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Decibels (dB)

The decibel is a logarithmic way of stating the ratio between two voltages (or other quantities), used because gain and attenuation in cascaded systems can then simply be added instead of multiplied. Halving the amplitude corresponds to about −6-6 dB.

∣H∣dB=20log⁡10∣H∣|H|_{dB}=20\log_{10}|H|decibels from a voltage ratio

Symbols

∣H∣|H|voltage ratio (gain)
∣H∣dB|H|_{dB}the ratio in decibelsdB

Example

∣H∣=0.5|H|=0.5:

∣H∣dB=20log⁡10(0.5)≈−6|H|_{dB}=20\log_{10}(0.5)\approx-6 dB.

−3-3 dB corresponds to about 1/2≈0.7071/\sqrt2\approx0.707 in amplitude, not half the amplitude.
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