What is the formula for Op-Amp RMS Noise?

The Op-Amp RMS Noise formula is Vn(rms) = en × √(NEB), where Vn—Total RMS noise (V); en—Input-referred noise density (V/√Hz); NEB—Noise-equivalent bandwidth (Hz).

Op-Amp RMS Noise

Q: How do you calculate Op-Amp RMS Noise?

Use the formula Vn(rms) = en × √(NEB). An amplifier’s output noise is its input-referred noise spectral density multiplied by the square root of the noise-equivalent bandwidth. Enter the values you know in the calculator above and it solves for the remaining variable.

Vn = en · √(NEB)

Calculator

RMS Noise

Noise Density

Noise Bandwidth

Result

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Formula

Vn(rms) = en × √(NEB)

Description

An amplifier’s output noise is its input-referred noise spectral density multiplied by the square root of the noise-equivalent bandwidth. Because noise grows only with the square root of bandwidth, halving the bandwidth reduces RMS noise by just √2. This sets the noise floor of a signal chain and shows why band-limiting is the simplest way to improve resolution.

Variables

Vn — Total RMS noise (V)
en — Input-referred noise density (V/√Hz)
NEB — Noise-equivalent bandwidth (Hz)

Practical Notes

Multiply by the noise gain to refer it to the output. Add (root-sum-square) current-noise and resistor thermal-noise contributions for a complete budget.

Related Concepts

All Op-Amps formulas →

Non-Inverting Amplifier Inverting Amplifier Summing Amplifier Difference Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain Op-Amp Differentiator Gain

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