dB Voltage Ratio
Gain in dB from two voltages — the 20·log flavor.
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The engineering
Twenty, not ten, because power goes with V² and the 2 comes down out of the logarithm. Same decibel, same 3-dB-is-double-power rule — but in volts, 6 dB is the doubling.
This only equals power dB when both voltages see the same impedance; across different impedances, say which one you mean.
Where this math comes from
Same Bell System 1920s origin as the power dB, with the 20·log form falling directly out of P ∝ V²/R. The convention that trips every sophomore — 6 dB per voltage doubling versus 3 dB per power doubling — is just that square, taken through Napier's logarithm.
Audio and EMC work run almost entirely in this flavor: dBu, dBV, dBµV are all 20·log references.
- 1614John NapierLogarithms — the machinery.
- 1928Bell SystemDecibel adopted; the 10·log/20·log power-voltage pair standardizes.
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