The decibel formula changes from 10·log to 20·log when comparing voltages instead of powers

The decibel is a logarithmic ratio. For power ratios: dB = 10 · log(P₁/P₂). Because power is proportional to voltage squared (P ∝ V²), for voltage ratios the formula becomes dB = 20 · log(V₁/V₂). Practical consequences: doubling power = +3 dB; doubling voltage = +6 dB; multiplying power by 10 = +10 dB; multiplying voltage by 10 = +20 dB. All audio level calculations use the 20·log form because audio equipment is voltage-sensitive. The 10·log form appears in acoustics (sound power, PWL) and when dealing with actual wattages.

Examples

A console output that rises from 0.775 V to 1.55 V has increased by +6 dB (20·log(2) = 6.02). The same 2× voltage change would be only +3 dB if mistakenly expressed as a power ratio.

Assessment

Calculate the dB change when voltage triples. Now calculate the dB change when power triples. Explain why the answers differ.