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Common Mode gain is the response of a circuit where the input changes relative to some common point, such as ground. A single transistor amplifier is an example. An op-amp can also be an example, if one input is grounded.
Differential Mode gain is the response of a circuit where the input is measured across two pins, and the difference between those two pins controls the output, rather than the common mode value of those pins relative to ground. An op-amp in balanced or bridge mode is an example.
One way to verify/understand this is to take a properly designed op-amp, connect the two inputs together, and drive them together relative to ground. A properly balanced system will exhibit little or no response on the output. Note: This is also true for AC, so a typical test includes both DC and AC response. In the AC test, imbalance often results from unequal capacitance, whereas DC imbalance results from unequal resistance.
ya. In my project i have to connect my potential transformer output to input of an amplifier which is in common mode now and i am planing to change it to differential mode,what will happen if i changed the mode of operation?