Don't mix up 3dB and 6dB: voltage ratio versus power ratio in dB
Told something "dropped 6dB," if you can't immediately say whether that means the voltage halved or the power fell to a quarter, you'll misread both filter calculations and EMI limits. A dB expresses a ratio on a log scale, with a coefficient of 10 for power and 20 for voltage.
Defined on power; voltage gets 20log because it's squared
The decibel is defined on a power ratio: dB = 10 × log₁₀(P₂ ÷ P₁). Double the power and that is 3.01dB; 10x is 10dB; 100x is 20dB.
Power is proportional to voltage squared (P = V² ÷ R), so for voltage the formula is 20 × log(V₂ ÷ V₁). Double the voltage and that is 6.02dB; 10x is 20dB; 100x is 40dB. The same "doubling" is 3dB for power and 6dB for voltage. Across the same impedance there is no contradiction: double the voltage is four times the power.
The trip-up is reading "−3dB" as a voltage ratio. At the cutoff frequency (the −3dB point), voltage is at 0.707x and power is at 0.5x. "Half" refers to power. Voltage reaches half at −6dB.
| dB | Voltage ratio | Power ratio | Common example |
|---|---|---|---|
| 0dB | 1 | 1 | Reference |
| +3dB | 1.41 | 2 | Power ×2 |
| +6dB | 2 | 4 | Voltage ×2 |
| +10dB | 3.16 | 10 | Power ×10 |
| +20dB | 10 | 100 | Voltage ×10; a typical amplifier gain |
| +40dB | 100 | 10,000 | Voltage ×100 |
| −3dB | 0.707 | 0.5 | Filter cutoff |
| −6dB | 0.5 | 0.25 | Voltage halved; a 1/2 divider |
| −20dB | 0.1 | 0.01 | A first-order filter's roll-off at 10x frequency |
| −40dB | 0.01 | 10⁻⁴ | A second-order filter at 10x frequency; a typical CMRR figure |
| −60dB | 0.001 | 10⁻⁶ | 1/1000 |
dB with a fixed reference: dBm, dBV, dBu, dBµV
A dB is a ratio. It becomes an absolute value once you fix a reference, written after the unit.
- dBm: power referenced to 1mW at 0dBm. Standard in RF. In a 50Ω system, 0dBm = 0.224Vrms (0.632Vp-p), +10dBm = 10mW = 0.707Vrms, −30dBm = 1µW = 7.07mVrms, −100dBm = 0.1pW = 2.2µVrms.
- dBV: voltage referenced to 1Vrms at 0dBV. −20dBV = 0.1V.
- dBu: voltage referenced to 0.775Vrms at 0dBu, the voltage that delivers 1mW into 600Ω. Used for audio line levels (+4dBu = 1.23Vrms, for example).
- dBµV: voltage referenced to 1µVrms at 0dBµV. Used in EMI measurement. 60dBµV = 1mV, 120dBµV = 1V. A CISPR limit of "40dBµV/m" is 100µV/m.
In a 50Ω system, dBµV = dBm + 107. Useful when switching an EMI receiver's display between the two.
dB adds where ratios multiply
The reason to use dB is that gains through a cascade simply add. Filter attenuation works the same way: a first-order RC filter gives −20dB at 10x the cutoff frequency and −40dB at 100x.
For antennas, dBi is referenced to an isotropic radiator and dBd to a half-wave dipole, and dBi = dBd + 2.15. A catalog's 5dBi is 2.85dBd: the same antenna.
Common mix-ups
- Mixing up the coefficient. Writing "output doubled" as 6dB is wrong (3dB for power), and so is writing a 1/2 divider as −3dB (−6dB for voltage).
- Comparing voltage ratios in dB across two points with different impedances. With a 1kΩ input and an 8Ω output, 0dB voltage gain is still 10log(1000 ÷ 8) = 21dB of power gain.
- Confusing a dB difference with a dB value. "SNR improved by 3dB" means the signal-to-noise power ratio doubled. "The noise is 3dB" means nothing without a stated reference.
Calculators
The dB to ratio calculator gives both the voltage ratio and the power ratio. Voltage to dB uses 20log and power to dB uses 10log, so decide first whether your quantity is voltage or power.
Frequently asked questions
Is −3dB half, or 70%?
How many volts is 0dBm?
What's the power gain, in dB, of an amplifier with 20dB of voltage gain?
How do dBµV and dBm convert?
Standards and references
- IEC 60027-3 — Definitions of logarithmic quantities and units (the bel and the neper)
- CISPR 16-1-1 — EMI test receiver specifications and dBµV notation
- ITU-R V.574 — Notation for dB reference values (dBm, dBW, dBµV, and others)