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. 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. 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 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. 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. 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 ADC on R-DAS Voltage

Pressure sensors-altimeter MPX4115A(IMU) / MPXA6115A (R-DAS) 1

Pressure sensors- MPX4115A 1 Pressure units Pressure units Pascal (Pa)=N/m 2 : standard atmosphere P 0 = Pa= kPa Bar: 1 bar=100 kPa Bar: 1 bar=100 kPa Psi= (Force) pound per square inch: 1 Psi= KPa Psi= (Force) pound per square inch: 1 Psi= KPa MPX4115A measures pressure in the range: kPa MPX4115A measures pressure in the range: kPa Sensitivity: 45.9mV/kPa (pressure range 100kPa  voltage range 4.59V) Sensitivity: 45.9mV/kPa (pressure range 100kPa  voltage range 4.59V) Typical supply voltage 5.1V Typical supply voltage 5.1V Output analog voltage Output analog voltage Offset voltage (V off ) is the output voltage measured at minimum rated pressure 0.204V) Offset voltage (V off ) is the output voltage measured at minimum rated pressure 0.204V) Full scale output (Vfso) measured at maximum rated pressure V) Full scale output (Vfso) measured at maximum rated pressure V)

How does voltage correlate to pressure Nice it’s linear!!! V V y=ax+b Calibration!

Signal Conditioning Circuitry - From sensor voltage to ADC on R-DAS V (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 Measure voltage and pressure in the lab After ADC, the digital readings (0-1024)  (0-5V) analog voltage After ADC, the digital readings (0-1024)  (0-5V) 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 choose your calibration curve or units freely. 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 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. 1 Voltage Error=Pressure Error x Temperature Error Factor x0.009 x Vs Voltage Error=Pressure Error x Temperature Error Factor x0.009 x Vs Temperature Error Factor=1 (0 o C-85 o C), otherwise higher Temperature Error Factor=1 (0 o C-85 o C), otherwise higher Pressure Error: +/- 1.5KPa Pressure Error: +/- 1.5KPa

Find a and b in calibration curve y=ax+b Collect data sets (x 1,y 1 ) (x 2, y 2 )……(x n, y n ), n>2 Collect data sets (x 1,y 1 ) (x 2, y 2 )……(x n, y n ), n>2 Best fit (regression or least square) line Best fit (regression or least square) line Excel, Matlab or KlaidaGraph, of course LabView…… 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:

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) h = altitude (above sea level) (Units in feet) P 0 = standard atmosphere pressure= Pa P 0 = standard atmosphere pressure= Pa T 0 = K (+15ºC) T 0 = K (+15ºC) dT/dh= K/m: thermal gradient or standard temperature lapse rate dT/dh= K/m: thermal gradient or standard temperature lapse rate R = for air m 2 /s 2 /K R = for air m 2 /s 2 /K g = ( m/s²) g = ( m/s²) Reference: (1976 US standard atmosphere)

How to relate pressure to altitude? Plug in all the constants h is measured in feet. This equation is calibrated up to 36,090 feet (11,000m). Reference: 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 widely used for temperature sensing purposes (sensitivity, accuracy, reliability) Thermistors are temperature dependent resistors Thermistors are temperature dependent resistors Most common: Negative-Temperature Coefficient (NTC) thermistors Most common: Negative-Temperature Coefficient (NTC) thermistors NTC themistors have nonlinear R-T characteristics NTC themistors have nonlinear R-T characteristics Steinhart-Hart equation is widely used to model the R-T relationship. Steinhart-Hart equation is widely used to model the R-T relationship. More background:

Examples: thermistors in your car Air conditioning and seat temperature controls. 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. 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. Warning indicators such as oil and fluid temperatures, oil level and turbo-charger switch off. Fan motor control, based on cooling water temperature Fan motor control, based on cooling water temperature Frost sensors, for outside temperature measurement Frost sensors, for outside temperature measurement

Basic characteristics of thermistors (1) Operating temperature range (2) Zero power resistance of thermistor R=R 0 expB(1/T-1/T 0 ), T, T 0 are ambient temperatures, R, R 0 are corresponding resistances and B is the B-constant (or β constant ) of the thermistor R=R 0 expB(1/T-1/T 0 ), T, T 0 are ambient temperatures, R, R 0 are corresponding resistances and B is the B-constant (or β constant ) of the thermistor Or B=ln(R/R 0 )/(1/T-1/T 0 ) (3) Since thermistor is a resistor, power dissipation P=C(T 2 -T 1 ), where C is the thermal dissipation constant (mW/ºC). This causes self-heating. P=C(T 2 -T 1 ), 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: 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 can solve three unknowns C 1, C 2 and C 3. Measure 3 resistances and 3 temperatures, you can solve three unknowns C 1, C 2 and C 3. Matrix inversion (linear algebra) Matrix inversion (linear algebra) Minimize (least square) error in curve fitting Minimize (least square) error in curve fitting Once C 1, C 2 and C 3 are known, S-H equation (for your sensor) can be used to predict T based on R measurement. Once C 1, C 2 and C 3 are known, S-H equation (for your sensor) can be used to predict T based on R measurement.

Solve C 1, C 2 and C 3

Matrix inversion Matrix determinant Matrix transpose

Measure thermistor resistance with R T embedded? Measure thermistor resistance with R T embedded? (1) Voltage divider circuit Relating Vout to R T Relating Vout to R T (2) Wheatstone bridge circuit* Balancing the Bridge circuit Balancing the Bridge circuit Relating Vout to R T Relating Vout to R T

Embed a thermistor in voltage divider Design considerations: V out voltage range (signal conditioning in order to interface with ADC ) V out voltage range (signal conditioning in order to interface with ADC ) V out sensitivity varies at different temperature range (R-T characteristics curve) V out sensitivity varies at different temperature range (R-T characteristics curve) Recall BEM Lab #3: Where R T varies with T

Bridge circuit to embed a thermistor* Design considerations: More sensitive to small changes More sensitive to small changes V out voltage range (to interface with ADC) V out voltage range (to interface with ADC) Reference: Fsect2.PDF Fsect2.PDF Fsect2.PDF

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

Thermistor on rocket! Voltage Reading Resistance R T Temperature on rocket S-H equation (with calibration constants C 1, C 2 and C 3 ) 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