735317 849058268369033Fsect2.PDF Thermistor signal conditioning circuits buffer REF195 +5 V reference 10k - To ADC Vout + Thermistor nominal at 10k 1/4 AD8606 (AD8605) Voltage divider and a unity gain buffer is required! Thermistor on rocket! Voltage Reading Just a voltage divider Resistance RT S-H equation (with calibration constants C1, C2 and C3) Temperature on rocket In summary calibrate sensors in the lab Pressure sensor on rocket Measurement circuitry Signal Analog Analog voltage conditioning 0-5V ADC Pressures chamber Computer LabVIEW Thermistor on rocket Measurement circuitry Environment with different temperatures Signal Analog Analog voltage conditioning 0-5V ADC