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Decibels and dbm

Decibels are dimensionless numbers used to represent the ratio of two quantities of power: db = 10 log P₁/P₀ . This is a base 10 logarithm. For the common unit of "dbm" the reference power P₀ is defined as 1 milliwatt : dbm = 10 log P₁/1mw. Easy, right?

This equation can be inverted to gives power in terms of a reference power: P₁= P₀10^db/10. For the common unit of dbm the equation is P₁= 1mw·10^dbm/10

Why? It is not unusual in a radio, radar, or microwave system to have 100,000 watts of transmit power, 1 microwatt of receive power, and various gains and losses from antennas, distance, and absorbing media. Adding and subtracting db is more convenient than multiplying, particularly if you are using a slide rule and trying to keep track of the decimal point.

For signals trapped on a wire it is much easier to measure volts or amps with a voltmeter or current probe, but dbm can still be used. Since Watts are proportional to Amps squared or Volts squared, db (in power) = 20 log V₁/V₀ or db = 20 log I₁/I₀ . This is only useful in cases where the voltage or current is measured at the same impedance or resistance, which allows the ratio of two powers I²R or V²/R to cancel out the R.

Fun facts: the "bell" in Decibel is named after Alexander Graham Bell, the telephone inventor. The concept was developed at Bell Labs, but for some reason of economy or humor when they named it they left out the second "L" in his name. Originally it was called the TU, or "transmission unit." The term "logit" was also bounced around for a while.

We hope that this information is helpful. Now go out and design something that needs a charger, power supply, or battery pack!