Decibel (Voltage)
Voltage ratio in decibels.
Formula
Variables
How it works
The decibel formula turns a voltage ratio into a logarithmic scale, which makes very large or very small changes easier to compare. The factor of 20 appears because power is proportional to voltage squared when the resistance stays the same, and decibels are fundamentally based on power ratios. In practice, this means a doubling of voltage is not "2 dB"; it is about 6.02 dB.
When to use it
Use this when comparing two voltages in audio, RF, signal processing, or electronics measurements, especially when you want to express gain or attenuation compactly. It is most appropriate when the voltages are measured across the same impedance or into the same load.
Worked example, step by step
Given: V1 = 0.25 V, V2 = 2.0 V Step 1: Form the voltage ratio: V2 / V1 = 2.0 / 0.25 = 8 Step 2: Take the base-10 logarithm: log10(8) ≈ 0.9031 Step 3: Multiply by 20: dB = 20 × 0.9031 ≈ 18.06 dB Answer: The voltage increase is about 18.1 dB.
Common mistakes to avoid
- Using 10 log10(V2/V1) instead of 20 log10(V2/V1)
- Applying the formula to voltages measured across different impedances without checking the load conditions
- Forgetting that a negative dB result means V2 is smaller than V1
Did You Know?
For voltage, a 6 dB rise means doubling, reflecting power's dependence on voltage squared.
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