What is the formula for a decibel of voltage?

The formula for measuring voltage in decibels is defined as 20 times the logarithm of the ratio of the voltage under consideration (V) to a reference voltage (V0). This is derived from the general formula for decibels, which is 10 log (P1/P2) for power measurements. However, since power is proportional to the square of voltage (P ∝ V²), when dealing with voltage ratios, the logarithmic expression must be adjusted accordingly.

Specifically, when converting voltage levels to decibels, the square relationship implies that the factor of 10 for power must be doubled, leading to the factor of 20 in the voltage formula. Therefore, the correct formulation to express a decibel measurement based on voltage is 20 log (V/V0). This captures the change in voltage level relative to a defined reference voltage and allows for a meaningful representation of how much the voltage has increased or decreased in decibels.

Understanding this relationship is critical, particularly in fields involving telecommunications and audio engineering, where voltage comparisons are routinely made to evaluate performance and signal integrity.