Application Note 43
June 1990
Bridge Circuits
Marrying Gain and Balance
Jim Williams
Bridge circuits are among the most elemental and powerful
electrical tools. They are found in measurement, switch-
ing, oscillator and transducer circuits. Additionally, bridge
techniques are broadband, serving from DC to bandwidths
well into the GHz range. The electrical analog of the me-
chanical beam balance, they are also the progenitor of all
electrical differential techniques.
Resistance Bridges
Figure 1 shows a basic resistor bridge. The circuit is
usually credited to Charles Wheatstone, although S. H.
Christie, who demonstrated it in 1833, almost certainly
preceded him.
1
If all resistor values are equal (or the two
sides
ratios
are equal) the differential voltage is zero. The
excitation voltage does not alter this, as it affects both
sides equally. When the bridge is operating off null, the
excitation’s magnitude sets output sensitivity. The bridge
output is nonlinear for a single variable resistor. Similarly,
two variable arms (e.g., R
C
and R
B
both variable) produce
nonlinear output, although sensitivity doubles. Linear
outputs are possible by complementary resistance swings
in one or both sides of the bridge.
A great deal of attention has been directed towards this
circuit. An almost uncountable number of tricks and tech-
niques have been applied to enhance linearity, sensitivity
Bridge Output Amplifiers
A primary concern is the accurate determination of the
differential output voltage. In bridges operating at null the
absolute scale factor of the readout device is normally
less important than its sensitivity and zero point stability.
An off-null bridge measurement usually requires a well
calibrated scale factor readout in addition to zero point
stability. Because of their importance, bridge readout
mechanisms have a long and glorious history (see Ap-
pendix B, “Bridge Readout—Then and Now”). Today’s
investigator has a variety of powerful electronic techniques
available to obtain highly accurate bridge readouts. Bridge
amplifiers are designed to accurately extract the bridges
differential output from its common mode level. The
ability to reject common mode signal is quite critical. A
typical 10V powered strain gauge transducer produces
only 30mV of signal “riding” on 5V of common mode
level. 12-bit readout resolution calls for an LSB of only
7.3μV…..almost 120dB below the common mode signal!
Other significant error terms include offset voltage, and
its shift with temperature and time, bias current and gain
stability. Figure 2 shows an “Instrumentation Amplifier,”
which makes a very good bridge amplifier. These devices
are usually the first choice for bridge measurement,
and bring adequate performance to most applications.
Note 1:
Wheatstone had a better public relations agency, namely himself.
For fascinating details, see reference 19.
L,
LT, LTC, LTM, Linear Technology and the Linear logo are registered trademarks of Linear
Technology Corporation. All other trademarks are the property of their respective owners.
an43f
and stability of the basic configuration. In particular, trans-
ducer manufacturers are quite adept at adapting the bridge
to their needs (see Appendix A, “Strain Gauge Bridges”).
Careful matching of the transducer’s mechanical charac-
teristics to the bridge’s electrical response can provide a
trimmed, calibrated output. Similarly, circuit designers
have altered performance by adding active elements (e.g.,
amplifiers) to the bridge, excitation source or both.
R
A
DIFFERENTIAL
OUTPUT
VOLTAGE
R
B
R
C
EXCITATION
VOLTAGE
Figure 1. The Basic Wheatstone Bridge,
Invented by S. H. Christie
+
R
D
AN43 F01
AN43-1
Application Note 43
In general, instrumentation amps feature fully differential
inputs and internally determined stable gain. The absence
of a feedback network means the inputs are essentially pas-
sive, and no significant bridge loading occurs. Instrumenta-
tion amplifiers meet most bridge requirements. Figure 3
lists performance data for some specific instrumentation
amplifiers. Figure 4’s table summarizes some options
for DC bridge signal conditioning. Various approaches
are presented, with pertinent characteristics noted. The
constraints, freedoms and performance requirements of
any particular application define the best approach.
+
–
NO FEEDBACK RESISTORS USED
GAIN FIXED INTERNALLY (TYP 10 OR 100)
OR SOMETIMES RESISTOR PROGRAMMABLE
AN43 F02
BALANCED, PASSIVE INPUTS
100, with additional trimmed gain supplied by A1B. The
configuration shown may be adjusted for a precise 10V
output at full-scale pressure. The trim at the bridge sets
the zero pressure scale point. The RC combination at A1B’s
input filters noise. The time constant should be selected
for the system’s desired lowpass cutoff. “Noise” may
originate as residual RF/line pick-up or true transducer
responses to pressure variations. In cases where noise
is relatively high it may be desirable to filter ahead of A3.
This prevents any possible signal infidelity due to nonlinear
A3 operation. Such undesirable outputs can be produced
by saturation, slew rate components, or rectification
effects. When filtering ahead of the circuits gain blocks
remember to allow for the effects of bias current induced
errors caused by the filter’s series resistance. This can be
a significant consideration because large value capacitors,
particularly electrolytics, are not practical. If bias current
induced errors rise to appreciable levels FET or MOS input
amplifiers may be required (see Figure 3).
To trim this circuit apply zero pressure to the transducer
and adjust the 10k potentiometer until the output
just
comes off 0V. Next, apply full-scale pressure and trim the
1k adjustment. Repeat this procedure until both points
are fixed.
Common Mode Suppression Techniques
Figure 6 shows a way to reduce errors due to the bridges
common mode output voltage. A1 biases Q1 to servo the
bridges left mid-point to zero under all operating condi-
tions. The 350Ω resistor ensures that A1 will find a stable
operating point with 10V of drive delivered to the bridge.
This allows A2 to take a single-ended measurement,
LTC1043
(USING LTC1050 AMPLIFIER)
0.5μV
50nV/°C
10pA
1.6μV
Resistor Programmable
Resistor Limited 0.001% Possible
Resistor Limited <1ppm/°C Possible
Resistor Limited 1ppm Possible
160dB
Single, Dual 18V Max
2mA
1mV/ms
10Hz
Figure 2. Conceptual Instrumentation Amplifier
DC Bridge Circuit Applications
Figure 5, a typical bridge application, details signal con-
ditioning for a 350Ω transducer bridge. The specified
strain gauge pressure transducer produces 3mV output
per volt of bridge excitation (various types of strain-based
transducers are reviewed in Appendix A, “Strain Gauge
Bridges”). The LT
®
1021 reference, buffered by A1A and
A2, drives the bridge. This potential also supplies the
circuits ratio output, permitting ratiometric operation of
a monitoring A/D converter. Instrumentation amplifier
A3 extracts the bridge’s differential output at a gain of
PARAMETER
Offset
Offset Drift
Bias Current
Noise (0.1Hz to 10Hz)
Gain
Gain Error
Gain Drift
Gain Nonlinearity
CMRR
Power Supply
Supply Current
Slew Rate
Bandwidth
LTC1100
10μV
100nV/°C
50pA
2μV
P-P
100
0.03%
4ppm/°C
8ppm
104dB
Single or Dual, 16V Max
2.2mA
1.5V/μs
8kHz
LT1101
LT1102
500μV
2.5μV/°C
50pA
2.8μV
10,100
0.05%
5ppm/°C
10ppm
100dB
Dual, 44V Max
5mA
25V/μs
220kHz
160μV
2μV/°C
8nA
0.9μV
10,100
0.03%
4ppm/°C
8ppm
100dB
Single or Dual, 44V Max
105μA
0.07V/μs
33kHz
Figure 3. Comparison of Some IC Instrumentation Amplifiers
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AN43-2
Application Note 43
CONFIGURATION
+V
RATIO
OUT
ADVANTAGES
Best general choice. Simple,
straightforward. CMRR typically
>110dB, drift 0.05μV/°C to 2μV/°C,
gain accuracy 0.03%, gain drift
4ppm/°C, noise 10nV√Hz – 1.5μV
for chopper-stabilized types. Direct
ratiometric output.
DISADVANTAGES
CMRR, drift and gain stability
may not be adequate in highest
precision applications. May require
second stage to trim gain.
+
OUT
–
INSTRUMENTATION
AMPLIFIER
AN43 F04a
+V
RATIO
OUT
+
OUT
–
CMRR > 120dB, drift 0.05μV/°C.
Gain accuracy 0.001% possible.
Gain drift 1ppm with appropriate
resistors. Noise 10nV√Hz – 1.5μV
for chopper-stabilized types. Direct
ratiometric output. Simple gain
trim. Flying capacitor commutation
provides lowpass filtering. Good
choice for very high performance—
monolithic versions (LTC1043)
available.
Multi-package—moderately
complex. Limited bandwidth.
Requires feedback resistors to set
gain.
OP AMP
AN43 F04b
+
OUT
CMRR > 160dB, drift 0.05μV/°C to
0.25μV/°C, gain accuracy 0.001%
possible, gain drift 1ppm/°C with
appropriate resistors plus floating
supply error, simple gain trim,
Noise 1nV√Hz possible.
Requires floating supply. No direct
ratiometric output. Floating supply
drift is a gain term. Requires
feedback resistors to set gain.
+V
–V
+
–
AN43 F04c
OP AMP
CMRR ≈ 140dB, drift 0.05μV/°C to
0.25μV/°C, gain accuracy 0.001%
possible, gain drift 1ppm/°C with
appropriate resistors plus floating
supply error, simple gain trim,
noise 1nV√Hz possible.
+
OUT
–
AN43 F04d
No direct ratiometric output.
Zener supply is a gain and offset
term error generator. Requires
feedback resistors to set gain.
Low impedance bridges require
substantial current from shunt
regulator or circuitry which
simulates it. Usually poor choice if
precision is required.
OP AMP
Figure 4. Some Signal Conditioning Methods for Bridges
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AN43-3
Application Note 43
CONFIGURATION
+V
RATIO
OUT
ADVANTAGES
CMRR > 160dB, drift 0.05μV/°C to
0.25μV/°C, gain accuracy 0.001%
possible, gain drift 1ppm/°C with
appropriate resistors, simple gain
trim, ratiometric output, noise
1nV√Hz possible.
OUT
DISADVANTAGES
Requires precision analog level
shift, usually with isolation
amplifier. Requires feedback
resistors to set gain.
–
+
OP AMP
AN43 F04e
+V
RATIO
OUT
+
OUT
–
AN43 F04f
OP AMP
–V
+V
RATIO
OUT
+
–
+
OUT
–
AN43 F04g
OP AMP
Figure 4. Some Signal Conditioning Methods for Bridges (Continued)
eliminating all common mode voltage errors. This approach
works well, and is often a good choice in high precision
work. The amplifiers in this example, CMOS chopper-sta-
bilized units, essentially eliminate offset drift with time and
temperature. Trade-offs compared to an instrumentation
amplifier approach include complexity and the require-
ment for a negative supply. Figure 7 is similar, except that
low noise bipolar amplifiers are used. This circuit trades
slightly higher DC offset drift for lower noise and is a good
candidate for stable resolution of small, slowly varying
measurands. Figure 8 employs chopper-stabilized A1 to
AN43-4
+
+
CMRR ≈ 120dB to 140dB, drift
0.05μV/°C to 0.25μV/°C, gain
accuracy 0.001% possible, gain
drift 1ppm/°C with appropriate
resistors, simple gain trim, direct
ratiometric output, noise 1nV√Hz
possible.
Requires tracking supplies.
Assumes high degree of bridge
symmetry to achieve best CMRR.
Requires feedback resistors to set
gain.
CMRR = 160dB, drift 0.05μV/°C to
0.25μV/°C, gain accuracy 0.001%
possible, gain drift 1ppm/°C,
simple gain trim, direct ratiometric
output, noise 1nV√Hz possible.
Practical realization requires two
amplifiers plus various discrete
components. Negative supply
necessary.
reduce Figure 7’s already small offset error. A1 measures
the DC error at A2’s inputs and biases A1’s offset pins to
force offset to a few microvolts. The offset pin biasing at
A2 is arranged so A1 will always be able to find the servo
point. The 0.01μF capacitor rolls off A1 at low frequency,
with A2 handling high frequency signals. Returning A2’s
feedback string to the bridges mid-point eliminates A4’s
offset contribution. If this was not done A4 would require
a similar offset correction loop. Although complex, this
approach achieves less than 0.05μV/°C drift, 1nV√Hz noise
and CMRR exceeding 160dB.
an43f
Application Note 43
15V
15V
15V
+
A2
LT1010
A1A
1/2 LT1078
LT1021
10V
–
350Ω STRAIN GAGE
PRESSURE TRANSDUCER
15V
10k
ZERO
301k*
10V RATIO
OUTPUT
+
–
A3
LT1101
A = 100
100k
0.33
+
A1B
1/2 LT1078
–
OUTPUT
0V TO 10V =
0 TO 250 PSI
10k*
*1% FILM RESISTOR
PRESSURE TRANSDUCER =
BLH #DHF-350—3MV/VOLT GAIN FACTOR
3.65k*
1k – GAIN
AN43 F05
Figure 5. A Practical Instrumentation Amplifier-Based Bridge Circuit
350Ω
1/2W
15V
OUTPUT
TRIM
100Ω
RATIO
OUTPUT
10μF
0.02
250*
100k*
A1
LTC1150
1k
*1% FILM RESISTOR
Q1
2N2905
–15V
Figure 6. Servo Controlling Bridge Drive Eliminates Common Mode Voltage
Single Supply Common Mode Suppression Circuits
The common mode suppression circuits shown require a
negative power supply. Often, such circuits must function
in systems where only a positive rail is available. Figure 9
shows a way to do this. A2 biases the LTC
®
1044 positive-
to-negative converter. The LTC1044’s output pulls the
bridge’s output negative, causing A1’s input to balance at
0V. This local loop permits a single-ended amplifier (A2)
to extract the bridge’s output signal. The 100k-0.33μF RC
filters noise and A2’s gain is set to provide the desired
output scale factor. Because bridge drive is derived from
the LT1034 reference, A2’s output is not affected by supply
shifts. The LT1034’s output is available for ratio operation.
Although this circuit works nicely from a single 5V rail the
transducer sees only 2.4V of drive. This reduced drive
an43f
+
100k
350Ω
STRAIN
GAUGE
BRIDGE
3MV/V
TYPE
–
A2
LTC1150
OUTPUT
0V TO 10V
AN43 F06
+
–
+
AN43-5
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