Op-Amp RMS Noise
Vn = en · √(NEB)
Quick answer
This calculator solves Vn(rms) = en × √(NEB) for RMS Noise. With Noise Density 10 nV/√Hz, Noise Bandwidth 100 kHz, the result is 3.162 µV. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vn | RMS Noise | µV | pV, nV, µV, mV, V, kV |
| en | Noise Density | nV/√Hz | nV/√Hz, µV/√Hz |
| NEB | Noise Bandwidth | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Noise Density 10 nV/√Hz, Noise Bandwidth 100 kHz
- 2. The relation: Vn(rms) = en × √(NEB)
- 3. Substitute: en = 10 nV/√Hz, NEB = 100 kHz
- 4. Result: RMS Noise = 3.162 µV
Worked examples
Minimum range
Given: Noise Density 0.1 nV/√Hz, Noise Bandwidth 100 Hz
Result: RMS Noise = 1 nV
Low range
Given: Noise Density 1 nV/√Hz, Noise Bandwidth 1 kHz
Result: RMS Noise = 31.62 nV
Typical
Given: Noise Density 10 nV/√Hz, Noise Bandwidth 100 kHz
Result: RMS Noise = 3.162 µV
High range
Given: Noise Density 100 nV/√Hz, Noise Bandwidth 0.5 MHz
Result: RMS Noise = 70.71 µV
Maximum range
Given: Noise Density 1 µV/√Hz, Noise Bandwidth 5 MHz
Result: RMS Noise = 2.236 mV
Solving for each variable
Solve for RMS Noise
Noise Density 0.1 nV/√Hz, Noise Bandwidth 100 Hz → 1 nV
Solve for Noise Density
RMS Noise 1 µV, Noise Bandwidth 100 Hz → 100 nV/√Hz
Solve for Noise Bandwidth
RMS Noise 1 µV, Noise Density 0.1 nV/√Hz → 100 MHz
How RMS Noise changes with Noise Density
| Noise Density (input) | RMS Noise (result) |
|---|---|
| 1 nV/√Hz | 0.3162 µV |
| 2.5 nV/√Hz | 0.7906 µV |
| 5 nV/√Hz | 1.581 µV |
| 7.5 nV/√Hz | 2.372 µV |
| 10 nV/√Hz | 3.162 µV |
| 15 nV/√Hz | 4.743 µV |
| 20 nV/√Hz | 6.325 µV |
| 40 nV/√Hz | 12.65 µV |
| 70 nV/√Hz | 22.14 µV |
| 100 nV/√Hz | 31.62 µV |
The same result in other units
| Unit | Value |
|---|---|
| pV | 3162000 |
| nV | 3162 |
| µV | 3.162 |
| mV | 0.003162 |
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<p><a href="https://vbatpower.com/formulas/opamp-rms-noise/">Op-Amp RMS Noise</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Op-Amp RMS Noise?
Use Vn(rms) = en × √(NEB). With Noise Density 10 nV/√Hz, Noise Bandwidth 100 kHz, RMS Noise works out to 3.162 µV.
What is the formula for Op-Amp RMS Noise?
The formula is 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.
How do you find Noise Density when you know the other values?
Rearrange for Noise Density: with RMS Noise 1 µV, Noise Bandwidth 100 Hz, Noise Density is 100 nV/√Hz.
How do you find Noise Bandwidth when you know the other values?
Rearrange for Noise Bandwidth: with RMS Noise 1 µV, Noise Density 0.1 nV/√Hz, Noise Bandwidth is 100 MHz.
What units does Op-Amp RMS Noise use?
RMS Noise is shown in pV, nV, µV, mV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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