Decibel (Power)
Power ratio expressed in decibels.
Formula
Variables
Example
×10 ⇒ 10 dB
How it works
Decibels turn a power ratio into a logarithmic scale, so very large increases or decreases can be written as manageable numbers. The factor of 10 appears because a decibel is defined for power, and the logarithm compares how many times larger one power is than another relative to a reference. This is especially useful because many physical systems respond to ratios rather than absolute power values.
When to use it
Use this formula whenever you need to compare two power levels in audio, radio, signal processing, or communications. It is also common when describing gains and losses through amplifiers, filters, antennas, and transmission lines.
Worked example, step by step
Suppose an amplifier raises signal power from 2 mW to 50 mW. P1 = 2 mW P2 = 50 mW Ratio = P2 / P1 = 50 / 2 = 25 Use the formula: dB = 10 log10(25) log10(25) ≈ 1.398 So dB ≈ 10 × 1.398 = 13.98 dB Final answer: the power increase is about 14 dB
Common mistakes to avoid
- Using 20 log10 instead of 10 log10 for a power ratio
- Putting the larger power in the denominator and getting a negative result when a gain was expected
- Trying to use this formula on voltage or current directly without first converting to power or using the appropriate voltage/current form
Did You Know?
Every 3 dB gain doubles power, so decibels turn huge multiplicative ranges into manageable additions.
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