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Operational Amplifier basics

Operational Amplifier is an specialized linear integrated circuit  that consists of several transistors, resistors, diodes, and capacitors, interconnected to produce gain over a wide range of frequencies.
A single amplifier can contain several amplifiers.
The devices can be used with resistance-capacitance (RC) network combinations to build active filters for use at audio frequencies or other applications .
Operational amplifiers (op amps )are used to amplify signals that range from DC through the higher radio frequencies (RF).
The amplifier may respond to microvolt signals originating in a transducer, which is used to measure temperature, pressure, density, acceleration, and so on.
Originally, the term, “Operational Amplifier” was used in the computing field to describe amplifiers that performed various mathematical operations. It was found that the application of negative feedback around a high gain DC amplifier would produce a circuit with a precise gain characteristic that depended only on the feedback used. By the proper selection of feedback components, operational amplifier circuits could be used to add, subtract, average, integrate, and differentiate.
What the operational amplifier can do is limited only by the imagination and ingenuity of the user.
An ideal operational amplifier is a dc-coupled amplifier having two inputs and  normally one output .
The inputs are designated as non inverting (designated + or NI) and inverting (designated – or Inv.). The amplified signal is the differential signal between the two inputs . Although it certainly must have power supply connections, they are not generally included on schematic diagrams.
operational amplifier diagram
The general characteristics of an ideal op amp can be summarized as follows :
ideal operational amplifier
The open-loop gain AOLis infinite. Or, since the output signal vout is finite, then the differential input signal ve must approach zero.
The input resistance RIN is infinite, while the output resistance RO is zero.
The input impedance of an op amp can be represented by an internal resistance between the input terminals .This is so the driving source won’t be affected by power being drawn by the ideal operational amplifier.
The amplifier has zero current at the input (iA and iB are zero), but the op amp can either sink or source an infinite current at the output.
The op amp is not sensitive to a common signal on both inputs (i.e., vA = vB ); thus, the output voltage change due to a common input signal will be zero. This common signal is referred to as a common mode signal, and manufacturers specify this effect by an op amp’s common-mode rejection ratio which relates the ratio of the open-loop gain of the op amp to the common-mode gain .
Power-supply rejection ratio (PSRR)  relates the ratio of a power supply voltage change to an equivalent input voltage change produced by the change in the power supply but an ideal op amp can operate with any power supply, without restriction.
Gain: The primary function of an amplifier is to amplify, so the more gain the better. It can always be reduced with external circuitry, so we assume gain to be infinite.
An amplifier generally accepts a small signal at its input and produces a amplified signal at its output. The gain (A) or amplification is expressed mathematically as
gain formula
There are no units for gain; it is simply a ratio of two numbers ; it is also convenient to express a gain ratio in its equivalent decibel (dB) form like in equations listed below:
current gain formula in db
power gain formula in db
voltage gain formula in db
Output Impedance: The output impedance of the ideal operational amplifier is assumed to be zero. It then can supply as much current as necessary to the load being driven.
Response Time: The output must occur at the same time as the inverting input so the response time is assumed to be zero. Phase shift will be 180 degree. Frequency response will be flat and bandwidth infinite because AC will be simply a rapidly varying DC level to the ideal amplifier.
The amplifier output will be zero when a zero signal appears between the inverting and non-inverting inputs. Operational amplifier can be connected in different mods ( inverting , non inverting , summing , difference , integrator , etc. ) to obtain what we want .
Most important Operational Amplifier basics connections are presented in schematics presented below .
inverting operational amplifier conection
non-inverting-operational-amplifier non-inverting-summing-operational-amplifier inverting-summing-operational-amplifier   diference-operational-amplifier

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