### AN168: Dynamic Temperature Compensation For Pressure Sensors

```Dynamic Temperature Compensation For
Pressure Sensors
®
Application Note
April 26, 2005
AN168.0
Author: Axel Kleinitz
Introduction
The Pressure Sensor
One of the fundamental tasks when dealing with any type of
sensors would be the compensation of offset and span drift
in regards to temperature. Looking at a typical pressure
sensor, we may come across the following thermal behavior:
The typical block diagram for a standard pressure sensor
driven with a current source could look as follows:
Figure 2. Pressure Sensor Block Diagram
Figure 1. Output vs. Pressure Differential1
IB
80
-40°C
OUTPUT (mVdc)
70
60
R + ∆R
+25°C
VS = 3Vdc
P1 > P2
50
SPAN
RANGE
(TYP)
+125°C
40
30
VB
V2
V1
20
kPa
R + ∆R
R - ∆R
OFFSET
(TYP)
10
0
PSI 0
R - ∆R
0.3
2.0
0.6
0.9
1.2
4.0
6.0
8.0
PRESSURE DIFFERENTIAL
1.5
10
The above curve easily demonstrates the relationship
between temperature, offset and span: with the increase of
temperature, span is reduced while offset is increased. The
traditional way to deal with this drift would be to build up a
simple signal conditioning circuit that would be calibrated at a
reference temperature (usually at 20°C), followed by a
characterization of the complete (analog) system (sensor +
signal conditioner) across the whole dynamic temperature
range. The measured curve would then be uploaded in a
nonvolatile lookup table that provides a compensational value.
This value would then be used in order to correct the drift in
the digital domain. More complex systems could also use this
value in order to retune span and offset in the analog domain
as a function of temperature in a dynamic way.2
Another alternative way to deal with this issue would be by
using a dynamic current source, with a thermal behavior that
compensates the sensor’s drift. With this analog approach,
the sensor’s overall performance would dramatically increase.
Under ideal conditions both resistor parameters R and ∆R
would be exactly the same for each sector of the bridge; the
total resistor value RB for one sensor would then be:
VB
R B = ( R + ∆R + R – ∆R ) || ( R + ∆R + R – ∆R ) = R = ------IB
(1)
The above relationship clearly demonstrates that an ideal
pressure sensor will not change its resistor value with
changing pressure (=>∆R), but should be totally balanced. In
such a case, the differential voltage VD = V1 – V2 could be
determined with the following matrix:
2R
------------------------2
2
R – ∆R
–
1
-----------------R
–
∆R • V
•
=
B
V2
2R
1
------------------------------------------2
2
R + ∆R
R – ∆R
–
V1
(2)
This term leads to the following relationship between V1 and
V2:
∆R
V D = V 1 – V 2 = -------- V B
R
(3)
1. Motorola MPX (V) 10
2. For further details on how to dynamically calibrate and
compensate span and offset in the analog domain by using
a constant voltage source, pls. refer to Adaptive Sensor
Biasing, Intersil App-Note, April 2002, by Dr. Axel Kleinitz
1
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Application Note 168
R
The Impact of Temperature
0
While ------would represent the Temperature Coefficient
∆T
The above mentioned discussion did not take into
consideration any possible thermal drift, since we were
initially dealing with ideal components. However, as Figure 1
clearly pointed out, a standard pressure sensor will face
significant changes in terms of its span and offset with
temperature. Assuming a linear behavior1, this impact will
have an effect on equation (1) in the following way:
B
(= TC) of the bridge resistor value, k ------reflects the TC of
VB
T
R B = R ( T ) =  1 + ------- R 0 = ------
IB
∆T
(4)
temperature depending, proportional factor. Equation (3)
essentially implies a linear dependency of VD with respect to
∆R, that is, the effect of pressure. However, assuming a first
order characteristic2 of the offset in regards to temperature,
equation (3) needs to be modified in the following way:
∆R
T
V D = V D (∆R,T) = ------------ V B +  1 + ------- kV B

R( T )
∆T
(5)
V
∆T
the sensor’s offset. Using both terms, equation (4) and (5)
we will get a useful expression in order to demonstrate to
link between VD and IB in the following way:
T 2
V D = V D (∆R,T) = ∆R +  1 + ------- kR 0 I B

∆T
(6)
The differential voltage VD is now not only a function of
pressure ( ⇒ ∆R ), but also a function of temperature
T
( ⇒ ------). This drift has to be compensated by a dynamic IB.
∆T
The Solution
The requirement of a dynamic current source would
traditionally be solved with a VBE-Multiplier right on top of
the sensor bridge. The main issue in such a case would be
the correct selection of the transistor (TC characteristic) and
proper resistor values (voltage divider value of the
transistor’s Basis) in order to provide an adequate thermal
characteristic that would compensate the sensor’s drift.
An alternative, more elegant approach would be using a
lookup-table driven current source, such as the X9530 of
Intersil. The block diagram of this concept is shown below.
1. This assumption is valid, at least within the operating
temperature range
2. In analogy to equations (1) and (4)
Figure 3. X9530 Block Diagram
Voltage
Reference
VRef
VSense
R2
Mux
Look-up
Table 2
Mux
DAC 2
I2
Mux
Look-up
Table 1
Mux
DAC 1
I1
Temperature
Sensor
SDA
SCL
WP
2-Wire
Interface
R1
Control
& Status
General
Purpose
Memory
A2, A1, A0
2
AN168.0
April 26, 2005
Application Note 168
based upon the relationship pointed out through the
equation (6). This can be performed through the I2C
interface. However, once the proper values are uploaded,
there won’t be any further need for an interacting µC. If
desired, the measured temperature value can be requested
and read out through the same interface. Finally, two
independent outputs can simultaneously be driven based
upon two independent table sectors in order to correct two
The signal flow for the above shown device is very simple:
an incoming analog signal VSense (like the voltage provided
by a temp sensor) or the value provided by the internal
thermal sensor will be converted into a digital value through
the ADC. This will represent a specific address of the lookup-table that will contain a compensational value. Once the
correction has been finished the corresponding output DAC
1 or 2 will be recalibrated.
Keeping in mind what had been said before, the only action
that is required would be the storage of appropriate
compensational factors in the memory sectors 1 and 2
This product is available with a variety of options, as pointed
out in the next matrix:
Figure 4. Sensor Conditioners Product Range
Int. Temp.
Sensor
Ext. Sensor
Input
VRef I/O
1K Memory
E2PROM
LU-Table Org.
# DAC
Outputs
X9530
yes
yes
yes
yes
Dual
Dual
X96010
no
yes
yes
no
Dual
Dual
X96011
yes
no
no
no
Single
Single
X96012
yes
yes
yes
yes
Dual
Dual
Device
The internal temperature sensor’s ADC resolution will
address an accuracy level of 6 Bit (64 values), which
K
- for a thermal range of -40°C ≤ T ≤
represents 2.22 ----------step
+100°C. Under normal conditions, this should be more then
enough for these type of applications. A limitation of the
operating temperature range would obviously increase the
The maximum DAC output current would be of ± 1.6 mA
with an accuracy of 8 Bit (256 values). This reflects a
µA
- . The DAC’s polarity can indepenprecision of 6.27 ----------step
dently be selected in order to provide a current sink or
current source.
Depending upon the complexity of the system and the board’s
physical dimensions, a solution with internal temp sensor,
internal reference voltage, general purpose memory and one
or two independent DAC outputs has to be selected.
Conclusion
The above concept combines therefore the advantages of a
digital approach (flexibility through programmability) and the
benefits of an analog solution (reduction of total error). The
available options and combinations will help to select best
fitting solution for a given system. The above presented
solutions are meant to cover the traditional requirements of
sensor signal conditioning.
Intersil Corporation reserves the right to make changes in circuit design, software and/or specifications at any time without notice. Accordingly, the reader is cautioned to
verify that the Application Note or Technical Brief is current before proceeding.
For information regarding Intersil Corporation and its products, see www.intersil.com
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AN168.0
April 26, 2005
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