Decibel Power Gain

Bell Telephone engineers needed a way to add up losses along a line instead of multiplying them, so they took logarithms; the bel proved too coarse and the decibel — a tenth of one — stuck. Ten times log of the power ratio means 3 dB is a doubling, 10 dB is ten times, 20 dB is a hundred times, and 100 W out of 1 W in is a 20 dB gain. Cascade stages and the decibels simply add.

The trap is the reference. A plain dB is a ratio and says nothing about absolute level; dBm fixes P₁ at 1 mW, so 30 dBm is exactly 1 W and 0 dBm is 1 mW. Mixing the two — treating a gain in dB as a level in dBm — is a classic RF blunder. Remember also that this 10-log form is only for power; voltage and current ratios use 20 log, since power goes as the square.