Decibel Formulas
Power: dB = 10 × log₁₀(P₂/P₁). Ratio = 10^(dB/10). Voltage: dB = 20 × log₁₀(V₂/V₁). Ratio = 10^(dB/20). dBm: dBm = 10 × log₁₀(P_mW). Add dB: total gain = sum of all stage gains in dB. +3dB ≈ 2× power, +10dB = 10× power, +20dB = 100× power.
Frequently Asked Questions
A decibel is a logarithmic unit that expresses ratios of power, voltage, or sound pressure on a scale that matches human perception. For power: dB = 10 × log10(P2/P1). For voltage: dB = 20 × log10(V2/V1). The logarithmic scale means +10dB = 10× power, +20dB = 100× power, +3dB ≈ 2× power.
Decibels are added when gains/losses are in series: total gain = G1 + G2 + G3 (all in dB). For example, a 10dB amplifier followed by a 3dB loss gives 10 - 3 = 7dB net gain. This only works when all values use the same dB reference.
dBm is power referenced to 1 milliwatt: dBm = 10 × log10(P_mW / 1 mW). 0dBm = 1mW, +10dBm = 10mW, +30dBm = 1W, -30dBm = 1µW. dBm is commonly used in RF and telecom to express signal power levels.
The dB formula for power (10×log10) differs from voltage (20×log10) because power is proportional to voltage squared (P = V²/R). These formulas are equivalent when the impedances are equal. Always specify whether you're working with power or voltage ratios when using dB.
dBm: power re 1mW. dBW: power re 1W. dBV: voltage re 1V. dBu: voltage re 0.775V (historically a power level in a 600Ω system). dBFS: digital audio level re full scale. dB SPL: sound pressure re 20µPa (threshold of human hearing). Always check the reference when interpreting dB values.
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