dm00133498

AN4586
Application note
Signal conditioning, differential to single-ended amplification
Sylvain Colliard Piraud
Introduction
There is a wide range of applications for which we need to amplify a differential signal and
convert it into a single-ended signal. Such applications can be used to condition the signal
of Wheatstone bridges, current measurements, or other small signal sources that require an
accurate measurement which rejects input common mode voltage (Vicm).
There are different ways to amplify a differential voltage into a single-ended signal. In this
document we will see the three more flexible methods that are based on operational
amplifiers (op amps):
• Differential amplifier
• 2-op amp instrumentation amplifier
• 3-op amp instrumentation amplifier
For each configuration, the output voltage is calculated to include the inaccuracies due to
the external components (the resistors) and the op amp itself. The common mode rejection
ratio (CMRR) is also calculated. If we consider a perfect op amp and if the resistors are
ideally matched, the CMRR should be infinite.
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19
Contents
AN4586
Contents
1
Error contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2
Differential configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3
2-op amp instrumentation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4
3-op amp instrumentation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6
Circuits with a single supply voltage . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7
Precision op amps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
8
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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Error contributions
Error contributions
The error contributions which are taken into account in this application note include:
•
Resistor inaccuracies
•
Main op amp contribution which is the input offset voltage (Vio) (see Figure 1).
Figure 1. Input offset voltage
9LR
The Vio can be either positive or negative. Also, it can vary with the op amp CMRR, but this
parameter is not taken into account in this document.
In the different configurations below, the output voltage formula is written with and without
the error inaccuracies.
When we consider the error inaccuracies, eR corresponds to the resistor accuracy. For
example, it can be 1 %.
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Differential configuration
2
AN4586
Differential configuration
The differential configuration needs only one op amp and is easily set-up. Consequently, it is
widely used.
Figure 2 shows the differential configuration schematic.
Figure 2. Differential configuration schematic
5I
5J
9
9
9LR
5J
5I
If we do not consider the inaccuracies, we have Equation 1 at the output.
Equation 1
Rf1
1 + ----------Rf1
Rf2
Rg1
Vout = V2 ----------- --------------------- – V1 ----------Rf2
Rg1
Rg2
1 + ----------Rg2
Considering Rf1 = Rf2 = Rf and Rg1 = Rg2 = Rg, we get Equation 2
Equation 2
Rf
Vout = ( V2 – V1 ) -------Rg
Note that the op amp must be used in dual supply if V1 > V2. An alternative option is to use
a reference voltage on Rf2 rather than ground and use the op amp in single supply.
Considering the op amp and resistor inaccuracies and with Rf1 = Rf2 = Rf and
Rg1 = Rg2 = Rg, we get Equation 3
Equation 3
Rg
⎛ Rf + Rg
⎛
--------⎞⎠ ( ε Rf1 – ε Rg1 ) + -------- ( ε Rf2 – ε Rg2 )⎞
⎝
⎜
⎟
2
2
Rf
Vout = ( V2 – V1 ) -------- ⎜ 1 + ---------------------------------------------------------------------------------------------------------------⎟
Rg ⎜
Rf + Rg
⎟
⎝
⎠
V1 + V2 Rf
Rf
+ --------------------- -------------------- ( ε Rf2 – ε Rf1 – ε Rg2 + ε Rg1 ) – Vio ⎛ 1 + -------- ( 1 + ε Rf1 – ε Rg1 )⎞
⎝
⎠
2
Rg + Rf
Rg
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Differential configuration
Considering all the resistors have the same tolerance, ε:
•
The worst case for the offset on the output voltage is:
Rf
±Vio ⎛ 1 + -------- ( 1 + 2ε )⎞
⎝
⎠
Rg
•
The worst case for the differential gain is:
Rf
-------- ( 1±2ε )
Rg
•
The worst case for the common mode gain is:
Rf
--------------------4ε
Rf + Rg
When we talk about differential configuration, it is important to note that a mismatching
between resistors impacts the output voltage. This impact is measured by the CMRR. Vicm
can only be partially rejected if the resistors are not perfectly marched. The following CMRR
calculations highlight the impact of the resistor inaccuracies. Note that for the CMRR
calculation, we do not take into account the Vio variation (caused by the CMRR of the op
amp).
Equation 4
V1 + V2
Vout = Gdiff ( V2 – V1 ) + Gcm --------------------2
Equation 5
Rf
⎛ 1 + --------⎞
Gdiff
Rg
CMRR = 20 log ⎛⎝ --------------⎞⎠ = 20 log ⎜⎜ ------------------⎟⎟
Gmc
4ε
⎝
⎠
Therefore, the CMRR can be calculated for different gain and resistor inaccuracies (see
Table 1).
Table 1. CMRR for differential configuration
CMRR (dB)
Resistor inaccuracy (%)
Gain = 1
Gain = 10
Gain = 100
10
14
29
48
1
34
49
68
0.1
54
69
88
Thus, for accurate measurements it is recommended to use high accuracy resistors. It helps
to reject Vicm.
Regarding Vicm, there is a last criterion that has to be considered for the differential
configuration. It is the Vicm range of the op amp. In order to make the application work, the
Vicm should not exceed the capabilities of the op amp (see example in Figure 3).
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Differential configuration
AN4586
Figure 3. Differential configuration example
NŸ
5I
NŸ
9 9
5J
5J
9 9
9LR
5I
NŸ
NŸ
In Figure 3, the Vicm of the op amp is 9 V. Thus, if the op amp is supplied by 5 V, we cannot
measure the voltage difference. We may even damage the op amp.
The op amp Vicm range is given as follows:
Rf2
V2 ⋅ ---------------------------Rf2 + Rg2
If Vref is applied on Rf2, the op amp Vicm range becomes:
Vref
V2
--------------------- + --------------------Rf2
Rg2
1 + ----------- 1 + ----------Rg2
Rf2
A drawback of the differential configuration is its input impedance. This is defined by the
resistors and consequently it may not be high enough. Below are given the differential and
common mode impedances respectively:
Zdiff = 2Rg
Rg + Rf
Zcm = -------------------2
A high input impedance may be mandatory in certain cases so as not to impact the signal
being measured. For this reason the instrumentation amplifier configuration has been
designed (see Section 3).
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2-op amp instrumentation amplifier
2-op amp instrumentation amplifier
The 2-op amp instrumentation amplifier configuration is composed of one additional op-amp
compared to the differential configuration. Because of this, the signal “sees” a high
impedance and consequently is not impacted.
Figure 4 shows the 2-op amp instrumentation amplifier schematic.
Figure 4. 2-op amp instrumentation amplifier schematic
5I
5I
5J
9LR
9RXW
5J
9LR
9RXW
9
9
If we do not consider the inaccuracies, we have Equation 6 at the output.
Equation 6
Rf2
Rf2
Rf1
Vout2 = V2 ⎛ 1 + -----------⎞ – V1 ----------- ⎛ 1 + -----------⎞
⎝
Rg2 ⎝
Rg2⎠
Rg1⎠
Considering Rf1 = Rg2 = Rβ, Rg1 = Rf2 = Rα, and the input offset voltage of the op
amp, we get Equation 7:
Equation 7
Rα
Rα
Vout2 = ( V2 – V1 ) ⎛⎝ 1 + -------⎞⎠ – ( Vio2 – Vio1 ) ⎛⎝ 1 + -------⎞⎠
Rβ
Rβ
So, we get Equation 8:
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Equation 8
í
Considering all the resistors have the same tolerance, ε:
•
The worst case for the offset on the output voltage is:
Rα
±2Vio ⎛ 1 + ------- ( 1 + 2ε )⎞
⎝
⎠
Rβ
•
The worst case for the differential gain is:
⎛ 1 + Rα
-------⎞⎠ ( 1±2ε )
⎝
Rβ
•
The worst case for the common mode gain is:
4ε
Similar to differential configuration, when there is mismatching between resistors, the
CMRR is impacted. Thus, the output voltage is also impacted and the measurement
accuracy deteriorates. In order to quantify this impact, we calculate the CMRR using
Equation 9.
Equation 9
Rα
⎛ 1 + -------⎞
Gdiff
Rβ
CMRR = 20 log ⎛⎝ --------------⎞⎠ ≈ 20 log ⎜⎜ -----------------⎟⎟
Gmc
4ε
⎝
⎠
For high gain, the CMRR of the 2-op amp instrumentation amplifier is similar to the CMRR of
the differential amplifier. However, the main advantage of the current configuration is that it
offers high input impedance. Note also that it cannot be used in unity gain.
Regarding the Vicm range, the following conditions must be met to make the 2-op amp
instrumentation amplifier work:
•
V1 and V2 must be included within the op amp’s Vicm range
•
To avoid that the output of the first op amp is saturated:
Vcc
V1 < --------------------Rf1
1 + ----------Rg1
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2-op amp instrumentation amplifier
Figure 5 shows where the second condition has not been met and the first op amp has
become saturated.
Figure 5. 2-op amp instrumentation amplifier example
5I
5I
N7
N7
5J
N7
9RXW
5J
N7
9RXW
9 9
9 9
In Figure 5, with Vcc = 5 V
Vcc
--------------------- = 4.17 V
Rf1
1 + ----------Rg1
Thus, we do not have
Vcc
V1 < --------------------Rf1
1 + ----------Rg1
This means that the first op amp is saturated and Vout2 is not equal to the expected value:
(4.3 V - 4.2 V) * (1 + 10 k / 2 k) = 0.6 V.
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3-op amp instrumentation amplifier
4
AN4586
3-op amp instrumentation amplifier
The 3-op amp instrumentation amplifier configuration has been designed to improve the
CMRR impacted by the resistors, and thus to improve measurement accuracy when Vicm
varies.
Figure 6 shows the schematic of a 3-op amp instrumentation amplifier.
Figure 6. 3-op amp instrumentation amplifier schematic
9
5
9RXW
9LR
5
5
9RXW
9LR
5J
5
9LR
9
5
5
9RXW
The output voltage of the 3-op amp instrumentation amplifier is defined by Equation 10.
Equation 10
Vout3 = Gdiff ⋅ Vdiff + Gcm ⋅ Vicm + Voffset
By considering R1 = Rx(1+εR1), R3 = Rx(1+εR3), R2 = Ry(1+εR2), R4 = Ry(1+εR4),
R5 = Rf(1+εR5), and R6 = Ry(1+εR6), the Gdiff, Gcm and Voffset parameters become as
shown in Equation 11, Equation 12, and Equation 13 respectively.
Equation 11
í
Equation 12
Ry
Gcm = --------------------- ( ε R1 + ε R4 – ε R2 – ε R3 )
Rx + Ry
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Equation 13
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Based on the above equations, the worst case for each parameter can be calculated by
considering:
ε diff = ε R1 = ε R2 = ε R3 = ε R4
and
ε instru = ε R5 = ε R6 = ε Rg
•
the worst case for the differential gain is:
Rf
Ry ⎛
Rf
------- 1 + 2 --------⎞ ( 1 + 2ε instru ) + ⎛ 1 + 2 --------⎞ 2ε diff
⎝
Rg⎠
Rx ⎝
Rg⎠
•
the worst case for the common mode gain is:
Ry
---------------------4ε diff
Rx + Ry
•
the worst case for offset on the output voltage is:
Ry
Rf
Rf
Ry
2Vio ------- ⎛ 1 + 2 --------⎞ ( 1 + 2ε instru ) + ⎛ 1 + 2 --------⎞ 2ε diff + Vio ⎛ 1 + ------- ( 1 + 2ε diff )⎞
⎝
⎝
⎠
Rx ⎝
Rg⎠
Rg⎠
Rx
To know how well this configuration rejects the Vicm, we calculate the CMRR using
Equation 14 and Equation 15.
Equation 14
V1 + V2
Vout = ( V2 – V1 )Gdiff + ---------------------Gcm
2
Equation 15
Rf
⎛ Ry
------- ⎛ 1 + 2 --------⎞ ⎞
⎝
⎠⎟
⎜
Rg
Rx
Gdiff
CMRR = 20 log ⎛ --------------⎞ = 20 log ⎜ ------------------------------------⎟
⎝ Gmc ⎠
Ry
⎜ ---------------------4ε ⎟
⎝ Rx + Ry diff⎠
We can see from Equation 15 that to have the best CMRR, the maximum gain should be
set at the first stage of the 3-op amp instrumentation amplifier structure without saturating
op amps 1 and 2. To achieve the global required gain, the remaining gain should be set at
the second stage.
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Table 2. CMRR for 3-op amp instrumentation amplifier configuration
CMRR (dB)
Resistor
inaccuracy (%)
Rf/Rg = 2
Ry/Rx = 0.5
Gain = 2.5
Rf/Rg = 15
Ry/Rx = 0.5
Gain = 15.5
Rf/Rg = 100
Ry/Rx = 0.5
Gain = 100.5
10
25.5
41.3
57.5
1
45.5
61.3
77.5
0.1
65.5
81.3
97.5
In Table 2 we can see that the 3-op amp instrumentation amplifier offers a better CMRR.
Moreover, it has a high input impedance thanks to the op amps in the first stage.
However, to amplify the signal properly, it is mandatory that the first stage is not saturated.
To achieve this, the following two conditions must be met:
G ⋅ Rx V1 + V2
Vccn < ( V2 – V1 ) ------------------- + --------------------- < Vccp
2Ry
2
G ⋅ Rx V1 + V2
Vccn < ( V1 – V2 ) ------------------- + --------------------- < Vccp
2Ry
2
with
Ry
Rf
G = ------- ⎛⎝ 1 + 2 --------⎞⎠
Rx
Rg
Figure 7 highlights the consequences if these two conditions are not met. If the voltage
intersection of V1 and V2 is within the green area, the output voltage of the first op amp
stage is not saturated.
Figure 7 also specifies the area which is in linear configuration at the output of the
instrumentation amplifier. As well as the two conditions listed above, the input voltages have
to be compliant with the following condition:
Vccn < ( V2 – V1 )G < Vccp
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Figure 7. V2 and V1 ranges
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Summary
5
AN4586
Summary
Table 3 summarizes the main features of the three most flexible methods (based on op
amps) which amplify a differential voltage into a single-ended signal.
Table 3. Main features of the three most flexible methods for amplifying a differential voltage into
a single-ended signal
Differential
configuration
2-op amp
instrumentation
amplifier
3-op amp
instrumentation
amplifier
Rf
-------Rg
Rα
1 + ------Rβ
Rf
⎛ 1 + Ry
-------⎞⎠ ⎛⎝ 1 + 2 --------⎞⎠
⎝
Rg
Rx
Gdiff including errors
Rf
-------- ( 1±2ε )
Rg
⎛ 1 + Rα
-------⎞ ( 1±2ε )
⎝
Rβ⎠
Rf
Ry ⎛
Rf
------- 1 + 2 --------⎞ ( 1 + 2ε instru ) + ⎛ 1 + 2 --------⎞ 2ε diff
⎝
Rg⎠
Rx ⎝
Rg⎠
Gcm including
resistor tolerance
Rf
--------------------4ε
Rg + Rf
4ε
Ry
---------------------4ε diff
Rx + Ry
CMRR due to resistor
inaccuracy
Rf
1 + -------Rg
-----------------4ε
Rf
1 + -------Rg
-----------------4ε
Rf
⎛ 1 + Ry
-------⎞⎠ ⎛⎝ 1 + 2 --------⎞⎠
⎝
Rg
Rx
-------------------------------------------------4ε
Example of CMRR
with gain = 100 and
resistor tolerance
=1%
68 dB
68 dB
74 dB if Rx = Ry
77.5 dB if Rx = 2Ry
Rf2
V2 ⋅ ---------------------------Rf2 + Rg2
V1 and V2 must ve
included within the
op amps Vicm range
Differential gain
(Gdiff)
Vicm limitation
Error on Vout due to
Vio
must be included in
the op amp Vicm
range
Vcc
V1 < ----------------Rβ
1 + ------Rα
G ⋅ Rx V1 + V2
Vccn < ( V2 – V1 ) ------------------- + --------------------- < Vccp
2Ry
2
G ⋅ Rx V1 + V2
Vccn < ( V1 – V2 ) ------------------- + --------------------- < Vccp
2Ry
2
Vccn < ( V2 – V1 )G < Vccp
Rf
Vio ⎛ 1 + --------⎞
⎝
Rg⎠
Rα
2Vio ⎛ 1 + -------⎞
⎝
Rβ⎠
Ry
Rf
Ry
( Vio1 – Vio2 ) ------- ⎛⎝ 1 + 2 --------⎞⎠ – Vio3 ⎛ 1 + -------⎞
⎝
Rx
Rg
Rx⎠
Zdiff
2Rg
∞(1)
∞(1)
Zcm
Rg + Rf
-------------------2
∞(1)
∞(1)
1. Only limited by op amp input impedance
For the 3-op amp instrumentation amplifier, the offset due to the op amp Vio on the output
voltage is bigger compared to the other configurations. Consequently, it is recommended to
use a high precision op amp such as the TSZ121 (or the TSZ124 for a quad version). The
TSZ121 has a maximum Vio of 5 µV and thus it makes accurate measurements.
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Circuits with a single supply voltage
Circuits with a single supply voltage
If the op amp configurations are used with a single supply voltage (i.e. non-symmetrical
supply voltage), it is necessary to add a reference voltage. On the three different
architectures, the reference voltage (Vref) has to replace the ground so as to shift the output
voltage.
Voltage references can be designed with several different configurations: with voltage
reference IC, programmable voltage reference IC, divider bridge with buffer, or even with a
DAC output. The different circuits are shown in Table 4.
Table 4. Reference voltage circuit examples
Voltage
reference IC
Programmable
voltage reference IC
DAC
Output
Divider bridge + buffer
9FF
9FF
9FF
5
9FF
5
5
9UHI
9UHI
5
5
9UHI
5
'$&
9UHI
&
&
The voltage generated by the circuits in Table 4 has to be added to the output voltage
formula. So, we need to take into account the resistor tolerances given earlier in this
document and the additional terms below.
•
Differential configuration:
Rf
Vref ⎛⎝ 1 + --------------------4ε ⎞⎠
Rf + Rg
•
2-op amp instrumentation amplifier configuration:
Vref ( 1 + 4ε )
•
3-op amp instrumentation amplifier configuration:
Ry
Vref ⎛⎝ 1 + ---------------------4ε diff⎞⎠
Ry + Rx
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Circuits with a single supply voltage
AN4586
One last term has to be taken into consideration, which is the accuracy of the voltage
reference itself. This accuracy depends on the voltage reference circuits chosen. The
accuracy for each circuit is given below.
•
Voltage reference IC (e.g. TS4041): 0.5 %
•
Programmable voltage reference IC (e.g. TL1431): 0.3 % plus the accuracy of the
resistors used for the Vka setting.
•
Divider bridge: ± 2ε considering the tolerance, ε, of the resistor used
•
DAC output: depends on the DAC specifications
Example
To understand the complete contribution of each parameter, we can consider an example
with a 3-op amp instrumentation configuration and a voltage reference IC.
The worst case output voltage is as follows:
Vout3 = Gdiff ⋅ Vdiff + Gcm ⋅ Vicm + Voffset + Vreference
When we use Gdiff, Gcm, and Voffset as calculated in the 3-op amp instrumentation
amplifier section we get the following:
Ry
Vreference = Vref ⎛ 1 + ---------------------4ε diff⎞ ( 1 + 0.5% )
⎝
⎠
Ry + Rx
Where 0.5 % is the accuracy of the voltage reference IC.
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Precision op amps
Precision op amps
Table 5 lists some precision op amps that might be used for differential to single-ended
measurements.
Table 5. Some precision op amps
8
Part number
Vio max (µV)
Vcc range (V)
GBP (Hz)
TSZ121
5
1.8 to 5.5
400 k
TSV731
200
1.5 to 5.5
900 k
TSX711
200
2.7 to 16
2.7 M
TS512A
500
6 to 30
3M
Conclusion
In this application note, we looked at the three main architectures that allow us to perform
differential measurements by rejecting the Vicm. Each has its own pros and cons such as a
better CMRR, simpler architecture, high input impedance, or a smaller offset on the output
voltage.
This document highlights the importance of having very accurate resistors. For precise
differential measurements, a 1 % resistor may be not enough. We also saw that a high
precision op amp is useful for limiting the offset on the output voltage.
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Revision history
9
AN4586
Revision history
Table 6. Document revision history
18/19
Date
Revision
27-Oct-2014
1
Changes
Initial release
DocID026915 Rev 1
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