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A decibel (dB) is a logarithmic way to express a ratio of two powers or voltages. Because our senses and wide-ranging signals are logarithmic, dB turns huge ratios into easy numbers and lets you add gains instead of multiplying them. Power uses 10·log; voltage uses 20·log (because power goes as voltage squared).
| Quantity | Formula |
|---|---|
| Power ratio | dB = 10·log10(Pout/Pin) |
| Voltage ratio | dB = 20·log10(Vout/Vin) |
| Ratio from dB | ratio = 10(dB/10) power, 10(dB/20) voltage |
| dBm (absolute power) | dBm = 10·log10(PmW), 0 dBm = 1 mW |
Handy reference points: +3 dB ≈ double the power, −3 dB ≈ half, +6 dB ≈ double the voltage, and +10 dB = 10× the power.
A decibel is a logarithmic unit expressing the ratio between two powers or voltages. It compresses very large ratios into manageable numbers and lets gains be added instead of multiplied.
Because power is proportional to voltage squared. Taking the log of a squared quantity brings the exponent out front, turning 10·log into 20·log for voltage (and current) ratios.
Approximately double the power (the exact factor is 1.995). Likewise −3 dB is about half the power — the basis of the "−3 dB" bandwidth point.
About double the voltage (or current), since 20·log(2) ≈ 6 dB. It is also four times the power.
An absolute power level referenced to 1 milliwatt: dBm = 10·log10(power in mW). So 0 dBm = 1 mW, 30 dBm = 1 W, and −30 dBm = 1 µW.
Power in mW = 10^(dBm/10), then divide by 1000 for watts. For example 20 dBm = 100 mW = 0.1 W.
Convert the power to milliwatts, then dBm = 10·log10(mW). 2 W is 2000 mW, so 10·log(2000) ≈ 33 dBm.
They let you add gains and losses along a signal chain instead of multiplying ratios, handle enormous dynamic ranges, and match how we perceive sound and light.
A ratio less than 1 — attenuation or loss. For example a cable that halves the power has a gain of −3 dB.
No. 0 dB means the ratio is exactly 1 (output equals input, i.e. no change). Zero signal would be minus infinity dB.
dB is a relative ratio between two quantities; dBm is an absolute power referenced to 1 mW. You can add dB gains to a dBm level to get a new dBm level.
Start with the transmit power in dBm, then add antenna gains and subtract cable and path losses in dB. The result is the received power in dBm.
The frequency where a filter's output power falls to half (voltage to 0.707) of the passband — the standard definition of bandwidth.
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