Measurements in Communication Systems - Decibels

The logarithmic language of electrical engineering. From signal amplification to noise floors, understand why engineers think in dB.

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Core Concepts

Why Logarithms?

Human senses (hearing, vision) perceive intensity logarithmically. In engineering, signals often vary over massive ranges (nanoWatts to MegaWatts).

1000x Power Gain = 30 dB
1,000,000x Power Gain = 60 dB

Power vs. Voltage

The decibel formula changes based on what you are measuring. Power is proportional to the square of voltage.

Power (W): 10·log₁₀(P₂/P₁)
Voltage (V): 20·log₁₀(V₂/V₁)

Quick Reference: Linear to Logarithmic

Power Ratio Voltage Ratio dB Value Engineering Note
0.5 0.707 -3 dB Half power point (Cutoff freq)
1 1 0 dB Unity Gain (No change)
2 1.414 +3 dB Double Power
10 3.162 +10 dB Order of Magnitude (Power)
100 10 +20 dB Factor of 10 (Voltage)
1000 31.62 +30 dB Factor of 1000 (Power)

Interactive Workbench

01. Ratio Converter

Using formula: dB = 10·log₁₀(P₂/P₁)

Gain / Attenuation

10.0
10 dB

02. Absolute dB Converter

Context: dBW is used in RF transmission (Satellites). 0 dBW = 1 Watt.

Signal Chain Visualizer

Input Power 1 mW
-20 dBm +20 dBm
Amplifier Gain +10 dB
-10 dB +30 dB
Cable Loss -3 dB
0 dB -20 dB
Source
0 dBm
1 mW
Amplifier
+10 dB
x10.0
+
Cable Loss
-3 dB
x0.5
-
Output
7 dBm
5.01 mW
Note: In dB calculations, addition/subtraction corresponds to multiplication/division in linear scale.

Knowledge Check

Question 1/5

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