Summing Amplifier (Op Amp)

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

The summing amplifier is a variation of the inverting amplifier.

Applying KCL at node $a$ gives

$i = i_{1} + i_{2} + i_{3} = \frac{v_{1} - v_{a}}{R_{1}} + \frac{v_{2} - v_{a}}{R_{2}} + \frac{v_{3} - v_{a}}{R_{3}}$

$i = \frac{v_{a} - v_{o}}{R_{f}}$

$\frac{v_{a} - v_{o}}{R_{f}} = \frac{v_{1} - v_{a}}{R_{1}} + \frac{v_{2} - v_{a}}{R_{2}} + \frac{v_{3} - v_{a}}{R_{3}}$

But $v_{a} = 0$ for an ideal op amp, since the non-inverting terminal is grounded. Hence,

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

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

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Operational Amplifier (Op Amp)

The op amp is a fundamental building block in modern electronic instrumentation. It is used extensively in many devices, along with resistors and other passive elements. Its numerous practical applications include instrumentation amplifiers, digital-to-analog converters, analog computers, level shifters, filters, calibration circuits, inverters, summers, integrators, differentiators, subtractors, logarithmic amplifiers, comparators, gyrators, oscillators, rectifiers, regulators, voltage-to-current converters, current-to-voltage converters, and clippers.
Analog Computer

Summing amplifiers