---
title: "Transmission impairments; attenuation of cable"
subject: "Data Communication"
chapter: 1
key: "semester_5/data_communication:attenuation-cable-numeric"
source: https://www.bctengineer.com/q/semester_5/data_communication/attenuation-cable-numeric
site: BCT Engineering
---

# Transmission impairments; attenuation of cable

Data Communication · Chapter 1: Introduction

- Asked in: 2069 Asar, 8 marks
- Video: [Transmission Impairments |  Data Communication | Lec-04 | Bhanu Priya](https://www.youtube.com/watch?v=GYAKUoeuFRQ) — Education 4u
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/attenuation-cable-numeric
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-1

## Question

Explain transmission impairments in detail. If the signal at the beginning of a cable with -0.3 dB/km has a power of 2 mW, what is the power of the signal at 5 km?

## Short answer

Transmission impairments include attenuation, distortion, and noise. With attenuation -0.3 dB/km over 5 km, total loss is -1.5 dB, so power reduces from 2 mW to 2 × 10^(-0.15) ≈ 1.42 mW.

## Answer

#### Transmission impairments
Impairments are the imperfections that make the received signal differ from the one transmitted. There are three main kinds.

1. **Attenuation**: loss of signal energy with distance in the medium. It grows with distance and frequency. It is measured in dB: dB = 10 log₁₀(P₂/P₁). Amplifiers or repeaters restore the strength.
2. **Distortion**: change of the signal shape because different frequency components travel at different speeds (delay distortion) or are attenuated differently. It causes inter-symbol interference; equalisers correct it.
3. **Noise**: unwanted signals added in the channel.
   - Thermal noise: random electron motion, N = kTB.
   - Intermodulation noise: sums/differences of frequencies in non-linear media.
   - Crosstalk: coupling between adjacent wires.
   - Impulse noise: sudden spikes (lightning, switching) causing burst errors.

SNR = signal power / noise power decides the error rate, and the capacity is C = B log₂(1 + SNR).

#### Numerical
Attenuation = -0.3 dB/km, length = 5 km, P₁ = 2 mW.

Total loss = -0.3 × 5 = -1.5 dB

dB = 10 log₁₀(P₂/P₁) = -1.5

P₂/P₁ = 10^(-0.15) = 0.7079

P₂ = 2 mW × 0.7079 = 1.416 mW

**Answer: power at 5 km ≈ 1.42 mW.**

## Check yourself

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

1. Loss over 5 km at -0.3 dB/km is
   A. -0.3 dB
   B. -15 dB
   C. -1.5 dB
   D. -0.06 dB
   Answer: C. 0.3 x 5 = 1.5 dB. (Key point: Total loss)

2. -1.5 dB corresponds to P2/P1 of
   A. 1.41
   B. 0.15
   C. 0.5
   D. 0.708
   Answer: D. 10^-0.15 = 0.7079. (Key point: Power ratio)

3. Power at 5 km is about
   A. 1.42 mW
   B. 2.83 mW
   C. 0.5 mW
   D. 1.5 mW
   Answer: A. 2 x 0.7079 = 1.416 mW. (Key point: Output power)

4. Distortion is caused by
   A. loss of energy only
   B. components travelling at different speeds or attenuated unequally
   C. unwanted added signals
   D. coupling
   Answer: B. Equalisers correct it. (Key point: Distortion)

## Related in Data Communication

- [Transmission impairments](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Atransmission-impairments) — Data Communication, chapter 1, asked 6×
- [Transmission characteristics of guided media](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aguided-media-transmission-characteristics) — Data Communication, chapter 4
- [Capacity for 3.1 kHz, SNR 0 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acapacity-3-1khz-0db) — 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
- [Optical fiber vs satellite transmission](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aoptical-fiber-vs-satellite) — Data Communication, chapter 4

## Related in other subjects

- [Impairments to voice channel transmission](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Avoice-channel-impairments) — Telecommunications, chapter 2
- [Normalization and 78 dB/90 dB attenuation numerical](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aattenuation-output-amplitude-normalization) — Filter Design, chapter 1
- [450 km 400 kV line, 420 MW, 0.9 pf](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3A450km-400kv-420mw-090) — Power System Analysis I, chapter 5
- [Conductor selection, 100 MW 70 km 132 kV](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aconductor-selection-100mw-70km-132kv) — Transmission and Distribution System Design, chapter 4