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Texas Instruments Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor (Rev. A) Application notes
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SLDA032A – May 2015 – Revised May 2019
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Application Report
SLDA032A – May 2015 – Revised May 2019
Connecting PGA900 Instrumentation Amplifier to
Resistive Bridge Sensor
Miro Oljaca, Peter Semig, Collin Wells.......................................... Enhanced Industrial and Precision Analog
ABSTRACT
Understanding the input and output limitations of an instrumentation amplifier (IA) is important in
interfacing a resistive bridge sensor to the PGA900. Adjusting the common mode voltage of the input
signal appropriately allows you to maximize the gain. Maximizing the gain yields the largest output signal
span for the 24-bit analog-to-digital converter (ADC). The largest signal span maximizes the code
utilization and effective noise-free resolution. This application report discusses the limitations of the signal
sensor, IA, and PGA900. This report shows that by adding two resistors to the bridge, it is possible to
increase the resolution compared to directly connecting the bridge to the PGA900.
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3
4
5
6
7
8
9
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Contents
Ideal Resistive Bridge Sensor .............................................................................................. 3
Real Resistive Bridge Sensor .............................................................................................. 5
Definition of the Differential Signal ........................................................................................ 7
Interfacing Resistive Bridge Sensor to PGA900 ......................................................................... 8
Input and Output Voltage Limitations of PGA900's IA .................................................................. 9
Selecting Bridge Excitation Voltage ...................................................................................... 10
Design Example ............................................................................................................ 11
Conclusion .................................................................................................................. 12
References .................................................................................................................. 12
1
Pressure Sensor Operating Principle ..................................................................................... 3
2
Resistive Bridge Sensor Without Pressure Applied ..................................................................... 3
3
Resistive Bridge Sensor With Pressure Applied ......................................................................... 4
4
Resistive Bridge Sensor .................................................................................................... 4
5
Real Resistive Bridge Sensor Without Pressure Applied............................................................... 5
6
Resistive Bridge Output Voltages
List of Figures
7
8
9
10
2
......................................................................................... 7
PGA900 Instrumentation Amplifier Input Stage .......................................................................... 8
Resistive Bridge Sensor With Added Top and Bottom Resistors .................................................... 10
P_Gain Transfer Function for Only Resistive Bridge .................................................................. 11
P_Gain Transfer Function for Resistive Bridge With Added Bottom and Top Resistor ........................... 12
Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor
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Ideal Resistive Bridge Sensor
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Ideal Resistive Bridge Sensor
Resistive bridge sensors are widely used in the industry for measuring different physical properties like
pressure and temperature. A real sensor differs from an ideal one by introducing limitations that the
designer must take into account when designing a measurement system. Figure 1 depicts a pressure
sensor element from Metallux AG. The center of the sensor element has four resistors. When pressure is
applied, two resistors are stretched and other two are compressed as shown in Figure 1.
Figure 1. Pressure Sensor Operating Principle
These four resistive sensor elements are connected as a Wheatstone bridge as shown in Figure 2. When
no external pressure is applied, four bridge resistors for the ideal sensor have the same initial value R and
output voltage between nodes B and D, VBD, is zero.
R
+
A
B
R
D
±
R
C
R
Figure 2. Resistive Bridge Sensor Without Pressure Applied
When the resistive bridge from Figure 1 and Figure 2 is exposed to the physical signal, in this case
pressure, the four resistors change value. The resistance of the stretched resistors increases, while the
resistance of the compressed resistors decreases. Referring to Figure 2, resistors with the same behavior
are placed on opposite sides of the bridge. Compressed resistors are placed between nodes A and B,
RAB, and nodes C and D, RCD. Stretched resistors are placed between nodes C and B, RCB, and nodes D
and A, RDA.
Change in resistance is proportional to the applied excitation or pressure. For the full range of physical
excitation, the bridge resistors have a maximum change in value, RSPAN, that produces the maximum
differential output voltage. Figure 3 shows that RSPAN is added or subtracted from the ideal resistance, R,
depending on whether the resistor is stretched or compressed, respectively.
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Ideal Resistive Bridge Sensor
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Compressed
R ± RSPAN
+
Stretched
R + RSPAN
A
B
D
±
Stretched
R + RSPAN
Compressed
R ± RSPAN
C
Figure 3. Resistive Bridge Sensor With Pressure Applied
For future analysis, the four bridge resistors R1, R2, R3, and R4 are defined in through Equation 1.
R1 =
R2 =
R3 =
R4 =
RAB = R − RSPAN
RBC = R + RSPAN
RDA = R + RSPAN
RCD = R − RSPAN
(1)
Using Equation 1, Figure 3 can be redrawn as shown in Figure 4.
R1
+
A
B
R3
D
±
R2
C
R4
Figure 4. Resistive Bridge Sensor
4
Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor
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Real Resistive Bridge Sensor
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Real Resistive Bridge Sensor
Despite good sensor manufacturing processes, imperfections can lead to differences in initial resistor
values. The initial values of the four bridge resistors are not equal, which results in different initial output
voltages for each sensor. For a real sensor, two parameters define the output voltages at nodes B and D.
First, Equation 2 defines the common-mode voltage (VCM).
VBC VDC
VCM
2
(2)
Secondly, Equation 3 defines the offset voltage (VOFFSET) with no external applied pressure.
VOFFSET = VBD
(3)
As previously mentioned, these two parameters are a consequence of the initial values of the bridge
resistor. Equation 4 and Figure 5 show this relationship.
R1 =
R2 =
R3 =
R4 =
R
R
R
R
+
+
+
+
ΔR1
ΔR2
ΔR3
ΔR4
(4)
R + ûR1
+
A
B
R + ûR3
D
±
R + ûR2
C
R + ûR4
Figure 5. Real Resistive Bridge Sensor Without Pressure Applied
An example of a real sensor is initial values for 10-kΩ sensor are shown in Equation 5.
R1 =
R2 =
R3 =
R4 =
9.4 kΩ
10.6 kΩ
9.6 kΩ
10.4 kΩ
(5)
Using the values from Equation 5, calculate the initial change in the resistance for every resistor by
applying Equation 4.
ΔR1 =
ΔR2 =
ΔR3 =
ΔR4 =
–0.6 kΩ
+0.6 kΩ
–0.4 kΩ
+0.4 kΩ
(6)
The initial change in resistance for each resistor in the bridge contributes to the common-mode and offset
error. You can rewrite Equation 6 using Equation 2 and Equation 3 as shown in Equation 7. RCM and
ROFFSET represent the common-mode and offset error contribution.
ΔR1 =
ΔR2 =
ΔR3 =
ΔR4 =
–RCM – ROFFSET
+RCM + ROFFSET
–RCM + ROFFSET
+RCM – ROFFSET
(7)
Three coefficients that are interesting in where describing a real sensor in a final application are the initial
common-mode voltage, initial offset voltage, and output span voltage. All three output voltages, VCM,
VOFFSET, and VSPAN are a function of the bridge excitation voltage, or voltage apply between inputs A and C,
VAC. For future analysis, it is more convenient to define the output voltage coefficients as shown in
Equation 8.
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Real Resistive Bridge Sensor
k CM
1 RCM
R
ROFFSET
R
0.5 u
k OFFSET
k SPAN
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RSPAN
R
(8)
To understand differential signal values, use following example. The restive bridge has a nominal value of
10 kΩ. Common mode resistance is 500 Ω, offset resistance is 100 Ω, and span resistance is 10 Ω. Based
on these values, you can now calculate corresponding voltage coefficients.
kCM = 525 mV/V
kOFFSET = 10 mV/V
kSPAN = 1 mV/V
(9)
Select a bridge excitation voltage of 1.25 V. Now it is easy to calculate corresponding components of the
differential voltage signal.
VCM = kCM × VEXT = 656.25 mV
VOFFSET = kOFFSET × VEXT = 12.5 mV
VSPAN = kSPAN × VEXT = 1.25 mV
6
Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor
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Definition of the Differential Signal
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Definition of the Differential Signal
Differential signaling is a method for electrically transmitting information using two complementary signals.
The technique sends the same electrical signal as a differential pair of signals, each in its own conductor.
The signals on the two conductors are of opposite polarity so their waveforms are mirror images. The
receiving circuit responds to the electrical difference between the two signals rather than the difference
between a single wire and ground.
A resistive bridge sensor as shown in Figure 2 provides a differential signal between nodes B and D. If
you include the previously defined common-mode, offset, and span voltages, you can replace the resistive
bridge sensor with an equivalent circuit as shown in Figure 6.
±
±
+
±
+
±
+
+
VCM
VSPAN / 2
+
VOFFSET / 2
B
D
±
C
VOFFSET / 2
VSPAN / 2
Figure 6. Resistive Bridge Output Voltages
The voltages at nodes B and D are given in Equation 11 and Equation 12, respectively.
VB = VCM + ½ VOFFSET + ½ VSPAN
VD = VCM – ½ VOFFSET – ½ VSPAN
(11)
(12)
Now you have all the values needed to calculate output voltages at the pins B and D in the example. Use
Equation 11, Equation 12, and Equation 10. Voltages from initial values to the full span are:
VB = 662.5 ... 663.13 mV
VD = 649.38 ... 650 mV
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Interfacing Resistive Bridge Sensor to PGA900
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Interfacing Resistive Bridge Sensor to PGA900
An instrumentation amplifier (IA) is typically used to interface with a resistor bridge sensor because of the
amplifier's high input impedance. Figure 7 shows the input gain stage of the IA as implemented in the
PGA900.
+
t
VINPP
VDIFF/2
VOPP
RF
RF
±
+
+
RG
±
+
VCM
±
VDIFF/2
VINPN
t
+
VOPN
PGA900
Figure 7. PGA900 Instrumentation Amplifier Input Stage
In Figure 7, offset and span signals are replaced with more commonly used input differential signal.
VDIFF = VOFFSET + VSPAN
(14)
The IA output voltages, VOPP and VOPN, are defined in Equation 15 and Equation 16, respectively.
VOPP = VCM +
9OPN
9CM ±
VDIFF §
u ¨1
2
©
VDIFF §
u¨
2
©
2
RF ·
¸
RG ¹
(15)
RF ·
¸
RG ¹
(16)
The PGA900 has digitally programmable gain that ranges from 5 V/V up to 400 V/V. This gain can be set
up using P_GAIN bits.
R
PGAIN = 1 + 2 F
RG
(17)
Replacing Equation 17 into Equation 15 and Equation 16, you have the final description of the output
voltages.
VDIFF
VOPP VCM
u PGAIN
(18)
2
V
9OPN 9CM ± DIFF u 3*$,1
2
(19)
8
Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor
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Input and Output Voltage Limitations of PGA900's IA
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Input and Output Voltage Limitations of PGA900's IA
The IA input stage of the PGA900 has a differential output. This output is fed directly into a 24-bit ΔΣ ADC.
The applied sensor signal to the PGA900 has two main constraints. The absolute value of the input signal
to VINPP and VINPN must be in the range from 0.3 V to 1.8 V. If one or both signals violate one of these
limits, the quality of the output signal is compromised.
VINPP, VINPN ∈ (0.3 V ...1.8 V)
(20)
The second limitation is related to the range of the IA output signals. Both output IA signals, VOPP and
VOPN, must be in the range from 0.1 to 2.0 V. If the input signal or IA gain is not properly set and the output
signal of one or both signals violate one of these limits, the integrity of the signal is not linear.
VOPP, VOPN ∈ (0.1 V ... 2.0 V)
(21)
Using Equation 20 and Equation 21 and the transfer function graph for the, IA, you can plot boundaries for
the input and output signals ensure optimal operation.
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Selecting Bridge Excitation Voltage
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Selecting Bridge Excitation Voltage
Before you analyzed voltages, that sensor provides to the input of IA and voltages on the output. You saw
that the input common-mode voltage is equal to the output common-mode voltage. Also, you saw that the
input differential voltage is much smaller than output. Based on these two parameters you can see that
ideally, you would like the common-mode voltage to be as close as possible to the middle point of the IA
output voltage range.
VCM_IN = VCM_OUT
VCM_IDEAL
(22)
0.1 V + 2.0 V
= 1.05 V
2
(23)
The PGA900 has an internal buffer with selectable voltage for the bridge supply. The bridge voltage can
be selected between 1.25, 2.0, and 2.5 V. These voltages are created from an internal 2.5-V precision
reference. The bridge supply voltage is selected using the VBRDG_CTRL register.
In some applications, it is important to minimize power dissipation in the sensor element. For that reason,
smaller excitation voltage applied to the sensor is desired. Unfortunately, smaller excitation voltages
reduces input signal common mode voltage and limits the IA gain. To overcome this problem, it is
desirable to add top and bottom resistors to the sensor bridge. These resistors reduce sensor excitation
voltage, and at the same time position, the input signal common mode voltage as close as possible to the
ideal value.
RTOP
R1
+
A
R3
B
D
±
R2
R4
C
RBOTTOM
Figure 8. Resistive Bridge Sensor With Added Top and Bottom Resistors
The resistive bridge sensor from Figure 4 is redrawn by adding top and bottom resistors and shown in
Figure 8.
Using resistive bridge values and added top and bottom resistors, you can now define the bridge voltage
between nodes A and C as:
R
VAC
u VEXT
R RTOP RBOTTOM
(24)
For the new common mode voltage calculation, use Equation 25 and Equation 26.
RBOTTOM
R
VCM
u VEXT k CM u
u VEXT
R RTOP RBOTTOM
R RTOP RBOTTOM
VCM
10
RBOTTOM
R RTOP
k CM u R
u VEXT
RBOTTOM
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Design Example
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Design Example
For this example, limit the maximum voltage at the sensor to 1.6 V and use a 10-kΩ resistive bridge
sensor.
First, calculate resolution when connecting the sensor directly to the PGA900 without any additional top or
bottom resistor. Select 1.25 V as a bridge excitation voltage. The next available option is 2.0 V, which
violates the initial design criteria. From Equation 10, you can see that the common mode voltage is 656.25
mV. The full span input differential signal is 13.75 mV. For this input voltage, you can apply gain of 80
V/V. With this gain, output voltages VOPP and VOPN are 1.206 V and 0.106 V respectively. The PGA900
P_Gain transfer function given these conditions is shown in Figure 9.
2.5
Output Voltage (V)
2
Unused
Range
1.5
1
Used
Range
0.5
0
0
0.5
1
1.5
2
Input Voltage (V)
2.5
D001
Figure 9. P_Gain Transfer Function for Only Resistive Bridge
Signal from P_Gain is passed to the 24-bit ADC with full scale range (FSR) of 5 V. After gaining the input
span voltage of 1.25 mV by 80 V/V, the output span voltage is 100 mV. The resolution of the ADC is 298
nV and span voltage can be presented with 335544 different codes. If you neglect noise, this gives you an
effective measurement signal resolution of 18.36 bit.
5V
1 LSB
298 nV
(27)
224
PGain u VSPAN
codes
335544
1 LSB
(28)
ln 335544
Effective measurement resolution
18.36 bit
ln 2
(29)
The second step is to add bottom and top resistors. This permits you to use higher excitation voltage and
have a maximum available voltage of 1.6 V on the bridge. Now, select PGA900 bridge output voltage of
2.0 V and add 1.33 kΩ at the bottom and 1.18 kΩ on the top of the resistor bridge. In this configuration,
the common mode voltage is 1.052 V, which is very close to ideal one calculated using Equation 23. Full
span input differential signal is 17.59 mV. For this input voltage, apply a gain of 100 V/V. With this gain
output, voltages VOPP and VOPN are 1.931 V and 0.173 V, respectively. The new PGA900 P_Gain transfer
function for these conditions is shown in Figure 10.
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Conclusion
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2.5
Output Voltage (V)
2
Unused Range
1.5
Used Range
1
0.5
Unused Range
0
0
0.5
1
1.5
Input Voltage (V)
2
2.5
D002
Figure 10. P_Gain Transfer Function for Resistive Bridge With Added Bottom and Top Resistor
After gaining input span voltage of 1.59 mV by 100 V/V output span, voltage is 159 mV. As you saw
before with ADC resolution of 298 nV, span voltage can be presented with 536442 different codes
compare to previous one of 335544. If you neglect noise, this gives you an effective measurement signal
resolution of 19.3 bit, which is an increase compared to the previous one of 18.36 bit.
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Conclusion
Understanding input and output limitations of the IA is important in interfacing resistive bridge sensor. If
the common mode voltage of the input signal is positioned close to ideal, it is possible to use a higher
gain. This produces a higher output signal span voltage for the 24-bit ADC. As the resolution of the ADC is
fixed, higher gain permits to measure input signal with a higher number of codes or ENOB is higher. In
this application report looked at the limitation of the signal sensor, IA, and PGA900. The application report
showed that it is possible to add two resistors in the signal path to increase resolution as compared to
directly connecting the bridge to the IA.
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References
1. Neil P. Albaugh, The Instrumentation Amplifier Handbook, Burr-Brown, 2000.
2. Texas Instruments, Op Amps for Everyone Design Guide (SLOD006)
3. Charles Kitchin and Lew Counts, A Designer’s Guide to Instrumentation Amplifiers, Third Edition,
Analog Devices, 2006.
4. Texas Instruments, Getting the Most Out of Your Instrumentation Amplifier Design Technical Brief
(SLYT226)
5. Peter Semig, Instrumentation Amplifier VCM vs. VOUT Plots: Part 1, EDN, December 2014
6. Peter Semig, Instrumentation Amplifier VCM vs. VOUT Plots: Part 2, EDN, December 2014
7. Peter Semig, Instrumentation Amplifier VCM vs. VOUT Plots: Part 3, EDN, December 2014.
8. Metallux AG, Pressure Sensors
12
Connecting PGA900 Instrumentation Amplifier to Resistive Bridge Sensor
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Revision History
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Revision History
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from Original (May 2015) to A Revision ........................................................................................................... Page
•
•
Edited application report for clarity. ..................................................................................................... 2
Updated content in the Ideal Resistive Bridge Sensor section. ..................................................................... 3
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