1. Instrumentation Amplifier

2. Common-mode rejection ratio
The common-mode rejection ratio (CMRR) of a differential amplifier (or other device) measures the tendency of the device to reject input signals common to both input leads. A high CMRR is important in applications where the signal of interest is represented by a small voltage fluctuation superimposed on a (possibly large) voltage offset, or when relevant information is contained in the voltage difference between two signals.
Ideally, a differential amplifier takes the voltages V + and V − on its two inputs and produces an output voltage Vo = Ad(V + − V − ), where Ad is the differential gain.
V − Vo
V +

3. Common-mode rejection ratio
However, the output of a real differential amplifier is better described as
where As is the common-mode gain, which is typically much smaller than the differential gain.
The CMRR is defined as the ratio of the powers of the differential gain over the common-mode gain, measured in positive decibels (thus using the 20 log rule):
As differential gain should exceed common-mode gain, this will be a positive number, and the higher the better.
The CMRR is a very important specification, as it indicates how much of the common-mode signal will appear in your measurement. The value of CMRR is often important in reducing noise on transmission lines. For example, when measuring a thermocouple in a noisy environment, the noise from the environment appears as an offset on both input leads, making it a common-mode voltage signal. The CMRR of the measurement instrument determines the attenuation applied to the offset or noise.

4. Instrumentation Amplifier
An instrumentation amplifier is a type of differential amplifier that has been outfitted with input buffers, which eliminate the need for input impedance matching and thus make the amplifier particularly suitable for use in measurement and test equipment. Additional characteristics include very low DC offset, low drift, low noise, very high open-loop gain, very high common-mode rejection ratio, and very high input impedances. Instrumentation amplifiers are used where great accuracy and stability needed.
Although the instrumentation amplifier is usually shown schematically identical to a standard op-amp, the electronic instrumentation amp is almost always internally composed of 3 op-amps.

5. The buffers
The ideal common-mode gain of an instrumentation amplifier is zero. In the circuit shown, common-mode gain is caused by mismatches in the values of the equally-numbered resistors and by the mis-match in common mode gains of the two input op-amps. Obtaining very closely matched resistors is a significant difficulty in fabricating these circuits, as is optimizing the common mode performance of the input op-amps.
The single resistor Rgain between the two inverting inputs is a elegant method to increases the differential-mode gain of the buffer pair while leaving the common-mode gain equal to 1
A set of switch-selectable resistors or even a potentiometer can be used for Rgain, providing easy changes to the gain of the circuit, without the complexity of having to switch matched pairs of resistors.

6. AD624 Determining gain with internal resistor

7. AD624 Determining gain with external resistor
Gain Is Defined as
G=(R56 + R57)/(RG) + 1
G= 40k/ RG +1

8. Thermocouple