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Operational Amplifiers

The op amp is an electronic unit that behaves like a voltage-controlled voltage source.

An op amp is an active circuit element designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation, and integration.

The equivalent circuit of the nonideal op amp.

v_{o} = A v_{d} = A (v_{2} - v_{1})

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Ider Op Amp

An ideal op amp is an amplifier with infinite open-loop gain, infinite input resistance, and zero output resistance.

The currents into both input terminals are zero:

i_{1} = 0, i_{2} = 0

The voltage across the input terminals is equal to zero:

\begin{aligned} v_{d} & = v_{2} - v_{1} = 0 \\ v_{1} & = v_{2} \end{aligned}

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Inverting Amplifier

An inverting amplifier reverses the polarity of the input signal while amplifying it.

v_{o} = - \frac{R_{f}}{R_{1}} v_{i}

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Noninverting Amplifier

A noninverting amplifier amplifies is an op amp circuit designed to provide a positive voltage gain.

v_{o} = (1 + \frac{R_{f}}{R_{1}}) v_{i}

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Voltage Follower.

When R_f = 0 (short circuit) or R₁ = ∞ (open circuit) or both, the gain becomes 1. Under these conditions (R_f = 0 and R₁ = ∞), the circuit in figure above becomes that shown in figure below, which is called a voltage follower (or unity gain amplifier) because the output follows the input. Thus, for a voltage follower

v_{o} = v_{i}

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Summing Amplifier

A summing amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs.

v_{o} = - (\frac{R_{f}}{R_{1}} v_{1} + \frac{R_{f}}{R_{2}} v_{2} + \frac{R_{f}}{R_{3}} v_{3})

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Differential Amplifier

A differential amplifier is a device that amplifies the difference between two input but rejects any signals common to the two inputs.

v_{o} = \frac{R_{2} (1 + R_{1} / R_{2})}{R_{1} (1 + R_{3} / R_{4})} v_{2} - \frac{R_{2}}{R_{1}} v_{1}

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Cascaded Op Amp Circuits

A cascaded op amp circuit is a head-to-tail arrangement of two or more op amp circuits such that the output of one is the input of the next.

A = A_{1} A_{2} A_{3}

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