---
title: "Short note: Noise equivalent bandwidth"
subject: "Communication Systems"
chapter: 9
key: "semester_6/communication_systems:short-note-neb"
source: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-neb
site: BCT Engineering
---

# Short note: Noise equivalent bandwidth

Communication Systems · Chapter 9: Noise in Communication Systems

- Asked in: 2072 Chaitra (CS II), 2.5 marks
- Video: [CT#34 Noise equivalent Bandwidth in a communication system || EC Academy](https://www.youtube.com/watch?v=GVSrpgnxH5I) — EC Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-neb
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9

## Question

Write a short note on noise equivalent bandwidth.

## Short answer

Noise equivalent bandwidth (NEB) is the width of an ideal rectangular filter with the same peak gain that passes the same white-noise power as the actual filter. It is BN = (1/|H(0)|²) ∫₀^∞ |H(f)|² df. Output noise is N0 BN |H(0)|², used in noise figure calculations.

## Answer

The **noise equivalent bandwidth (NEB)** $B_N$ of a filter is the bandwidth of an ideal rectangular filter, with the same maximum gain $\lvert H(0)\rvert$, that passes the same noise power as the real filter when both are driven by white noise:

$$
B_N=\frac{1}{\lvert H(0)\rvert^2}\int_0^{\infty}\lvert H(f)\rvert^2df
$$

- Output noise power can then be written simply as $N=N_0B_N\lvert H(0)\rvert^2$ (or $kTB_N$).
- It is used in noise figure, noise temperature and receiver SNR calculations.
- **Example:** RC low-pass filter, $B_N=\frac{1}{4RC}=\frac\pi2f_{3dB}\approx1.57f_{3dB}$.
- For sharp-cut-off filters $B_N\approx$ 3 dB bandwidth; for gentle roll-off filters $B_N$ is larger.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Noise equivalent bandwidth is given by:
   A. B_N = integral from 0 to infinity of |H(f)|^2 df, divided by |H(0)|^2
   B. B_N = |H(0)| times the 3 dB bandwidth
   C. B_N = integral of |H(f)| df
   D. B_N = |H(0)|^2 / integral of |H(f)|^2 df
   Answer: A. Equating the real filter's noise power with an ideal filter of gain |H(0)| gives B_N = (integral of |H|^2) / |H(0)|^2. (Key point: NEB formula)

2. What is NEB mainly used for?
   A. Computing group delay
   B. Writing output noise power simply as N0 B_N |H(0)|^2 (or kTB_N) in SNR and noise figure work
   C. Designing the carrier frequency
   D. Measuring signal energy
   Answer: B. NEB turns the noise integral into a simple product with a rectangular bandwidth. (Key point: Use of NEB)

3. For an RC low-pass filter, B_N compared to the 3 dB bandwidth is:
   A. Equal
   B. About 1.57 times larger, since the roll-off is gentle
   C. About 0.64 times as large
   D. Twice as large
   Answer: B. B_N = 1/(4RC) = (π/2) f_3dB ≈ 1.57 f_3dB. (Key point: NEB of RC filter)

## Related in Communication Systems

- [Noise equivalent bandwidth; optimum detector impulse response](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneb-optimum-detector) — Communication Systems, chapter 9
- [Noise equivalent bandwidth of RC low pass filter](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneb-rc-lowpass) — Communication Systems, chapter 9
- [Noise equivalent bandwidth; matched filter is time reversed](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneb-matched-filter-reverse) — Communication Systems, chapter 9
- [Moments of random variable; NEB of RC-LPF; output noise power](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amoments-neb-rc-lpf) — Communication Systems, chapter 9