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How to Stay Out of Deep
Water When Designing
with Bridge Sensors
By Gustavo Castro and Scott Hunt
Instrumentation amplifiers (in-amps) can condition the electrical
signals generated by sensors, allowing them to be digitized, stored,
or used to control processes. The signal is typically small, so the
amplifier may need to be operated at high gain. In addition, the
signal may sit on top of a large common-mode voltage, or it may be
embedded in a substantial dc offset. Precision in-amps can provide
high gain, selectively amplifying the difference between the two
input voltages while rejecting signals common to both inputs.
Wheatstone bridges are classic examples of this situation, but
galvanic cells such as biosensors have similar characteristics. The
bridge output signal is differential, so an in-amp is the preferred
device for high-precision measurements. Ideally, the unloaded
bridge output is zero, but this is true only when all four resistors
are exactly equal. Consider a bridge built with discrete resistors,
as shown in Figure 1. The worst case differential offset, VOS, is
VOS = ±VEX
TOL
100
(1)
VEX
R ± R
R ± R
BRIDGE
R ± R OFFSET (V )
OS
• Reducing the first-stage gain, removing the offset by
trimming the voltage on REF, and adding a second
amplifier circuit to achieve the desired gain
• Reducing the first-stage gain, digitizing the output with a
high-resolution ADC, and removing the offset in software
The two last options also need to account for worst-case deviations
from the original offset value, further reducing the maximum gain
of the first stage. These solutions are not ideal, as they require extra
power, board space, or cost to obtain the high first-stage gain needed
to obtain high CMRR and low noise. In addition, ac coupling is not
an option for measuring dc or very slow-moving signals.
TYPICAL SINGLE CHIP
–IN
RG
RF
OUT
RF
+IN
where V EX is the bridge excitation voltage and TOL is the resistor
tolerance (in percent).
R ± R
• Shunting the bridge with an external resistor on a caseby-case basis, but this is impractical for automated
production and does not allow for adjustments after
leaving the factory
REF
Figure 2. 3-op-amp instrumentation amplifier topology.
Indirect current feedback (ICF) in-amps, such as the AD8237
and AD8420, make it possible to remove the offset before it is
amplified. Figure 3 shows a schematic of the ICF topology.
R = R TOL(%)/100
OUT
Figure 1. Wheatstone bridge offset.
For example, with 0.1% tolerance for each one of the individual
elements and a 5-V excitation voltage, the differential offset can
be as high as 5 mV. If a gain of 400 is required to achieve the
desired bridge sensitivity, the offset becomes ±2 V at the amplifier
output. Assuming that the amplifier is powered by the same supply,
and that its output can swing rail-to-rail, more than 80% of the
output swing could be consumed by the bridge offset alone. As
the industry trends to smaller supply voltages, this problem only
gets worse.
The traditional 3-op-amp in-amp architecture, shown in Figure 2,
has a differential gain stage followed by a subtractor that removes
the common-mode voltage. The gain is applied on the first stage,
so the offset is amplified by the same factor as the signal of interest.
Thus, the only way to remove it is to apply the opposite voltage to
the reference (REF) terminal. The main limitation of this method
is that adjusting the voltage on REF cannot correct the offset if the
first stage of the amplifier is already saturated. A few approaches
to get around this limitation include:
Analog Dialogue 48-01, January (2014)
+IN
+
–
FB
–IN
–
+
REF
R2
R1
Figure 3. Indirect current feedback in-amp topology.
The transfer function for this instrumentation amplifier is of
the same form as that of the classical 3-op-amp topology, and is
given by

R 
VOUT = 1 + 2  (V+ IN − V− IN ) + VREF
R1 

(2)
Because the feedback to the amplifier is satisfied when the voltage
between the inputs is equal to the voltage between the feedback
(FB) and reference (REF) terminals, we can rewrite this as
 R 
VOUT = 1 + 2  (VFB − VREF ) + VREF
 R1 
www.analog.com/analogdialogue
(3)
1
This suggests that introducing a voltage equal to the offset across
the feedback and reference terminals allows the output to be
adjusted to zero volts even in the presence of a large input offset.
As shown in Figure 4, this adjustment can be accomplished by
injecting a small current into the feedback node through resistor
R A from a simple voltage source such as a low-cost DAC or a filtered
PWM signal from an embedded microcontroller.
To find a value of R A that will allow a maximum offset adjustment,
V IN(MAX), with a given adjustment voltage range, VA(MAX), set
VOUT = 0 and solve for R A, giving
 R R  VA ( MAX )
RA =  1 2 
 R1 + R2  VIN ( MAX )
where V IN(MAX) is the maximum offset expected from the sensor.
Equation (5) also shows that the insertion of the adjustment circuit
modifies the gain from the input to the output. Even though this
will generally have a small effect, the gain can be recalculated as
VEX
WHEATSTONE
BRIDGE
BRIDGE
OFFSET
OUT
A1
FB
REF
R2
R1
VA
Design Procedure
From Equation (3), the ratio of R1 and R 2 sets the gain as follows:

R 
G = 1 + 2 
R1 


R
R 
R
VOUT = 1 + 2 + 2  VIN − 2 (VA − VREF ) + VREF
R1 R A 
RA

Table 1. Suggested Resistors for Various Gains (1% Resistors)
R2 (k)
Gain
None
Short
1
49.9
49.9
2
20
80.6
5.03
10
90.9
10.09
5
95.3
20.06
2
97.6
49.8
1
100
101
1
200
201
1
499
500
1
1000
1001
(9)
This same result would be obtained if VOUT and VA were taken
relative to V REF in the original equations. VA(MAX) – V REF should
also replace VA(MAX) in Equation (7).
Design Example
Consider a single-supply bridge amplifier such as that shown in
Figure 4, where 3.3 V is used to excite the bridge and power the
amplifier. The full-scale bridge output is ±15 mV, and the offset
can be in the ±25-mV range. To obtain the desired sensitivity, the
amplifier gain needs to be 100, and the input range of the ADC
is 0 V to 3.3 V. Because the output of the bridge can be positive
or negative, the output is referenced to midsupply, or 1.65 V.
Simply by applying a gain of 100, the offset alone would force the
amplifier output to be anywhere from –0.85 V to +4.15 V, which
exceeds the supply rails.
This problem can be solved with the circuit shown in Figure 5.
Bridge amplifier A1 is an ICF instrumentation amplifier such as the
AD8237. Amplifier A 2, with R4 and R 5, sets the zero level output
of A1 at midsupply. The AD5601 8-bit DAC adjusts the output
to null the bridge offset through R A . The output of the amplifier
is then digitized by the AD7091 micropower 12-bit ADC.
To simplify the process of finding a value for R A, assume dualsupply operation, a grounded REF terminal, and a known bipolar
adjustment voltage VA . In this case, the output voltage is given by

R
R 
R
VOUT = 1 + 2 + 2  VIN − 2 VA
R1 R A 
RA

(5)
+3.3V
(6)
+3.3V
WHEATSTONE
BRIDGE
+VS
BRIDGE
OFFSET
Notice that the gain from VA to the output is inverting. An increase
in VA reduces the output voltage by a fraction given by the ratio
of resistors R 2 and R A . This ratio allows the adjustment range to
be maximized for a given input offset. Because the adjustment
range is referred to the input of the amplifier before gain, fine
adjustment steps can be achieved even with a low resolution source.
Since RA is typically much larger than R1, we can approximate
Equation (5) as

R 
R
VOUT = 1 + 2  VIN − 2 VA
R1 
RA

(8)
In general, for single-supply bridge conditioning applications,
the voltage on the reference terminal should be above the signal
ground. This is especially true if the bridge output can swing
positive and negative. If the reference voltage is driven to a voltage,
V REF, with a low-impedance source such as a resistor divider and
a buffer, as shown in Figure 5, Equation (5) becomes
(4)
The designer must determine the resistor values. Larger values
reduce power consumption and output loading; smaller values
limit the input bias current at FB and input impedance errors.
If the parallel combination of R1 and R 2 is greater than about
30 kΩ, the resistors start to contribute to the noise. Table 1 shows
some suggested values.
R1 (k)

R
R 
Gain = 1 + 2 + 2 
R1 R A 

RA
Figure 4. High gain bridge circuit with offset removal.
2
(7)
+3.3V
AD8237
FB
REF
–VS
+3.3V
R5
R3
OUT
A1
+3.3V
R2
AD7091
C1
R1
+1.65V
A2
AD8505
R4
+3.3V
AD5601
VDAC
RA
Figure 5. Offset removal circuit modified for
single-supply operation.
Analog Dialogue 48-01, January (2014)
From Table 1, we find that R1 and R 2 need to be 1 kΩ and
100 kΩ for a gain of 101. The circuit includes a DAC that can
swing from 0 V to 3.3 V, or ±1.65 V around the 1.65-V reference
voltage. To calculate the value of R A we use Equation (6). With
VA(MAX) = 1.65 V and V IN(MAX) = 0.025 V, R A = 65.347 kΩ. With
1% resistor tolerance, the closest available value is 64.9 kΩ.
This leaves no margin for errors caused by source accuracy
and temperature variation, however, so we choose a low cost,
commonly stocked 49.9-kΩ resistor. The trade-off is reduced
adjustment resolution, which results in a slightly larger postadjustment offset.
From Equation (7), the nominal gain value can be calculated to
be 103. If the designer wants to obtain a gain value closer to the
target of 100, it is easiest to reduce the value of R 2 by about 3% to
97.6 kΩ, which will have very little influence on the value of R A .
Under the new conditions, the nominal gain is 100.6.
Because the DAC can swing ±1.65 V, the total offset adjustment
range is given by the voltage divider formed by R A and the parallel
combination of R1 and R 2, which can be calculated as follows:
 R1 || R2 
 VA( MAX ) =
VA _ RANGE = 
 R1 || R2 + R A 
(10)
0.99 kΩ
(±1.65 V ) = ± 32.1 mV
0.99 kΩ + 49.9 kΩ
A ±32.1-mV adjustment over the ±25-mV maximum bridge offset
provides an additional 28% adjustment margin. With an 8-bit
DAC, the step size for the adjustment is
VA _ STEP =
2 × VIN ( MAX )
2
n
=
64.2 mV
≈ 250 μV
256
(11)
With a 250-µV adjustment resolution, the maximum residual offset
at the output is 12.5 mV.
The values of R 3 and C1 can be determined from the values
suggested in the ADC data sheet or from Reference 2. For an
AD7091 sampling at 1 MSPS, these values are 51 Ω and 4.7 nF.
Larger resistor and capacitor combinations can be used when
sampling at lower rates to further reduce noise and aliasing effects.
An additional advantage of this circuit is that the bridge
offset adjustment can be done at production or installation.
If environmental conditions, sensor hysteresis, or long-term
drift have an effect on the value of the offset, the circuit can
be readjusted.
Because of its true rail-to-rail input, the AD8237 works best in
bridge applications that employ very low supply voltages. For
traditional industrial applications where higher supply voltages
are required, the AD8420 is a good alternative. This ICF in-amp
operates with supply voltages from 2.7 V to 36 V and draws 60%
less current.
Analog Dialogue 48-01, January (2014)
Table 2 compares the two in-amps. Minimum and maximum
specifications have been used where available. See the product
data sheets for more detailed and up to date information.
Table 2. Comparison of AD8237 and AD8420
Specification
AD8237
AD8420
Technology
CMOS
(Zero-drift)
Bipolar
Quiescent Supply Current
130 µA
80 µA
Supply Voltage Range
1.8 V to 5.5 V
2.7 V to 36 V
Input Voltage Range
–VS – 0.3 V to
+VS + 0.3 V
–VS – 0.15 V to
+VS – 2.2 V
±1V
Differential Input Voltage Limit
±(VS – 1.2) V
Rail-to-Rail Output
Yes
Yes
CMRR (G = 100, dc to 60 Hz)
114 dB
100 dB
Offset Voltage
75 µV
125 µV
Offset Voltage Drift
0.3 µV/°C
1 µV/°C
Voltage Noise Spectral Density
68 nV/√Hz
55 nV/√Hz
Gain Error (G = 100)
0.005%
0.1%
Gain Drift
0.5 ppm/°C
10 ppm/°C
Bandwidth, –3 dB (G = 100)
10 kHz in
HBW mode
2.5 kHz
Package
MSOP-8
MSOP-8
References
1
AN212 Application Note. Handling Sensor Bridge Offset.
Honeywell International Inc., Rev 05-05.
2
HMC1001/HMC1002/HMC1021/HMC1022 1- and 2-Axis
Magnetic Sensors Data Sheet. Honeywell International Inc., 2008.
3
Kitchin, Charles and Lew Counts. A Designer’s Guide to
Instrumentation Amplifiers. 3rd Edition. Analog Devices, Inc., 2006.
4
NPC-410 Series Data Sheet. GE Sensing, 2006.
5
Product Training Module. Indirect Cur rent Feedback
Instrumentation Amplifier Applications Guide. Digi-Key
Corporation.
6
Walsh, Alan. “Front-End Amplifier and RC Filter Design for a
Precision SAR Analog-to-Digital Converter.” Analog Dialogue,
Volume 46, 2012.
Authors
Gustavo Castro [[email protected]]
is an applications engineer in the Precision Signal
Conditioning Group in Wilmington, MA. Prior to
joining Analog Devices in January 2011, he worked
for 10 years designing high precision instrumentation
such as digital multimeters and dc sources. Gustavo received
a bachelor’s degree in electronics engineering in 2000 from
Monterrey Institute of Technology, Mexico. He holds two patents.
Scott Hunt [[email protected]] is a product
applications engineer in the Linear Products Group
in Wilmington, MA. Scott joined Analog Devices in
2011 after receiving a bachelor’s degree in electrical
engineering from Rensselaer Polytechnic Institute.
Scott specializes in integrated precision amplifiers including
instrumentation amplif iers, differential amplif iers, and
thermocouple amplifiers.
3
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