---
title: "Capacity for 3.1 kHz, SNR 0 dB"
subject: "Data Communication"
chapter: 1
key: "semester_5/data_communication:capacity-3-1khz-0db"
source: https://www.bctengineer.com/q/semester_5/data_communication/capacity-3-1khz-0db
site: BCT Engineering
---

# Capacity for 3.1 kHz, SNR 0 dB

Data Communication · Chapter 1: Introduction

- Asked in: 2074 Asoj, 3+3 marks
- Video: [Channel Capacity by Shannon-Hartley | Basics, Proof & Maximum Bandwidth Condition](https://www.youtube.com/watch?v=3ekWsXeZ8TM) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/capacity-3-1khz-0db
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-1

## Question

Find the capacity of a channel for a signal with a bandwidth of 3.1 kHz and signal to noise ratio of 0 dB and comment on it.

## Short answer

With B = 3.1 kHz and SNR = 0 dB (S/N = 1), capacity C = B log2(2) = 3100 bps = 3.1 kbps. This shows even unity SNR can support error-free transmission up to the bandwidth rate.

## Answer

Given: B = 3.1 kHz, SNR = 0 dB.

1. S/N = 10^(0/10) = 1
2. C = B log₂(1 + S/N) = 3100 × log₂(1 + 1) = 3100 × 1

**Answer: C = 3100 bps = 3.1 kbps.**

#### Comment
- SNR of 0 dB means signal power equals noise power. Even then, Shannon says data can be sent without error at up to 3.1 kbps, but only with very good error-correcting codes and a large delay.
- The capacity in bits per second equals the bandwidth in Hz (1 bit/s/Hz). To get a higher rate in such a channel, the SNR must be improved: a low SNR makes a very poor channel.

## Check yourself

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

1. 0 dB corresponds to S/N of
   A. 0
   B. 10
   C. infinity
   D. 1
   Answer: D. 10^0 = 1, so signal power equals noise power. (Key point: dB conversion)

2. C for B = 3.1 kHz and 0 dB is
   A. 3100 bps
   B. 6200 bps
   C. 0 bps
   D. 31 kbps
   Answer: A. C = 3100 x log2(2) = 3100 bps. (Key point: Capacity)

3. What does the result show?
   A. Zero data can be sent
   B. Capacity in bps equals bandwidth in Hz; a low SNR makes a poor channel
   C. Capacity is infinite
   D. Noise does not matter
   Answer: B. Even at 0 dB, data can be sent at 1 bit/s/Hz only with good codes and delay. (Key point: Comment)

## Related in Data Communication

- [Channel capacity for 6 kHz, 6 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acapacity-6khz-6db) — Data Communication, chapter 1
- [Capacity and Nyquist levels, 3 to 4 MHz, 24 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Anyquist-shannon-bandwidth-3-4mhz) — Data Communication, chapter 1
- [Required SNR for 40 Mbps over 6 MHz](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acapacity-40mbps-6mhz) — Data Communication, chapter 1

## Related in other subjects

- [Maximum error-free data rate for 1 MHz, 10 dB SNR](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amax-data-rate-1mhz-10db) — Communication Systems, chapter 6
- [PCM: minimum channel bandwidth numerical](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-bandwidth-3khz-0-5pct) — Communication Systems, chapter 4
- [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
- [Information and entropy; capacity as bandwidth → ∞](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ainformation-entropy-capacity-infinite) — Communication Systems, chapter 6