Understanding CMR and instrumentation amplifiers
From the CMR (common-mode rejection) perspective, instrumentation amplifiers are systems in which various parts contribute to the CMR error at different system gains.
By Bonnie Baker -- EDN, November 26, 2009
The three-op-amp instrumentation amplifier in Figure 1 is seemingly a simple configuration in that it uses a basic, decades-old operational amplifier to gain a differential input signal. The op amp’s input offset-voltage error is easy to understand. The definition of an op amp’s open-loop gain has not changed. The simple idea of an op amp’s CMR (common-mode rejection) has been around since the beginning of op-amp time. So what is the hang-up?
Equation 1 yields the common CMR for a single op amp and instrumentation amplifier:
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(1) |
where G is the system gain, ΔVCM is the changing common-mode voltage that you apply equally to the system’s input terminals with respect to ground, and ΔVOUT is the change in the system’s output voltage with respect to the changing VCM values.
With CMR, the inner workings of the op amp are straightforward; the change of offset voltage is the only concern. Two factors influence an instrumentation amplifier’s CMR. The first and most dominant factor is the balance of the resistor ratios across A3. For instance, if R1 equals R3 and R2 equals R4, the CMR of the three-op-amp instrumentation amplifier is ideally infinite.
At a real-world level, however, the relationship of R1, R2, R3, and R4 to the instrumentation amplifier’s CMR—specifically, matching the R1-to-R2 ratio to the R3-to-R4 ratio—is critical. These four resistors combine with A3 to subtract and gain the signals from the outputs of A1 and A2. A mismatch be-tween the resistor ratios creates an error at the output of A3. Equation 2 gives the contribution to the CMR error with respect to the relationship of these resistors:
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(2) |
For instance, if R1, R2, R3, and R4 are approximately the same value and the ratio of R3 to R4 is 1.001 of R1/R2, this 0.1% mismatch will cause a degradation of the instrumentation amplifier’s CMR from ideal to a 66-dB level. At a gain of one, CMRA3 is equivalent to the CMR of the entire instrumentation amplifier.
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As Equation 1 states, the instrumentation amplifier’s CMR increases as the system’s gain increases—a nice feature. Equation 1 might motivate an instrumentation-amplifier designer to ensure that there is plenty of gain available, but A1 and A2’s open-loop gain error places a limit on this strategy. An amplifier’s open-loop gain is 20log(ΔVOUT/ΔVOS), where VOS is the offset voltage. As the gain of A1 and A2 increases, the offset errors from the amplifier’s open-loop gain also increase. The changes in output swing of A1 and A2 typically span the supply rails. At higher instrumentation-amplifier gains, the open-loop gain error of the op amps dominates. These errors degrade the CMR of the instrumentation amplifier at higher gains. Consequently, the instrumentation amplifier’s CMR performance values tend to reach a maximum value at higher gains.
So, from the CMR perspective, instrumentation amplifiers are systems in which various parts contribute to the CMR error at different system gains. This situation is not so mysterious when you think about the inside of this device. As you separate the parts, the picture becomes clear.
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