RMS voltage of a sine curve with offset

This function calculates the rms value of a sinusoidal voltage with superimposed DC voltage.

Formulas for sinusoidal voltage with offset

RMS value of a sinusoidal voltage

The rms value is defined as a DC voltage value with the same thermal effect as the specified AC voltage. With sinusoidal alternating current it is without offset:

\(\displaystyle U_{rms}=\frac{U_p}{\sqrt{2}}\)

In order to calculate the effective value of a superimposed sinusoidal voltage, the value of the voltage difference between the maximum and minimum voltage (U_pp) must first be determined.

\(\displaystyle U_{pp}=U_{max}-U_{min}\)

The peak value can be derived from this

\(\displaystyle U_p=\frac{ U_{pp} } {2} =\frac{U_{max}-U_{min}}{2}\)

The formula for the rms value of the sinusoidal voltage without DC voltage component is therefore:

\(\displaystyle U_{rms}=\frac{U_p}{\sqrt{2}}=\frac{ U_{pp} } {2 · \sqrt{2}} =\frac{U_{max}-U_{min}}{2 · \sqrt{2}}\)

RMS value with offset

To calculate the rms value with offset, the rms value of the sinusoidal voltage is added to the square of the value of the direct voltage. The formula is

\(\displaystyle U2_{rms}=\sqrt{U_{rms}^2 + U_{off}^2}\)

The mean value of the pure sine voltage is always 0V. If the voltage is superimposed on a DC voltage, the average value is identical to the superimposed DC voltage.

Legend

\(\displaystyle U_p\)	Peak voltage
\(\displaystyle U_{pp}\)	Peak-to-peak voltage
\(\displaystyle U_{rms}\)	RMS value of the AC voltage
\(\displaystyle U2_{rms}\)	Rms AC voltage with superimposed DC
\(\displaystyle U_{off}\)	Superimposed DC voltage (offset)