Decibels: Basics and Practical Applications

Aug 5, 2024

Software Defined Radio with Hack RF - Lesson Three: What is a Decibel?

Introduction

  • Michael Osman from Great Scott Gadgets
  • Focus on understanding decibels (dB)
  • Importance of decibels in the course

Understanding Decibels

  • Commonly seen in FFT plots in GNU Radio Companion
  • Many people make mistakes with decibels, even those experienced
  • Need to understand the basics of decibels.

Basic Definitions

  • Decibel: A logarithmic unit of ratio.
    • 1 dB = 1/10 Bell
    • 10 dB = 1 Bell
  • Bell: Describes the number of orders of magnitude (powers of 10) of a ratio.
    • Example:
      • Ratio of 10:1 = 1 Bell (10 dB)
      • Ratio of 100:1 = 2 Bells (20 dB)
      • General formula: Ratio A/B = 10^n, where n = number of Bells.

Examples of Decibel Calculation

  • Height Example:
    • Michael: 2m, Brother: 20m
      • Ratio: 20/2 = 10:1
      • Brother is 10 dB taller.
    • Brother: 200m
      • Ratio: 200/2 = 100:1
      • Brother is 20 dB taller.
    • Brother: 2000m
      • Ratio: 2000/2 = 1000:1
      • Brother is 30 dB taller.

Adding and Subtracting Decibels

  • Adding or subtracting dB = multiplying or dividing the ratios.
  • Common Tricks:
    • 3 dB ≈ ratio of 2:1
    • 10 dB = ratio of 10:1

More Height Examples

  • Brother at 4m:
    • Ratio: 4/2 = 2:1
    • 3 dB taller.
  • Brother at 40m:
    • Ratio: 40/2 = 20:1
    • 10 dB + 3 dB = 13 dB.
  • Brother at 1m:
    • Ratio: 1/2 = 1:2 (shorter)
    • Negative 3 dB.
  • Same height:
    • Ratio: 2/2 = 1:1
    • 0 dB.

Common Mistakes with Decibels

  1. Relative Measurement: It's important to specify what the decibels are relative to (e.g., dBm, relative to my height).
  2. Amplitude vs Power:
    • Power is proportional to the square of amplitude.
    • 10 dB is for power, 20 dB is for amplitude.
  3. Negatives: Be cautious with negative values; they can be confusing.
    • E.g., negative 5 dB loss means 5 dB loss, not a gain.

Practical Example of Decibel Use

  • Calculating power at an antenna:
    1. Output: 5 dBm
    2. Filter: -3 dB loss
    3. Amplifier: +12 dB gain
    4. Long cable: -2 dB loss
  • Calculate total: 5 - 3 + 12 - 2 = 12 dBm at the antenna.

Homework Assignment

  • Create a table from 0 dB to 30 dB:
    • Left column: dB values (0, 1, 2, ..., 30)
    • Right column: actual ratios (1:1 for 0 dB, 2:1 for 3 dB, etc.)
  • Use powers of 2 and known rules to fill out the table.
  • Consider the error in using the 3 dB approximation for a doubling.

Conclusion

  • Understanding decibels is fundamental for the course.
  • Knowing how to convert dB to ratios is a useful skill.
  • Next lesson will cover homework from lesson two.