AC foundations
Mean of a rectified sine wave
- where
- mean value of the rectified wave (V)
- sine-wave peak voltage (V)
Explain this equation
Gives the average (mean) voltage of a full-wave rectified sine wave with no smoothing. Useful when estimating the raw output of a bridge rectifier or reading an averaging meter on rectified DC.
Vₚ is the peak voltage of the original sine wave. Full-wave rectification flips the negative half-cycles positive, giving a string of positive humps. Vmean is the steady DC level that would have the same average.
Averaging one sine hump over its width gives 2/π of the peak, about 0.637. The π appears because the area under one hump is 2Vₚ and its width is π radians.
A 100 V peak gives about 63.7 V mean. For comparison the RMS value is 0.707 × Vₚ, so the mean is always lower than the RMS for a sine wave. Double the peak and the mean doubles.
Watch out: ideal diodes are assumed, with no forward voltage drop. A smoothing capacitor raises the average towards the peak, so this no longer applies. The mean of an unrectified sine wave over a whole cycle is zero.
An ideal full-wave rectifier turns negative half-cycles positive. The average of that unsmoothed waveform is about 0.637 times its peak.
The mean of the original signed sine wave over a complete cycle is zero. A smoothing capacitor changes the waveform and its average.
Enter your values to see the result.
Common mistake
Confusing rectified average with RMS or smoothed DC.
Limits
Ideal diodes, no smoothing capacitor and a sinusoidal input.
Sources
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