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.