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XIX IMEKO World Congress
Fundamental and Applied Metrology
September 6−11, 2009, Lisbon, Portugal
NOVEL AND LOW-COST TEMPERATURE COMPENSATION TECHNIQUE
FOR PIEZORESISTIVE PRESSURE SENSORS
Ferran Reverter 1, Goran Horak 2, Vedran Bilas 2, Manel Gasulla 1
1 Instrumentation, Sensors and Interfaces Group, Castelldefels School of Technology,
Universitat Politècnica de Catalunya, Castelldefels (Barcelona), Spain, reverter@eel.upc.edu
2 Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia, Vedran.Bilas@fer.hr
Abstract − This paper proposes a low-cost technique to
compensate for the temperature dependence of
piezoresistive pressure sensors configured in a Wheatstone
bridge. The sensor is treated as a resistive circuit and three
equivalent resistances are measured by setting appropriately
the bridge terminals. One of these equivalent resistances
depends on temperature but not on pressure and, hence, it
can be used to compensate for the temperature dependence
of the output parameter. In such a way, neither data of a
previous temperature calibration nor additional components
are required to compensate for the temperature dependence.
The proposed technique is applied to a commercial pressure
sensor, which is measured by means of a direct sensor-to-
microcontroller interface circuit. Experimental results show
that temperature effects on the pressure measurement
decrease more than ten times when the proposed technique
is applied.
Keywords: pressure sensor, piezoresistive sensor,
temperature compensation, sensor electronic interface,
microcontroller.
1. NOMENCLATURE
P Pressure applied to the sensor
Patm Atmospheric pressure
T Actual temperature
T0 Reference temperature defined by the sensor
manufacturer
T0’ Reference temperature defined by the sensor user
R1-R4 The four piezoresistors of the bridge sensor
Rn Nominal value of the piezoresistors at P = 0
R0 Resistance value of Rn at T = T0
R0’ Resistance value of Rn at T = T0’
α
R Temperature coefficient of Rn using T0 as a reference
α
R’ Temperature coefficient of Rn using T0’ as a reference
S Piezoresistive sensitivity
S0 Piezoresistive sensitivity at T = T0
α
S Temperature coefficient of S using T0 as a reference
M Output parameter that combines the measurement of
the equivalent resistances without compensation
M* Output parameter that combines the measurement of
the equivalent resistances with compensation
2. INTRODUCTION
Semiconductor sensors are widely used in current
measurement systems because of their low cost, small size
and easy integration with electronic circuits [1]. In the
automotive industry, for example, mechanical
semiconductor sensors have become very widespread,
especially those intended for the measurement of pressure
and acceleration [2]. Such mechanical sensors generally rely
on either piezoresistances or capacitances.
Semiconductor pressure sensors based on
piezoresistances are usually configured in a Wheatstone
bridge with four active arms, as shown in Fig. 1. In the event
of a pressure change, two piezoresistors (R1 and R4) undergo
a resistance change that is equal but opposite to that of the
other two piezoresistors (R2 and R3). In such a way, the
sensitivity of the bridge is higher than in bridges with only
one or two active arms [3].
Figure 1. Piezoresistive pressure sensor in a Wheatstone-bridge
configuration.
A remarkable drawback of piezoresistive pressure
sensors is their temperature dependence [1] and, for this
reason, several temperature compensation techniques have
been proposed. Generally, these techniques involve
additional components [4] (e.g. a thermistor) that increase
the effective voltage applied to the bridge when the
temperature increases so that the loss of sensitivity is
compensated [5]. The temperature dependence can also be
compensated by measuring the sensor temperature by means
of the sensor itself. For example, references [6, 7] propose a
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ISBN 978-963-88410-0-1 © 2009 IMEKO
relaxation oscillator in which the frequency of the output
signal carries information about the bridge unbalance
whereas the duty cycle carries information about the bridge
resistance and, hence, the temperature. Reference [8]
proposes (for metallic strain gages, not for semiconductor
ones) a technique based on two current sources and two
differential voltage measurements, one with information
about the mechanical stress and the other with information
about the temperature.
This paper proposes a novel technique to compensate for
the temperature dependence of piezoresistive pressure
sensors by using a simple and low-cost microcontroller-
based interface circuit. The proposed technique uses the
same pressure sensor to measure the temperature and, hence,
it does not require either data of a previous temperature
calibration or additional components.
3. TEMPERATURE DEPENDENCE
The four piezoresistors of the pressure sensor (Fig. 1)
can be modelled by [9]
[
]
14n
1
RRR SP
== +⋅
(1a)
[
]
23n
1
RRR SP
== −⋅
, (1b)
in which both Rn and S depend on temperature.
Consequently, if we assume a first-order temperature
dependence and the same temperature coefficients for the
four piezoresistors, these can be modelled by
(
)
(
)
(
)
140 R 0 0 S 0
111
RRR TT S TTP
αα
⎡⎤
== + − + + −
⎡⎤
⎣⎦
⎣⎦
(2a)
(
)
(
)
(
)
230 R 0 0 S 0
111
RRR TT S TTP
αα
⎡⎤
== + − − + −
⎡⎤
⎣⎦
⎣⎦
.(2b)
According to [1],
α
R is a positive temperature coefficient
(i.e.
α
R > 0) whereas
α
S is a negative temperature coefficient
(i.e.
α
S < 0). Data sheets of commercial pressure sensors
usually specify
α
R and
α
S by means of the “temperature
coefficient of input resistance” and the “temperature
coefficient of span”, respectively. These coefficients depend
on the temperature used as a reference by the manufacturer
(T0 according to our nomenclature).
If a constant supply voltage (VDD) is applied to the bridge
sensor and then the differential output voltage (vo) is read, as
shown in Fig. 1, the measurement result is
(
)
(
)
oDD0 S 0
1
vVS TTP
α
=+−
, (3)
which depends on pressure but also on temperature. Since
α
S < 0, for a given value of P, the value of vo decreases with
temperature. Generally, this temperature dependence is
compensated by using additional components that increase
the effective voltage applied to the bridge when the
temperature increases [4, 5].
Bridge sensors can also be measured by determining
three equivalent resistances of the bridge [10]. To do so, the
bridge terminals are appropriately set to ground or in high-
impedance state (HZ), as shown in Fig. 2, and the resulting
equivalent resistances are:
(
)
41 2 3
eq,A
1234
RR R R
R
RRRR
++
=+++ (4a)
(
)
1234
eq,B
1234
)(
RRRR
R
RRRR
++
=+++ (4b)
(
)
21 3 4
eq,C
1234
RR R R
R
RRRR
++
=+++ . (4c)
Replacing (2) in (4) yields
() ()
()
0
eq,A R 0 0 S 0
1321
4
R
RTTSTTP
αα
⎡⎤
≈+ − + +−
⎡⎤
⎣⎦
⎣⎦
(5a)
(
)
eq,B 0 R 0
1
RR TT
α
=+ −
⎡⎤
⎣⎦
(5b)
() ()
()
0
eq,C R 0 0 S 0
1321
4
R
RTTSTTP
αα
⎡⎤
≈+ − − +−
⎡⎤
⎣⎦
⎣⎦
. (5c)
Then, the measurand can be estimated by calculating the
parameter M that combines the measurement of the
equivalent resistances as follows [10]:
eq,A eq,C
eq,B
RR
MR
−
=. (6)
Replacing now (5) in (6) yields
(
)
(
)
0S 0
1
MS TTP
α
=+ − , (7)
which, the same as in (3), depends on pressure but also on
temperature. Therefore, since
α
S < 0, for a given value of P,
the value of M also decreases with temperature.
4. COMPENSATION TECHNIQUE
To compensate for the temperature dependence shown in
(7), we propose to estimate the sensor temperature by means
of the sensor itself. This can be done by using appropriately
the measurement of Req,B, which just depends on
temperature, as shown in (5b). Then, in order to achieve an
output independent of temperature (i.e. M* = S0P), we could
calculate the following parameter:
*
eq,B
S
R0
11
M
MR
R
α
α
=
⎛⎞
+−
⎜⎟
⎝⎠
, (8)
where M is calculated by (6),
α
S and
α
R are specified by the
sensor manufacturer, Req,B is the measured equivalent
resistance at a given temperature T, and R0 is the value of
Req,B at T = T0. Regrettably, the tolerance of R0 is either very
large (say, 20 % or higher) or not specified at all in sensor
data sheets. Of course, R0 could be measured at T = T0, but
this involves time and specific temperature-calibration
instrumentation.
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Figure 2. Bridge sensor treated as a resistive circuit and measurement of the equivalent resistances (a) Req,A, (b) Req,B and (c) Req,C.
To avoid the previous limitations, we propose to use T0’
as a reference instead of T0; T0’ can be, for example, room
temperature whenever it does not differ significantly from
T0. In such conditions, we can assume
α
R’ ≈
α
R and, hence,
Req,B can be expressed and approximated to
(
)
(
)
'' '' '
eq,B 0 R 0 0 R 0
11RR TTR TT
αα
⎡⎤⎡⎤
=+ −≈+ −
⎣⎦⎣⎦
. (9)
Then, instead of (8), we propose to calculate M* as follows:
*
eq,B
S
'
R0
11
M
MR
R
α
α
=
⎛⎞
+−
⎜⎟
⎝⎠
, (10)
where R0’ is the value of Req,B registered at T = T0’.
Replacing now (7) in (10) yields
(
)
(
)
*'
0S00
1
MS TTP
α
≈+ − . (11)
which just depends on pressure because the term (T0’ − T0) is
constant.
This compensation technique can also be applied to
conventional conditioning circuits based on the
measurement of the differential output voltage (Fig. 1). If
the circuit is able to measure both vo and Req,B, then the
information provided by the latter can be used to
compensate for the temperature dependence of the former
(see (3)).
5. MATERIALS AND METHOD
The proposed temperature compensation technique has
been applied to a commercial pressure sensor (SX15AD2,
SensorTechnics), which is intended for absolute pressure
measurements. This sensor is internally configured in a
Wheatstone bridge with four active arms (Fig. 1) and does
not include either compensation electronics or conditioning
circuits inside. Table I summarises the main features of this
sensor.
Table 1. Features of the SX15AD2 sensor.
Feature Value
Operating pressure range [0, 103] kPa
Sensitivity 214 µV/V/kPa (typ)
Operating temperature range [-40, +85] ºC
Temperature coefficient of input
resistance (
α
R) using T0 = 25 ºC
(not 100 % tested)
+690 ppm/ºC (min)
+750 ppm/ºC (typ)
+810 ppm/ºC (max)
Temperature coefficient of span
(
α
S) using T0 = 25 ºC
(not 100 % tested)
-2550 ppm/ºC (min)
-2150 ppm/ºC (typ)
-1900 ppm/ºC (max)
The sensor was subjected to atmospheric pressure, which
was equal to 101 kPa according to the Croatian national
meteorological institute. The temperature applied to the
sensor was controlled by a climatic chamber (Weiss Technik
125 SB) from -40 ºC to 70 ºC. For each test condition, the
three equivalent resistances (Fig. 2) were measured using
the direct sensor-to-microcontroller interface circuit
proposed in [10], which was controlled by the
dsPIC30F3012 microcontroller (Microchip). For the
temperature compensation, we used T0’ ≈ 26 ºC as a
reference, which is near to T0 = 25 ºC.
6. EXPERIMENTAL RESULTS AND DISCUSSION
Fig. 3 (solid line and crosses) shows the normalized
value of M versus temperature at P = Patm when the
compensation technique was not applied (Eq. (6)). The
parameter M clearly depended on temperature, to be precise,
the temperature coefficient was -2700 ppm/ºC. As predicted
by (7), the temperature coefficient of M is negative, however
its (absolute) value is slightly higher than the maximum one
expected (-2550 ppm/ºC according to Table 1). In the worst
case (i.e. for T ≈ -40 ºC), the relative error in M (and, hence,
in the pressure measurement) due to temperature was about
17 %.
2086
Fig. 3 (dashed line and squares) also shows the
normalized value of M* versus temperature at P = Patm when
the compensation technique was applied (Eq. (10)). The
parameter M* was more insensitive to temperature, as
predicted by (11). The use of the typical values of
α
R and
α
S
in (10) and/or the temperature dependence of the interface
circuit can explain why the response in Fig. 3 is not
completely flat. Even so, in the worst case (i.e. for
T ≈ 70 ºC), the relative error due to temperature was about
1.6 %, which is more than ten times smaller than that
obtained when the compensation technique was not applied.
-40 -20 020 40 60 80
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Temperature (ºC)
Normalized output parameter
Without compensation
With compensation
Figure 3. Temperature dependence of the output parameter at
P = Patm = 101 kPa.
7. CONCLUSIONS
A novel and low-cost technique to compensate for the
temperature dependence of piezoresistive pressure sensors
has been proposed. This compensation technique relies on
estimating the temperature of the sensor by means of the
sensor itself, without using any additional component. Once
the temperature is known, the output parameter can easily be
corrected. This idea has been tested in a commercial
pressure sensor and the experimental results agree with the
theoretical predictions. Other semiconductor sensors (such
as acceleration sensors and magnetoresistive sensors) can
also benefit from the results of this work.
ACKNOWLEDGMENTS
This work has been funded by the Spanish Ministry of
Education and Science and the European Regional
Development Fund through Project DPI2006-04017, and by
the Croatian Ministry of Science, Education and Sport
through Project 036-0361621-1625. Authors appreciate the
initial proposal provided by Prof. Ramon Pallàs-Areny.
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