AN1097 Calibration-Free Pressure Sensor System

Freescale Semiconductor
Application Note
AN1097
Rev 3, 05/2005
Calibration-Free Pressure Sensor System
by: Michel Burri, Senior System Engineer
Geneva, Switzerland
INTRODUCTION
The MPX2000 series pressure transducers are
semiconductor devices which give an electrical output signal
proportional to the applied pressure. The sensors are a single
monolithic silicon diaphragm with strain gauge and thin-film
resistor networks on the chip. Each chip is laser trimmed for
full scale output, offset, and temperature compensation.
The purpose of this document is to describe another
method of measurement which should facilitate the life of the
design. The MPX2000 series sensors are available both as
unported elements and as ported assemblies suitable for
pressure, vacuum and differential pressure measurements in
the range of 10 kPa through 200 kPa.
The use of the on-chip A/D converter of the MC68HC05B6
HCMOS MCU makes possible the design of an accurate and
reliable pressure measurement system.
+ Vs
Pin 3
Rs1
RP
Pin 2
+
RIN
VOUT
Pin 4
SYSTEM ANALYSIS
The measurement system is made up of the pressure
sensor, the amplifiers, and the MCU. Each element in the
chain has its own device-to-device variations and temperature
effects which should be analyzed separately. For instance, the
8-bit A/D converter has a quantization error of about ±0.2
percent. This error should be subtracted from the maximum
error specified for the system to find the available error for the
rest of elements in the chain. The MPX2000 series pressure
sensors are designed to provide an output sensitivity of 4.0
mV/V excitation voltage with full-scale pressure applied or 20
mV at the excitation voltage of 5.0 VDC.
An interesting property must be considered to define the
configuration of the system: the ratiometric function of both the
A/D converter and the pressure sensor device. The ratiometric
function of these elements makes all voltage variations from
the power supply rejected by the system. With this advantage,
it is possible to design a chain of amplification where the signal
is conditioned in a different way.
Thermistor
Laser
Trimmed
On-Chip
RS2
Pin 1
GND
Figure 1. Seven Laser-Trimmed Resistors and Two
Thermistors Calibrate the Sensor for Offset, Span,
Symmetry and Temperature Compensation
The op amp configuration should have a good commonmode rejection ratio to cancel the DC component voltage of
the pressure sensor element which is about half the excitation
voltage value VS. Also, the op amp configuration is important
when the designer's objective is to minimize the calibration
procedures which cost time and money and often don't allow
the unit-to-unit replacement of devices or modules.
One other aspect is that most of the applications are not
affected by inaccuracy in the region from 0 kPa to 40 kPa.
Therefore, the goal is to obtain an acceptable tolerance of the
system from 40 kPa through 100 kPa, thus minimizing the
inherent offset voltage of the pressure sensor.
PRESSURE SENSOR CHARACTERISTICS
Figure 2 shows the differential output voltage of the
MPX2100 series at +25°C. The dispersion of the output
voltage determines the best tolerance that the system may
© Freescale Semiconductor, Inc., 2005. All rights reserved.
achieve without undertaking a calibration procedure, if any
other elements or parameters in the chain do not introduce
additional errors.
VOUT (mV)
20
VS = 5
VDCTA = 25°C
The instrument amplifier does provide an excellent CMRR
and a symmetrical buffered high input impedance at both noninverting and inverting terminals. It minimizes the number of
the external passive components used to set the gain of the
amplifier. Also, it is easy to compensate the temperature
variation of the Full Scale Output of the Pressure Sensor by
implementing resistors “Rf” having a negative coefficient
temperature of -250 PPM/°C.
The differential-mode voltage gain of the instrument
amplifier is:
FULL-SCALE
10
Avd =
5
V1-V2
2 Rf
= 1+
Vs2-Vs4
Rg
(1)
OFFSET
+VS
0
P
(kPa)
-5
0
20
40
60
80
100
Figure 2. Spread of the Output Voltage versus the
Applied Pressure at 25°C
The effects of temperature on the full scale output and
offset are shown in Figure 3. It is interesting to notice that the
offset variation is greater than the full scale output and both
have a positive temperature coefficient respectively of +8.0
µV/degree and +5.0 µV excitation voltage. That means that
the full scale variation may be compensated by modifying the
gain somewhere in the chain amplifier by components
arranged to produce a negative TC of 250 PPM/°C. The dark
area of Figure 3 shows the trend of the compensation which
improves the full scale value over the temperature range. In
the area of 40 kPa, the compensation acts in the ratio of
40/100 of the value of the offset temperature coefficient.
VOUT (f) ∆T
+85°C
Positive
Full Scale
Variation
-15°C
Offset Variation
0
20
40
60
80
100
+
V1
3
2
Rf
RG
4
1
+
V2
0V
Figure 4. One Power Supply to Excite the Bridge and to
Develop a Differential Output Voltage
The major source of errors introduced by the op amp is
offset voltages which may be positive or negative, and the
input bias current which develops a drop voltage ∆V through
the feedback resistance Rf. When the op amp input is
composed of PNP transistors, the whole characteristic of the
transfer function is shifted below the DC component voltage
value set by the Pressure Sensor as shown in Figure 5.
The gain of the instrument amplifier is calculated carefully
to avoid a saturation of the output voltage, and to provide the
maximum of differential output voltage available for the A/D
Converter. The maximum output swing voltage of the
amplifiers is also dependent on the bias current which creates
a ∆V voltage on the feedback resistance Rf and on the Full
Scale output voltage of the pressure sensor.
P
(kPa)
Figure 3. Output Voltage versus Temperature. The Dark
Area Shows the Trend of the Compensation
OP AMP CHARACTERISTICS
For systems with only one power supply, the instrument
amplifier configuration shown in Figure 4 is a good solution to
monitor the output of a resistive transducer bridge.
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V1, V2
lib (nA)
5 VDC
VCC
600
V2X
1/2
VCC
UNIT 2
300
V1X
V2
VEE
UNIT 1
450
V1
0
5
10
15
150
20
VPS
(mV)
T
(°C)
0
-50
-25
0
25
50
75
100
125
Figure 5. Instrument Amplifier Transfer Function with
Spread of the Device to Device Offset Variation
Figure 7. Input Bias Current versus Temperature
Figure 5 shows the transfer function of different instrument
amplifiers used in the same application. The same sort of
random errors are generated by crossing the inputs of the
instrument amplifier. The spread of the differential output
voltage (V1-V2) and (V2x-V1x) is due to the unsigned voltage
offset and its absolute value. Figure 6 and Figure 7 show the
unit-to-unit variations of both the offset and the bias current of
the dual op amp MC33078.
MCU CONTRIBUTION
As shown in Figure 5, crossing the instrument amplifier
inputs generated their mutual differences which can be
computed by the MCU.
+VS
+
Vio (mV)
3
+2
2
UNIT 1
Rg
+1
4
UNIT 2
1
0V
-2
-50
-25
0
25
50
75
V2
P
UNIT 3
-1
Rf
+
0
V1
-
100
125
T
(°C)
Figure 6. Input Offset Voltage versus Temperature
To realize such a system, the designer must provide a
calibration procedure which is very time consuming. Some
extra potentiometers must be implemented for setting both the
offset and the Full Scale Output with a complex temperature
compensation network circuit.
The new proposed solution will reduce or eliminate any
calibration procedure.
Figure 8. Crossing of the Instrument Amplifier Input
Using a Port of the MCU
Figure 8 shows the analog switches on the front of the
instrument amplifier and the total symmetry of the chain. The
residual resistance RDS(on) of the switches does not introduce
errors due to the high input impedance of the instrument
amplifier.
With the aid of two analog switches, the MCU successively
converts the output signals V1, V2.
Four conversions are necessary to compute the final result.
First, two conversions of V1 and V2 are executed and stored
in the registers R1, R2. Then, the analog switches are
commuted in the opposite position and the two last
conversions of V2x and V1x are executed and stored in the
registers R2x and R1x. Then, the MCU computes the following
equation:
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RESULT = (R1-R2) + (R2x-R1x)
(2)
The result is twice a differential conversion. As
demonstrated below, all errors from the instrument amplifier
MC74HC4053
MPX2100AP
are cancelled. Other averaging techniques may be used to
improve the result, but the appropriated algorithm is always
determined by the maximum bandwidth of the input signal and
the required accuracy of the system.
+5V
MC33078
+
-
3
VRH
V1
CH1
Rf
2
Pressure
Sensor
System
Rg
4
1
Rf
+
-
VDD
I/O
MC68HC05B6
P
CH2
V2
VRL
VSS
0V
Figure 9. Two Channel Input and One Output Port Are Used by the MCU
SYSTEM CALCULATION
Sensor out 2
Vs2 = a (P) + of2
Sensor out 4
Vs4 = b (P) + of4
Amplifier out 1
V1 = Avd (Vs2 + OF1)
Amplifier out 2
V2 = Avd (Vs4 + OF2)
Inverting of the amplifier input
V1x = Avd (Vs4 + OF1)
V2x = Avd (Vs2 + OF2)
Delta = V1-V2
1st differential result
= Avd * (Vs2 of OF1) - Avd * (Vs4 + OF2)
Deltax = V2x-V1x
2nd differential result
= Avd * (Vs2 + OF2) - Vdc * (Vs4 + OF1)
Adding of the two differential results
VoutV = Delta + Deltax
= Avd*Vs2 + Avd*OF2 + Avd*OF2 - Avd*OF1
+ Avd*OF1 - Avd*OF2 + Avd*OF2 - Avd*OF1
= 2 * Avd * (Vs2 -Vs4)
= 2 * Avd * [(a (P) + of2) - (b (P) + of4)]
= 2 * Avd * [V(P) + Voffset]
There is a full cancellation of the amplifier offset OF1 and
OF2. The addition of the two differential results V1-V2 and
V2x-V1X produce a virtual output voltage VoutV which
becomes the applied input voltage to the A/D converter. The
result of the conversion is expressed in the number of counts
or bits by the ratiometric formula shown below:
255 is the maximum number of counts provided by the A/D
converter and VRH-VRL is the reference voltage of the
ratiometric A/D converter which is commonly tied to the 5.0 V
supply voltage of the MCU.
When the tolerance of the full scale pressure has to be in
the range of ± 2.5 percent, the offset of the pressure sensor
may be neglected. That means the system does not require
any calibration procedure.
The equation of the system transfer is then:
count = 2 * Avd * V(P) * 51/V where:
Avd is the differential-mode gain of the instrument amplifier
which is calculated using the equation (1). Then with Rf = 510
kΩ and Rg = 9.1 kΩ Avd = 113.
The maximum counts available in the MCU register at the
Full Scale Pressure is:
count (Full Scale) = 2 * 113 * 0.02 V * 51/V = 230
knowing that the MPX2100AP pressure sensor provides 20mV
at 5.0 excitation voltage and 100 kPa full scale pressure.
The system resolution is 100 kPa/230 that give 0.43 kPa
per count.
255
count = VoutV *
VRH-VRL
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+5V
VDD
FINE
CAL.
VRH
I/O
CH1
MC68HC05B6
P
CH2
VRL
VSS
0V
Figure 10. Full Scale Output Calibration Using the Reference Voltage VRH-VRL
When the tolerance of the system has to be in the range of
±1percent, the designer should provide only one calibration
procedure which sets the Full Scale Output (counts) at 25°C
100 kPa or under the local atmospheric pressure conditions.
+5V
MC74HC4053
MPX2100AP
MC33078
+
1/3
MC74HC4053
V1
3
Rf
2
Rg
4
1
Rf
+
VRH
P1
I/O
MC68HC05B6
CH1
P2
V2
VRL
Pressure
Sensor
System
VDD
VSS
0V
Figure 11. One Channel Input and Two Output Ports are used by the MCU
Due to the high impedance input of the A/D converter of the
MC68HC05B6 MCU, another configuration may be
implemented which uses only one channel input as shown in
Figure 11. It is interesting to notice that practically any dual op
amp may be used to do the job but a global consideration must
be made to optimize the total cost of the system according to
the requested specification.
When the Full Scale Pressure has to be sent with accuracy,
the calibration procedure may be executed in different ways.
For instance, the module may be calibrated directly using
Up/Down push buttons.
The gain of the chain is set by changing the VRH voltage of
the ratiometric A/D converter with the R/2R ladder network
circuit which is directly driven by the ports of the MCU. (See
Figure 12.)
Using a communication bus, the calibration procedure may
be executed from a host computer. In both cases, the setting
value is stored in the EEPROM of the MCU.
The gain may be also set using a potentiometer in place of
the resistor Rf. But, this component is expensive, taking into
account that it must be stable over the temperature range at
long term.
AN1097
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5
+ 5.0 V
RO
2R
I/O
VDD
VRH
2R
R
2R
R
2R
R
2R
R/2R
Ladder
Network
P3
P2
BUS
MC68HC05B6
P1
+ 5.0 V
P0
CH1
CH2
VRL
VSS
UP
DOWN
0V
Figure 12. R/2R Ladder Network for an MCU
Table 1. Pressure Conversion Table
Unity
mbar
Torr
1
0.01
7.5 10-3
-
-
-
-
100
1
0.75
-
-
0.0102
0.014
1 N/m2 = 1 Pascal
1 mbar
atm
at=kp/cm2
Pa
mWS
psi
1 Torr = 1 mmHg
133.32
1.333
.1
-
-
-
0.019
1 atm (1)
101325
1013.2
760
1
1.033
10.33
14.69
1 at = 1 kp/cm2(2)
98066.5
981
735.6
0.97
1
10
14.22
1 m of water
9806.65
98.1
73.56
0.097
0.1
1
1.422
1 lb/sqin = 1 psi
6894.8
68.95
51.71
0.068
-
-
1
NOTES:
1. Normal atmosphere
2. Technical atmosphere
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NOTES
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AN1097
Rev 3
05/2005
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