The voltage that is “common” to both input leads of a differential amplifier is known as the common-mode voltage. This is equal to the smaller of the two input voltages.
If the two inputs are equal, then the common modevoltage is obviously equal to each one of the two inputs. When ui1=ui2, ideally, the output voltage uo should be zero. In other words, ideally, any common-mode signals are rejected by a differential amplifier.
But,since commercial op-amps are not ideal and since they usually do not have exactly identical gains with respectto the two input leads, the output voltage uo will not be zero when the two inputs are identical.
This common mode error can be compensated for by providing a variable resistor with fine resolution at one of the two inputleads of the differential amplifier. to compensate for the common-mode error (i.e., toachieve a satisfactory level of common-mode rejection), first the two inputs are made equal and then dR4 isvaried carefully until the output voltage level is sufficiently small (minimum).
Usually, dR4 that is required toachieve this compensation is small compared to the nominal feedback resistance R4.Since ideally dR4=0 we can neglect dR4 in the derivation of the instrumentation amplifier equation. Now, notefrom a basic property of an op-amp with no saturation (specifically, the voltages at the two input leads have tobe almost identical) that in Figure 4.9(b), the voltage at point 2 should be ui2 and the voltage at point 1 shouldbe ui1.
Next we use the property that the current through each input lead of an op-amp is negligible.Accordingly, current through the circuit path BÕ2Õ1ÕA has to be the same. This gives the current continuityEquations
Note that only the resistor R2 is varied to adjust the gain (differential gain) of the amplifier.
the two input op-amps (the voltage-follower op-amps) do not have to be identical as long as the resistors R1 and R2 are chosen to be accurate.
This is so because the op-amp parameters such as open-loop gain and input impedance do not enter into the amplifier equations provided that their values are sufficiently high, as noted earlier.