Mathematics for Studying Radio
Decibels

The decibel (dB) is a unit that is used to measure electrical power. A dB is one-tenth of a Bel, which is a larger unit of sound named for Alexander Graham Bell. The dB is measured on a base 10 logarithmic scale . The base increases ten-fold for every ten dB measured. This scale allows people to work more easily with large numbers. A similar scale called the Richter Scale is used in measuring earthquakes. For example a magnitude 6.3 earthquake is 10 times stronger than a 5.3 earthquake.

Calculating dB
The formula for calculating dB is as follows:

dB = 10 log10 (Pfinal/Pref)
  • dB = The amount of decibels. This usually represents a loss in power such as when the wave travels or interacts with matter, but it can also represent a gain as when traveling through an amplifier.
  • Pfinal = The final power. This is the delivered power after some process has occurred.
  • Pref = The reference power. This is the original power.

There are also some general rules for approximating the dB and power relationship:

  • An increase of 3 dB = Double the power
  • A decrease of 3 dB = Half the power
  • An increase of 10 dB = Ten times the power
  • A decrease of 10 dB = One-tenth the power