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Asked: 2026-05-16T08:24:00+00:00

i need the derivations that how these formulae comes Vavg=Vpeak/pi for half wave rectifier

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i need the derivations that how these formulae comes 

Vavg=Vpeak/pi for half wave rectifier
Vavg=2Vpeak/pi for full wave
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  1. Editorial Team

    Full wave is double of half wave because both ‘bumps’ are used. That is easy.

    Now derive the halfwave:

    V(t) = Vpeak*sin(t);

    2 PI is a full circle and we only use half of that : 0->PI

    Vavg = Vpeak*integral(sin(t),0 -> PI)/2*PI

    indefinite integral of sin(x) = -cos(x)

     = Vpeak*(-cos(PI) + cos(0))/2*PI 
 = Vpeak*(-(-1) +  1) / 2*PI
 = Vpeak ( 1 + 1) / 2*PI
 = Vpeak / PI

    that’s it.

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