Vpeak(out)=Vm−Vdcap V sub p e a k open paren o u t close paren end-sub equals cap V sub m minus cap V sub d The adjusted DC formula becomes:
In a half-wave rectifier, the diode only conducts during the positive half-cycle. The average value is the integral of the sine wave over one full period ( ), divided by that period: calculate output voltage half wave rectifier
Vdc=12π∫0πVmsin(θ)dθ=Vm2π[−cos(θ)]0π=Vmπcap V sub d c end-sub equals the fraction with numerator 1 and denominator 2 pi end-fraction integral from 0 to pi of cap V sub m sine open paren theta close paren space d theta equals the fraction with numerator cap V sub m and denominator 2 pi end-fraction open bracket negative cosine open paren theta close paren close bracket sub 0 raised to the pi power equals the fraction with numerator cap V sub m and denominator pi end-fraction 3. Account for Diode Forward Bias Real diodes have a forward voltage drop ( Vdcap V sub d ), typically for silicon. This reduces the peak output: Vpeak(out)=Vm−Vdcap V sub p e a k open