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:

The output voltage for a half-wave rectifier is defined by the average value and the effective value Vmcap V sub m is the peak input voltage.

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.,

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

Vdc≈Vm−Vdπcap V sub d c end-sub is approximately equal to the fraction with numerator cap V sub m minus cap V sub d and denominator pi end-fraction 4. Calculate RMS Output Voltage

from a wall outlet), you must first convert it to the peak voltage Vmcap V sub m

Vm=Vrms(input)×2cap V sub m equals cap V sub r m s open paren i n p u t close paren end-sub cross the square root of 2 end-root 2. Determine Average (DC) Voltage

The RMS value represents the effective heating power of the waveform. Since the negative half-cycle is zero, the integration is: