Instrumentation amplifier VCM vs. VOUT
plots: part 2
Peter Semig - December 10, 2014
In Part 1 we introduced the VCM vs. VOUT plot, common-mode versus differential-mode voltage, and
instrumentation amplifier (IA) topologies. In Part 1 we also derived the internal node equations and
transfer function of a traditional 3-op amp IA.
In Part 2 we introduce the input common-mode and output swing limitations of operational
amplifiers (op amps), which are the fundamental building blocks of IAs. The internal node equations
from Part 1 are modified to yield equations that represent each op amp’s input common-mode and
output swing limitation at the output of the IA as a function of the device’s input common-mode
voltage. We examine a generic VCM vs. VOUT plot in detail and compare it to plots from device
datasheets to corroborate the theory.
Op amp limitations
In order for an op amp to output a linear voltage, the input signal must be within the device’s input
common-mode range specification (VCM) and the output must be within the device’s output swing
range specification (VOUT). These ranges depend on the supply voltages, V+ and V– (Figure 1).
Figure 1: Op amp input common-mode (green) and output swing (red) ranges depend on
supplies
Figure 2 depicts the datasheet specifications and corresponding VCM and VOUT ranges for an op amp,
such as the OPA333, given a 3.3V supply. For this device, the output swing is more restrictive than
the input common-mode voltage range.
Figure 2. Op amp VCM and VOUT ranges for 3.3V supply
The VCM vs. VOUT Plot
The VCM vs. VOUT plot for an instrumentation amplifier is a representation of all internal op amp input
common-mode and output swing limitations. Figure 3 depicts a typical VCM vs. VOUT plot. Operating
outside the boundaries of the plot violates at least one input common-mode or output swing
limitation of the internal amplifiers. Depending on the severity of the violation, the output waveform
may depict anything from minor distortion to severe clipping.
Notice that the plot is specified for a particular supply voltage (VS = +/–2.5V), reference voltage
(VREF=0V), and gain (all gains for this device).
Figure 3. Instrumentation amplifier VCM vs. VOUT plot (INA333)
Figure 4 depicts the linear output range given two different input common-mode voltages. For
example, if the common-mode input of the IA is 2.0V, the output will be valid only from
approximately –0.8V to +0.8V. However, if the common-mode input is mid-supply (0V), the maximum
output swing of nearly ±2.5V is available.
Figure 4. Output voltage range for different common-mode voltages
Each line in the IA VCM vs. VOUT plot corresponds to a limitation, either VCM or VOUT, of one of the three
internal amplifiers. Therefore, a review the internal node equations derived in Part 1 is necessary.
Figure 5 depicts the standard 3-op amp IA and equations (1 – 6) define the voltage at each internal
node.
Figure 5. Three-op amp instrumentation amplifier
(1)
(2)
(3)
(4)
(5)
(6)
In order to plot the node equation limits on a graph with VCM and VOUT axes, solve equation (6) for VD
as shown in equation (7).
(7)
Substituting equation (7) for VD in equations (1 – 6) and solving for VOUT yield Equations (8 – 13).
These equations represent each amplifier’s input common-mode (VIA) and output (VOA) limitation at
the output of the IA, and as function of the device’s input common-mode voltage.
(8)
(9)
(10)
(11)
(12)
(13)
One important observation of equations (8 – 9) is that the IA limitations due to the common-mode
range of A1 and A2 depend on the gain of the input stage, GIS. The output limitations, however, do
not depend on GIS as shown by equations (11 – 12).
Plotting each of these equations yields Figure 6
Plotting each of these equations for the minimum and maximum input common-mode and output
swing limitations for each op amp (A1, A2, and A3) yields the VCM vs. VOUT plot. Figure 6 depicts a
generic VCM vs. VOUT plot. The linear operation of the IA is the interior of all plotted equations.
Figure 6. Example of a generic VCM vs. VOUT plot
Dotted lines represent the input common-mode limitations for A1 (blue) and A2 (red). Notice that the
slope of the dotted lines depend on GIS, which is consistent with equations (8 – 9).
Solid lines represent the output swing limitations for A1 (blue), A2 (red), and A3 (green). The slope
of these lines do not depend on GIS, as shown by Equations (11 – 13).
The line for VIA3 is not shown because the R2/R1 voltage divider attenuates the output of A2, so the
output swing limitation for A2 is typically reached before violating A3’s input common-mode range.
The lines plotted in quadrants one and two (positive common-mode voltages) use maximum input
common-mode and output swing limits for A1 and A2. The dual applies to quadrants three and four
(negative common-mode voltages).
Considering only positive common-mode voltages from Figure 6, Figure 7 depicts the linear
operating region of the IA when G=1V/V. In this example, the input common-mode limitation of A1
and A2 is more restrictive than the output swing.
Figure 7. G=1V/V, A1 & A2 input common-mode range limits linear region
Increasing the gain of the device changes the slope of VIA1 and VIA2 (Figure 8). Now both the input
common-mode and output swing limitations define the linear operating region.
Figure 8. G>1V/V, A1 & A2 input common-mode and output swing limit linear region
Regardless of gain, the output swing always limits the linear operating region when it is more
restrictive than the input common-mode limit (Figure 9).
Figure 9. A1 & A2 output swing limits linear region, independent of gain
Datasheet examples
Figure 10 depicts the VCM vs. VOUT plot from the INA111 datasheet. Notice that the output swing of
A1 and A2 limits the linear operating region. Therefore, output swing limitations of A1 and A2 must
be equal to or more restrictive than the input common-mode limitations.
Figure 10. VCM vs. VOUT plot (INA111)
Figure 11 depicts the VCM vs. VOUT plot from the INA121 datasheet. Notice that the linear operating
region changes with gain. At G=1V/V, the input common-mode must limit the linear operating
region. However, as gain increases, the linear operating region is limited by both the output swing
and input common-mode limitations (Figure 8).
Figure 11: VCM vs. VOUT plot (INA121)
Summary
In Part 2 we discussed the common-mode range and output swing limits of op amps, which are the
fundamental building blocks of IAs. We modified the internal node equations from Part 1 to yield
equations that represent each amplifier’s input common-mode and output swing limitation at the
output of the IA as a function of the device’s input common-mode voltage. We also examined a
generic VCM vs. VOUT plot in detail. Finally, we showed the VCM vs. VOUT plots from the INA111 and
INA121 datasheets correlate with the theory discussed.
Stay tuned for Part 3, where we will discuss how to build a model that simulates custom VCM vs. VOUT
plots. This allows a designer to generate plots for their design parameters, which may not be the
same as the plots given in an instrumentation amplifier’s data sheet. We will also explore the use of
level shifting, which increases output swing at common-mode voltages near the negative supply rail.
References
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Download these datasheets: OPA333, INA333, INA111, and INA121
Acknowledgements
The author would like to thank Collin Wells at Texas Instruments for his contributions to this article.