sqrtVdc2

sqrtVdc2 is a compact notation used to denote the square root of the square of a direct-current voltage, Vdc. If Vdc is real-valued, sqrtVdc2 is defined as sqrt(Vdc^2). Because squaring removes sign and the real square root yields a non-negative result, sqrt(Vdc^2) equals |Vdc|, the absolute value of Vdc. This quantity represents the magnitude or non-negative amplitude associated with the DC voltage.

In practical terms, sqrtVdc2 behaves as the magnitude of the DC component. For example, if Vdc = 5 V, sqrtVdc2 = sqrt(25) = 5 V; if Vdc = -3 V, sqrtVdc2 = sqrt(9) = 3 V. It does not carry information about sign, only about size.

Relation to RMS: For a constant DC signal, the root-mean-square (RMS) value is equal to the absolute value of the DC level, so sqrtVdc2 coincides with the RMS value of that constant signal. For time-varying or AC signals, RMS is generally defined differently (as the square root of the mean of squared values over time) and need not equal sqrtVdc2.

Cautions: If Vdc is complex, or if a particular branch of the complex square root is used, sqrt(Vdc^2) may not equal |Vdc|. In standard real-valued DC usage, sqrtVdc2 is interpreted as the non-negative magnitude |Vdc|.

See also: Absolute value, RMS, Direct current, Square and square root principles.