The Totally Misunderstood Three-Op-Amp Instrumentation Amplifier

         The three-op-amp instrumentation amplifier shown in Figure 1 appears to be a simple structure because it uses the basic operational amplifier (op amp) that has been around for decades to obtain a differential input signal. The input offset voltage error of an op amp is well understood. The definition of op amp open-loop gain has not changed. Simple methods for op amp common-mode rejection (CMR) have been around since the dawn of the op amp era. So, what’s the problem?

　　Figure 1: A three-op-amp instrumentation amplifier with VCM being the common-mode voltage and VDIFF being the differential inputs of the same instrumentation amplifier.

　　The shared CMR equation for a single op amp and an instrumentation amplifier is as follows:

　　In this equation, G is equivalent to the system gain, VCM is the changing voltage applied to the system input relative to ground, and VOUT is the change in system output voltage relative to the changing VCM value.

　　In terms of CMR, the internal activity of the op amp is simple, and its offset voltage variation is the only concern. In the case of an instrumentation amplifier, there are two factors that affect the CMR of the device. The first and most important factor involves the balance of the resistor ratios of the third amplifier (Figure 1, A3). For example, if R1 equals R3 and R2 equals R4, the CMR of the ideal three-op-amp instrumentation amplifier is infinite. However, we have to return to the real world and study the relationship between R1, R2, R3, and R4 and the CMR of the instrumentation amplifier.

　　Specifically, it is critical to match R1:R2 with R3:R4. Combined with A3, these four resistors subtract and gain the signal from the outputs of A1 and A2. Mismatches between the resistor ratios create errors at the output of A3. Equation 2 creates CMR errors with respect to these resistor relationships:

　　For example, if R1, R2, R3, and R4 are close to the same value, and R3:R4 equals 1.001 of R1/R2, then this 0.1% mismatch will result in a degradation of the instrumentation amplifier’s CMR from the ideal level to the 66dB level.

　　According to Equation 1, the instrumentation amplifier CMR increases as the system gain increases. This is a very good characteristic. Equation 1 may motivate the instrumentation amplifier designer to ensure that there are many gains available, but this approach has certain limitations. A1 and A2 open-loop gain error and noise. The open-loop gain of the amplifier is equal to 20log(ΔVOUT/ΔVOS). As the gain of A1 and A2 increases, the amplifier open-loop gain offset error also increases. The output amplitude variation of A1 and A2 generally covers the supply rails. At higher instrumentation amplifier gains, the open-loop gain error and noise of the op amp dominate. Through the RSS formula, these errors reduce the instrumentation CMR at higher gains. Therefore, you can see that the CMR performance of the instrumentation amplifier tends to reach a maximum value at higher gains.

　　So, from a CMR perspective, the instrumentation amplifier is like a system with each part of the device contributing CMR errors at different system gains. When you look under the hood of the device, it’s not such a mystery anymore. You separate the parts and it becomes clear.