The Instrumentation Amplifier 

The basic difference amplifier suffers from three fundamental problems: First, the input impedances to the two inputs are relatively low, because of the resistors in the circuit; second, those two input impedances are not matched; and third, changing the gain of the overall amplifier requires identical changes to at least two resistors, and possibly four.
We can solve the first two problems by placing a unitygain noninverting amplifier in front of each input. This will isolate the input signals from the actual difference amplifier, so the input impedance for each signal will now be the the high input impedance of a noninverting amplifier. However, it doesn't solve the third problem. Can we modify the difference amplifier, with the input amplifier/buffers, so that a single resistor can be used to set or adjust the gain of the overall circuit?
The solution, shown to the right, isn't directly intuitive but does work well. The first step is to make all resistors identical, except for the single resistor, designated R_{1} in the schematic diagram, which will be used to set the gain of the circuit. Since all of the other resistors are the same, only a single value of precision resistor is required everywhere else in the circuit, probably close to 10K in most applications.
To understand how adjustments to R_{1} can control the overall gain of this circuit, we first note that opamp A will develop whatever output voltage is required to hold Point 1 at the same voltage as V_{1}. Likewise, opamp B will hold Point 2 at the same voltage as V_{2}. Therefore the voltage across R_{1} is equal to (V_{2}  V_{1}), and by Ohm's Law, the current I_{R1} through this resistor is (V_{2}  V_{1})/R_{1}.
At the same time, neither of the input opamps draws current from this set of seriesconnected resistors, the same current must also flow through the resistors, R, between points 1 and 3, and between points 2 and 4. Therefore the total voltage between points 3 and 4 must (again by Ohm's Law) be equal to I_{R1} × (R_{1} + 2R). This same voltage difference is also applied to the difference amplifier consisting of opamp C and its associated input and feedback resistors.
Now, all resistors associated with opamp C are the same, so this is a unitygain difference amplifier. Its output will be V_{43}. Therefore the overall voltage gain of this circuit is V_{43}/(V_{2}  V_{1}). Since we have already computed V_{43} in terms of (V_{2}  V_{1}) and the three series resistors, we can apply a small amount of algebra and state that the voltage gain of this circuit is:
Note that the minimum possible gain for this circuit as shown is 1, which occurs when R_{1} is infinite or open. As R_{1} decreases in value, circuit gain increases. But if R_{1} becomes too small, opamps A and B will saturate with larger input signals. It is therefore very important to keep R_{1} large enough, relative to the input signal amplitudes, to ensure that the input opamps remain within their normal operating output voltage ranges.
Instrumentation amplifiers are very useful in sensing systems where some physical phenomenon is being monitored. Strain sensors, pressure sensors, many temperature sensors, and other similar devices operate by changing their internal resistance according to changes in whatever they are sensing. However, the change in resistance is relatively small, and the inherent resistance of the sensor as a whole is typically large.
A very common way to use these sensing devices is to incorporate them as one leg in a Wheatstone Bridge circuit. The Wheatstone Bridge is very sensitive to changes to its balance, and the instrumentation amplifier can amplify changes in the bridge's differential output voltage without loading (and thereby reducing the sensitivity) of the bridge.
The number of variations on this theme is limited primarily by your imagination and the number of different types of sensing devices available. And of course the instrumentation amplifier isn't limited to amplifying the output of bridge circuits. Any number of other applications may develop from here.


 
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