of RMS Value of a DC Offset Sinusoid
Here's a derivation of the RMS value of a sinusoid
offset by a DC value.
Vrms= sqrt(1/T*Integral([Vdc+ Vpk*sin(t)]^2)*dt )
Where T is 2*pi
Vrms= sqrt( 1/T* Integral( Vdc^2+ 2*Vdc*Vpk*sin(t)+
Vpk^2*sin(t)^2 )*dt )
The middle term get's dropped because the
average of a sine over a period is zero.
Vrms= sqrt( 1/T* Integral( Vdc^2*dt))
+ 1/T* Integral(Vpk^2*sin(t)^2 )*dt )
Vrms= sqrt( Vdc^2 + [ Vpk^2/T*(t/2-
sin(2*t)/4) (from 0 to T)] )
The sin terms cancel.
Vrms= sqrt( Vdc^2 + Vpk^2/2 )
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