Inverting Op-Amp Gain

\[A_v=-\frac{R_f}{R_{in}}\]

Variables

Avvoltage gain

Rffeedback resistor (Ω)

Rininput resistor (Ω)

Description

What is this formula?

The Inverting Op-Amp Gain formula calculates the voltage amplification of an inverting operational amplifier configuration. The output signal is inverted by 180 degrees relative to the input signal.

When to use it

Use this formula when designing or analyzing operational amplifier circuits that require signal inversion and controlled voltage amplification.

Example

An inverting amplifier uses a feedback resistor of 47 kΩ and an input resistor of 4.7 kΩ.

Given:

Rf = 47 kΩ

Rin = 4.7 kΩ

Formula:

Av = -(Rf / Rin)

Substitution:

Av = -(47 / 4.7)

Result:

Av = -10

The operational amplifier provides a voltage gain of -10, meaning the signal is inverted.

Applications

Audio amplifiers, active filters, analog signal processing, sensor conditioning circuits, instrumentation systems, and control electronics.