Decibels

The idea

RF signals span absurd ranges. A transmitter might put out 1 watt while the receiver at the far end decodes a signal a hundred million times weaker — and real radio chains multiply gains and losses like this at every stage. Comparing a whisper to a jet engine with plain numbers gets clumsy fast.

Decibels (dB) are a logarithmic counting system that shrinks these monsters into friendly two-digit numbers, like a magical ruler that measures both ant steps and dinosaur footprints on the same scale. A million-fold power difference becomes simply "60 dB". And the real magic: multiplication becomes addition. Chain an amplifier and a lossy cable? Just add and subtract dB values.

Plain dB is a ratio. dBm anchors that ratio to 1 milliwatt, so it measures actual power: 0 dBm = 1 mW, 20 dBm = 100 mW (a typical WiFi router), 30 dBm = 1 W, and −70 dBm is a weak but usable WiFi signal — just 0.0000001 mW. dBW uses 1 watt as the anchor instead (dBW = dBm − 30). dBi expresses antenna gain relative to an ideal isotropic radiator.

Memorize the landmarks:

• +3 dB = power doubled; −3 dB = power halved
• +6 dB = power ×4
• +10 dB = power ×10; −10 dB = power ÷10

Stack them for anything else: 13 dB = 10 + 3 = ×20, and 23 dB = ×200.

The math

For power ratios:

$$P_{dB} = 10 \log_{10}\left(\frac{P_2}{P_1}\right)$$

For absolute power referenced to 1 milliwatt:

$$P_{dBm} = 10 \log_{10}\left(\frac{P}{1\,\text{mW}}\right)$$

Worked example: an amplifier takes 2 mW in and delivers 200 mW out. The ratio is 100, and 10·log₁₀(100) = 20 dB of gain. Or by landmarks: 100× = 10× × 10× = 10 dB + 10 dB = 20 dB. Chaining is just addition: a 0 dBm signal through a 10 dB amplifier and a cable losing 4 dB comes out at 0 + 10 − 4 = 6 dBm.

For voltage ratios the multiplier is 20 instead of 10, because power scales with voltage squared.

Common misconceptions

• Myth: dB is a unit of power, like watts. Reality: Plain dB is a ratio with no absolute meaning. Only anchored forms like dBm or dBW state actual power.
• Myth: A negative dBm value means no signal. Reality: It just means less than 1 mW. Your phone works happily at −70 dBm; WiFi is considered excellent at −50 dBm, which is only 10 nanowatts.
• Myth: Doubling power doubles the dB value. Reality: Doubling power always adds exactly 3 dB, whatever the starting level — 20 dBm doubled is 23 dBm, not 40 dBm.

Try it

Open the dB Converter and check your mental math: convert 1000 mW to dBm (it should be 30), then halve and double values and watch the 3 dB steps. The Decibels Explorer lab walks the same landmarks interactively.