log10V1Vref

Log10V1Vref is an informal notation encountered in some technical texts and software to denote the base-10 logarithm of the ratio between a signal voltage V1 and a reference voltage Vref. In standard mathematical form it represents log10(V1/Vref). Since the ratio V1/Vref is dimensionless when both quantities are voltages, the result is also dimensionless.

In practice, this expression is often used as a stepping stone to decibel calculations. For voltage ratios, the corresponding decibel measure is 20 times the base-10 logarithm: 20·log10(V1/Vref). For power ratios, the decibel form is 10·log10(P1/Pref). The log10V1Vref form thus provides a compact way to describe relative levels or gains, with Vref serving as a reference baseline.

Interpretation considerations include the requirement that the ratio be defined, typically meaning V1 and Vref are positive voltages or magnitudes. The same quantity can be computed as log10(V1) − log10(Vref); both expressions are equivalent when V1 and Vref are positive. Ambiguities can arise if parentheses are omitted in notation, so the intended meaning is usually log10(V1/Vref).

Example: If V1 = 2 V and Vref = 1 V, log10(V1/Vref) = log10(2) ≈ 0.3010. In the context of voltage software gains, this would correspond to a 6.02 dB increase when used as 20·log10(V1/Vref).

See also: decibel, dBV, logarithm base-10, voltage ratio.