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Decibels: Basics and Practical Applications
Aug 5, 2024
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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
Relative Measurement
: It's important to specify what the decibels are relative to (e.g., dBm, relative to my height).
Amplitude vs Power
:
Power is proportional to the square of amplitude.
10 dB is for power, 20 dB is for amplitude.
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:
Output: 5 dBm
Filter: -3 dB loss
Amplifier: +12 dB gain
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.
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