The output stage of the instrumentation amplifier is a difference amplifier, whose output V_out is the amplified difference of the input signals applied to its input terminals. If the outputs of op-amp 1 and op-amp 2 are V_o1 and V_o2 respectively, then the output of the difference amplifier is given by,

V_out = (R₃/R₂)(V_o1-V_o2)

The expressions for Vo1 and Vo2 can be found in terms of the input voltages and resistances. Consider the input stage of the instrumentation amplifier as shown in the figure below.

The potential at node A is the input voltage V₁. Hence the potential at node B is also V₁, from the virtual short concept. Thus, the potential at node G is als o V₁.

The potential at node D is the input voltage V₂. Hence the potential at node C is also V₂, from the virtual short. Thus, the potential at node H is also V₂.

Ideally the current to the input stage op-amps is zero. Therefore the current I through the resistors R₁, R_gain and R₁ remains the same.

Applying Ohm’s law between the nodes E and F,

Note: The overall voltage gain of an instrumentation amplifier can be controlled by adjusting the value of resistor R_gain. The common mode signal attenuation for the instrumentation amplifier is provided by the difference amplifier.