Pressure sensors and thermistors
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Transcript Pressure sensors and thermistors
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 Analogvoltagefromsensor
1024
1 Psi 6.89465kPa
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
Interceptb 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 1.454410 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
NoteC1 ' 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
ln R2 3 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
R2
RT
+
R1
Vout
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
T hen: 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