The first installment of this series introduced the boundary plot, an often-misunderstood plot found in instrumentation amplifier (IA) datasheets. It also discussed various IA topologies: traditional three operational amplifier (op amp), two op amp, two op amp with a gain stage, current mirror, current feedback with super-beta transistors, and indirect current feedback.
Part 1 also included derivations of the internal node equations and transfer function of a traditional three-op-amp IA.
The second installment will introduce the input common-mode and output swing limitations of op amps, which are the fundamental building blocks of IAs. Modifying the internal node equations from Part 1 yields 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.
The article will also examine a generic boundary plot in detail and compare it to plots from device datasheets to corroborate the theory.
Op-amp limitations
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 (VOUT) must be within the device’s output swing range specification. 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. Source: Texas Instruments
Figure 2 depicts the datasheet specifications and corresponding VCM and VOUT ranges for an op amp, such as TI’ OPA188, given a ±15V 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 are shown for a ±15 V supply of the OPA188 op amp. Source: Texas Instruments
The boundary plot
The boundary plot for an IA is a representation of all internal op-amp input common-mode and output swing limitations. Figure 3 depicts a boundary 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.
Figure 3 Here is how an IA boundary plot looks like for the INA188 instrumentation amplifier. Source: Texas Instruments
This plot is specified for a particular supply voltage (VS = ±15 V), reference voltage (VREF = 0 V), and gain of 1 V/V.
Figure 4 illustrates the linear output range given two different input common-mode voltages. For example, if the common-mode input of the IA is 8 V, the output will be valid only from approximately –11 V to +11 V. If the common-mode input is mid supply (0 V), however, an output swing of ±14.78 V is available.
Figure 4 Output voltage range is shown for different common-mode voltages. Source: Texas Instruments
Notice that the VCM (blue arrows) ranges from –15 V to approximately +13.5 V. Both the mid-supply output swing and VCM ranges are consistent with the op-amp ranges depicted in Figure 2.
Each line in the boundary plot corresponds to a limitation—either VCM or VOUT—of one of the three internal amplifiers. Therefore, it’s necessary to review the internal node equations first derived in Part 1. Figure 5 depicts the standard three-op-amp IA, while Equations 1 through 6 define the voltage at each internal node.
Figure 5 Here is how a three-op-amp IA looks like. Source: Texas Instruments
(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 through 6 and solving for VOUT yields Equations 8 through 13. These equations represent each amplifier’s input common-mode (VIA) and output (VOA) limitation at the output of the IA, and as a function of the device’s input common-mode voltage.
(8) 
(9) 
(10) 
(11) 
(12) 
(13) 
One important observation from Equations 8 and 9 is that the IA limitations from the common-mode range of A1 and A2 depend on the gain of the input stage, GIS. These output limitations do not depend on GIS, however, as shown by Equations 11 and 12.
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 boundary plot. Figure 6 depicts a generic boundary plot. The linear operation of the IA is the interior of all plotted equations.
Figure 6 Here is an example of a generic boundary plot. Source: Texas Instruments
The dotted lines in Figure 6 represent the input common-mode limitations for A1 (blue) and A2 (red). Notice that the slope of the dotted lines depends on GIS, which is consistent with Equations 8 and 9.
Solid lines represent the output swing limitations for A1 (blue), A2 (red) and A3 (green). The slope of these lines does not depend on GIS, as shown by Equations 11 through 13.
Figure 6 doesn’t show the line for VIA3 because the R2/R1 voltage divider attenuates the output of A2; A2 typically reaches the output swing limitation before violating A3’s input common-mode range.
The lines plotted in quadrants one and two (positive common-mode voltages) use the maximum input common-mode and output swing limits for A1 and A2, whereas the lines plotted in quadrants three and four (negative common-mode voltages) use the minimum input common-mode and output swing limits.
Considering only positive common-mode voltages from Figure 6, Figure 7 depicts the linear operating region of IA when G = 1 V/V. In this example, the input common-mode limitation of A1 and A2 is more restrictive than the output swing.
Figure 7 The input common-mode range limit of A1 and A2 defines the linear operation region when G = 1 V/V. Source: Texas Instruments
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 The input common-mode range and output swing limits of A1 and A2 define the linear operating range when G > 1 V/V. Source: Texas Instruments
Regardless of gain, the output swing always limits the linear operating region when it’s more restrictive than the input common-mode limit (Figure 9).
Figure 9 The output swing limit of A1 and A2 define the linear operating region independent of gain. Source: Texas Instruments
Datasheet examples
Figure 10 illustrates the boundary plot from the INA111 datasheet. Notice that the output swing limit of A1 and A2 define the linear operating region. Therefore, the output swing limitations of A1 and A2 must be equal to or more restrictive than the input common-mode limitations.
Figure 10 Boundary plot for the INA111 instrumentation amplifier shows output swing limitations. Source: Texas Instruments
Figure 11 depicts the boundary plot from the INA121 datasheet. Notice that the linear operating region changes with gain. At G = 1 V/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 Boundary plot is shown for the INA121 instrumentation amplifier. Source: Texas Instruments
Third installment coming
The third installment of this series will explain how to use these equations and concepts to develop a tool that automates the drawing of boundary plots. This tool enables you to adjust variables such as supply voltage, reference voltage, and gain to ensure linear operation for your application.
Peter Semig is an applications manager in the Precision Signal Conditioning group at TI. He received his bachelor’s and master’s degrees in electrical engineering from Michigan State University in East Lansing, Michigan.
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