ElectricalElectronicsmediumFE ExamCoursework

Average Output of a Half-Wave Rectifier

An ideal half-wave rectifier is driven by a sinusoid of peak value $V_m = 170\ \text{V}$ .

Find the average (DC) output voltage.

Given

170 V

Peak input voltage

Hint 1

Half of every cycle is blocked, but the average is still taken over the whole period.

Hint 2

V_avg = V_m/π for half-wave rectification.

Hint 3

Full-wave would give twice this.

Worked solution — try the problem first

A half-wave rectifier passes one half-cycle and blocks the other. Averaging over a full period:

$V_{avg} = \frac{1}{2\pi}\int_0^{\pi} V_m\sin\theta\, d\theta = \frac{V_m}{\pi}$

$V_{avg} = \frac{170}{\pi} = 54.1\ \text{V}$

$\boxed{V_{avg} = 54.1\ \text{V}}$

Compare with full-wave, which passes both half-cycles and therefore averages $2V_m/\pi = 108.2$ V — exactly double. Mixing the two formulas is the usual error.

Concepts:RectifiersAverage valueDiode circuits

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