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's 3.01dB; 10x is 10dB; 100x is 20dB.
Express it in voltage instead, and because power is proportional to voltage squared (P = V² ÷ R), 10 × log(V₂² ÷ V₁²) becomes 20 × log(V₂ ÷ V₁). Double the voltage and that's 6.02dB; 10x is 20dB; 100x is 40dB. The same "doubling" is 3dB for power and 6dB for voltage.
The two agree when measured across the same impedance. Double the voltage and power quadruples — 6dB either way you calculate it. Double the power and voltage rises by √2 = 1.414 — 3dB either way. This isn't a contradiction; it's the same event viewed through power or through voltage.
The trip-up is reading "−3dB" as a voltage ratio. At a filter's cutoff frequency (the −3dB point), voltage is at 0.707x and power is at 0.5x. "Half" refers to power — voltage still has 70% of it left. Voltage reaching half is −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 by itself is a ratio, not a magnitude. Pin down a reference and it becomes an absolute value, with the reference written into 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, +20dBm = 100mW, +30dBm = 1W. −30dBm = 1µW = 7.07mVrms, −100dBm = 0.1pW = 2.2µVrms (receiver-sensitivity territory).
dBV: voltage referenced to 1Vrms at 0dBV. −20dBV = 0.1V, −60dBV = 1mV.
dBu: voltage referenced to 0.775Vrms at 0dBu. That figure comes from the voltage that delivers 1mW into 600Ω, and it's the standard for audio line inputs and outputs (+4dBu = 1.23Vrms, for example).
dBµV: voltage referenced to 1µVrms at 0dBµV. Used in EMI measurement. 60dBµV = 1mV, 120dBµV = 1V. A CISPR limit written as "40dBµV/m" is a field strength of 100µV/m.
In a 50Ω system, dBm and dBµV have a fixed relationship, dBµV = dBm + 107. 0dBm = 107dBµV. Useful when switching an EMI test receiver's display between the two.
dB adds where ratios multiply
The reason to use dB at all is that gains through a cascade of circuits simply add. Follow a 20dB amplifier with a −6dB divider and you get 14dB. In plain ratios that's 10 × 0.5 = 5x, and 20log(5) = 14dB.
Filter attenuation adds the same way. A first-order RC filter rolls off −20dB at 10x the cutoff frequency and −40dB at 100x. Cascade two stages (isolated so they don't load each other) and that becomes −40dB and −80dB.
An op-amp's gain-bandwidth product (GBW) works on the same principle. Set 40dB (100x) of gain on a 1MHz-GBW op-amp and the bandwidth is 1MHz ÷ 100 = 10kHz. Drop the gain to 20dB (10x) and the bandwidth stretches to 100kHz.
Antenna gain in dBi and dBd use different references. dBi is referenced to an isotropic radiator, dBd to a half-wave dipole, and dBi = dBd + 2.15. A catalog's 5dBi is 2.85dBd — the same antenna.
Common mix-ups
- Using 20log for a power ratio. Writing "output doubled" as 6dB — for power, it's 3dB.
- Using 10log for a voltage ratio. Writing a 1/2 divider as −3dB — for voltage, it's −6dB.
- Comparing voltage ratios in dB across two points with different impedances. An amplifier with a 1kΩ input and an 8Ω output can show "0dB voltage gain" while still having a power gain of 10log(1000 ÷ 8) = 21dB.
- Treating dBm as a voltage. dBm is power, so the corresponding voltage changes with impedance: 0dBm is 0.224V at 50Ω but 0.775V at 600Ω.
- Reading −3dB as "barely different." It's half the power. That may sound like a small change in audio, but it's a large number in power efficiency or an RF link budget.
- 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 from a dB value. Voltage to dB and power to dB use 20log and 10log respectively. Which calculator applies depends on the coefficient, so decide first whether the quantity you're working with 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)