Decibel (Amplitude Ratio)
Express a voltage/amplitude ratio in decibels.
Formula
Variables
Example
A_2 = 2×A_1: L ≈ 6 dB
How it works
This formula converts an amplitude or voltage ratio into decibels, which are a logarithmic way to compare sizes. The factor of 20 appears because power is proportional to the square of amplitude, and decibels are fundamentally defined using power ratios; taking the square root relationship gives 20 log10 for amplitude. A positive result means the measured amplitude is larger than the reference, while a negative result means it is smaller.
When to use it
Use this when comparing two voltages, sound-pressure amplitudes, or other signal amplitudes in audio and electronics. It is especially useful when values span a wide range and you want a compact, easy-to-read scale.
Worked example, step by step
Given A_1 = 0.5 V and A_2 = 1.5 V L = 20 log10(A_2 / A_1) L = 20 log10(1.5 / 0.5) L = 20 log10(3) L ≈ 20 × 0.4771 L ≈ 9.54 dB Final answer: the amplitude increased by about 9.5 dB
Common mistakes to avoid
- Using 10 log10 instead of 20 log10 for amplitude or voltage ratios
- Swapping A_1 and A_2 and getting the sign backwards
- Forgetting that the formula uses a ratio, so the units must cancel before taking the logarithm
Did You Know?
Doubling voltage is +6 dB, but doubling power is only +3 dB — the factor of 20 vs 10 catches many engineers out.
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