Noise-Equivalent Bandwidth (1-pole)
NEB = (π/2) · f−3dB
Quick answer
This calculator solves NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB for Noise Bandwidth. With −3 dB Bandwidth 0.22 MHz, the result is 0.3456 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The noise-equivalent bandwidth is the width of an ideal brick-wall filter that would pass the same total noise power as a real filter. For a single-pole RC roll-off it is π/2 times the −3 dB bandwidth, because the gentle skirt passes extra noise beyond the corner. Use this, not the −3 dB bandwidth, when computing total RMS noise.
Variables
- NEB — Noise-equivalent bandwidth (Hz)
- f−3dB — Filter −3 dB cutoff frequency (Hz)
Practical Notes
Higher-order filters have NEB closer to f−3dB (e.g. ×1.22 for 2-pole, ×1.16 for 3-pole). Always convert a real corner to NEB before multiplying by noise density.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| NEB | Noise Bandwidth | kHz | Hz, kHz, MHz, GHz |
| f3dB | −3 dB Bandwidth | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: −3 dB Bandwidth 0.22 MHz
- 2. The relation: NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB
- 3. Substitute: f3dB = 0.22 MHz
- 4. Result: Noise Bandwidth = 0.3456 MHz
Worked examples
Minimum range
Given: −3 dB Bandwidth 0.22 kHz
Result: Noise Bandwidth = 0.3456 kHz
Low range
Given: −3 dB Bandwidth 2.2 kHz
Result: Noise Bandwidth = 3.456 kHz
Typical
Given: −3 dB Bandwidth 0.22 MHz
Result: Noise Bandwidth = 0.3456 MHz
High range
Given: −3 dB Bandwidth 1.1 MHz
Result: Noise Bandwidth = 1.728 MHz
Maximum range
Given: −3 dB Bandwidth 11 MHz
Result: Noise Bandwidth = 17.28 MHz
Solving for each variable
Solve for Noise Bandwidth
−3 dB Bandwidth 0.22 kHz → 0.3456 kHz
Solve for −3 dB Bandwidth
Noise Bandwidth 100 Hz → 63.66 Hz
How Noise Bandwidth changes with −3 dB Bandwidth
| −3 dB Bandwidth (input) | Noise Bandwidth (result) |
|---|---|
| 48.4 kHz | 76.03 kHz |
| 121 kHz | 0.1901 MHz |
| 0.242 MHz | 0.3801 MHz |
| 0.363 MHz | 0.5702 MHz |
| 0.484 MHz | 0.7603 MHz |
| 0.726 MHz | 1.14 MHz |
| 0.968 MHz | 1.521 MHz |
| 1.936 MHz | 3.041 MHz |
| 3.388 MHz | 5.322 MHz |
| 4.84 MHz | 7.603 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 345600 |
| kHz | 345.6 |
| MHz | 0.3456 |
| GHz | 0.0003456 |
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<p><a href="https://vbatpower.com/formulas/noise-equivalent-bandwidth/">Noise-Equivalent Bandwidth (1-pole)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Noise-Equivalent Bandwidth (1-pole)?
Use NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB. With −3 dB Bandwidth 0.22 MHz, Noise Bandwidth works out to 0.3456 MHz.
How do you calculate equivalent bandwidth rc?
Rearrange for Noise Bandwidth: with −3 dB Bandwidth 2.2 kHz, Noise Bandwidth is 3.456 kHz.
What is the formula for Noise-Equivalent Bandwidth (1-pole)?
The formula is NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB. The noise-equivalent bandwidth is the width of an ideal brick-wall filter that would pass the same total noise power as a real filter.
How do you find −3 dB Bandwidth when you know the other values?
Rearrange for −3 dB Bandwidth: with Noise Bandwidth 100 Hz, −3 dB Bandwidth is 63.66 Hz.
What units does Noise-Equivalent Bandwidth (1-pole) use?
Noise Bandwidth is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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