Power Decibels
Ratio of two power levels expressed logarithmically.
Formula
Variables
Example
P1=100, P2=1: dB = 20
How it works
Decibels let you compare two power levels on a logarithmic scale, which is useful because power values in telecom can vary by huge factors. The factor of 10 appears because decibels were defined for power ratios, and the logarithm turns multiplication of power gains/losses into simple addition and subtraction. A positive result means the output power is greater than the reference power; a negative result means it is smaller.
When to use it
Use this formula when comparing signal power before and after an amplifier, attenuator, antenna, or transmission path. It is common in radio, audio, and networking whenever you want to express a power change compactly in dB.
Worked example, step by step
Suppose a transmitter output power is 250 mW and the reference power is 10 mW. Step 1: Write the ratio: P1/P2 = 250/10 = 25 Step 2: Take the base-10 logarithm: log10(25) ≈ 1.39794 Step 3: Multiply by 10: dB = 10 × 1.39794 ≈ 13.98 dB Final answer: the power level is about 14 dB above the reference.
Common mistakes to avoid
- Using the power formula for voltage or current without the needed 20 log10 relationship
- Forgetting that the ratio must be P1 divided by P2, not the other way around
- Treating dB as an absolute unit instead of a ratio between two powers
Did You Know?
Every 3 dB represents a doubling of power — a handy mental shortcut for engineers.
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