Half-wave rectifier mean output: For a sinusoidal input with peak value Vp, the average value of a half-wave rectified output is approximately what fraction of Vp?

Introduction / Context:
Average (mean) output voltage is a primary performance indicator for rectifier circuits. For a half-wave rectifier, only one half of the sine wave contributes to the unidirectional output, leading to a lower mean compared to full-wave rectification. Memorizing the correct percentage helps with quick design estimates and exam questions.

Given Data / Assumptions:

• Ideal half-wave rectifier (no diode drop) and resistive load.
• Input waveform is sinusoidal with peak Vp.
• We need the mean value over one full period.

Concept / Approach:
The mean of the half-wave rectified sine is V_avg = Vp/π. Converting to a percentage of Vp gives (1/π) * 100% ≈ 31.8%. In contrast, the full-wave rectified mean is (2/π) * Vp ≈ 63.6% of Vp, and the RMS of the original sine is 0.707 * Vp (70.7%). Distinguishing these constants avoids common mix-ups.

Step-by-Step Solution:

Verification / Alternative check:
Check plausibility: the average must be less than 50% of Vp because only positive half-cycles contribute; 31.8% meets this sanity check.

Why Other Options Are Wrong:

• 63.6%: That is the full-wave average fraction (2/π), not half-wave.
• 70.7%: This is the RMS fraction of a sine (1/√2), not the mean of a rectified output.
• 100%: Impossible for a rectified sine without regulation.
• 22.5%: Not associated with standard rectifier metrics.

Common Pitfalls:
Mixing up mean and RMS values; forgetting that half of the cycle is zero in half-wave rectification, which depresses the mean.

Final Answer:
31.8%