LINEAR INTEGRATED CIRCUITS

Differential amplifier

Differential amplifier symbol

The inverting and non-inverting inputs are distinguished by “−” and “+” symbols (respectively) placed in the amplifier triangle. Vs+ and Vs−are the power supply voltages; they are often omitted from the diagram for simplicity, but of course must be present in the actual circuit.

A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs.  It is an analog circuit with two inputs  \scriptstyle V_{{\text{in}}}^{-} and  \scriptstyle V_{{\text{in}}}^{+} and one output  \scriptstyle V_{{\text{out}}} in which the output is ideally proportional to the difference between the two voltages

 V_{{\text{out}}}=A(V_{{\text{in}}}^{+}-V_{{\text{in}}}^{-})

where  \scriptstyle A is the gain of the amplifier.

THEORY

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

 V_{{\text{out}}}=A_{{\text{d}}}(V_{{\text{in}}}^{+}-V_{{\text{in}}}^{-})

Where  V_{{\text{in}}}^{+} and  V_{{\text{in}}}^{-} are the input voltages and  A_{{\text{d}}} is the differential gain.
In practice, however, the gain is not quite equal for the two inputs. This means, for instance, that if  V_{{\text{in}}}^{+} and  V_{{\text{in}}}^{-} 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.

 V_{{\text{out}}}=A_{{\text{d}}}(V_{{\text{in}}}^{+}-V_{{\text{in}}}^{-})+A_{{\text{c}}}\left({\frac {V_{{\text{in}}}^{+}+V_{{\text{in}}}^{-}}{2}}\right)

 A_{{\text{c}}} 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:

 {\mathrm {CMRR}}=10\log _{{10}}\left({\frac {A_{{\mathrm {d}}}}{A_{{\mathrm {c}}}}}\right)^{2}=20\log _{{10}}\left({\frac {A_{{\mathrm {d}}}}{|A_{{\mathrm {c}}}|}}\right)

In a perfectly symmetrical differential amplifier,  A_{{\text{c}}} 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.

OPERATIONAL AMPLIFIER

An Operational Amplifier, or op-amp for short, is fundamentally a voltage amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals. These feedback components determine the resulting function or “operation” of the amplifier and by virtue of the different feedback configurations whether resistive , capacitive or both, the amplifier can perform a variety of different operations, giving rise to its name of “Operational Amplifier”.

An Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs, one called the Inverting Input, marked with a negative or “minus” sign, ( – ) and the other one called the Non-inverting Input, marked with a positive or “plus” sign ( + ).