To calculate the output voltage of a half-wave rectifier, you primarily need to determine the ( Vdccap V sub d c end-sub ) and the RMS output voltage ( Vrmscap V sub r m s end-sub ). For an ideal rectifier with an input peak voltage Vmcap V sub m Average (DC) Voltage : RMS Voltage : 1. Identify the Peak Input Voltage
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:
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:
The input to a rectifier is typically a sinusoidal AC voltage defined as . If you are given the RMS value of the AC input (e.g.,
Vrms=12π∫0π(Vmsin(θ))2dθ=Vm2cap V sub r m s end-sub equals the square root of the fraction with numerator 1 and denominator 2 pi end-fraction integral from 0 to pi of open paren cap V sub m sine open paren theta close paren close paren squared space d theta end-root equals the fraction with numerator cap V sub m and denominator 2 end-fraction Final Result
from a wall outlet), you must first convert it to the peak voltage Vmcap V sub m