Differential Amplifier - Theory

Theory

Many electronic devices use differential amplifiers internally. The output of an ideal differential amplifier is given by:

Where and are the input voltages and is the differential gain.
In practice, however, the gain is not quite equal for the two inputs. This means, for instance, that if and are equal, the output will not be zero, as it would be in the ideal case. A more realistic expression for the output of a differential amplifier thus includes a second term.

is called the common-mode gain of the amplifier.
As differential amplifiers are often used to null out noise or bias-voltages that appear at both inputs, a low common-mode gain is usually desired.

The common-mode rejection ratio (CMRR), usually defined as the ratio between differential-mode gain and common-mode gain, indicates the ability of the amplifier to accurately cancel voltages that are common to both inputs. The common-mode rejection ratio is defined as:

In a perfectly symmetrical differential amplifier, is zero and the CMRR is infinite. Note that a differential amplifier is a more general form of amplifier than one with a single input; by grounding one input of a differential amplifier, a single-ended amplifier results.