- 2072 Chaitra · 4 marks
Average and RMS of full-wave rectified wave
Short answer
Full-wave rectified sine wave: average = 2Em/π ≈ 0.637 Em, RMS = Em/√2 ≈ 0.707 Em. RMS equals original sine wave RMS.
Calculate the average and rms value of full-wave rectified sine wave as shown below. [Figure: full-wave rectified sine pulses of peak Em; the first hump from 0 to π, the second hump from π and so on; marked at π/4, π, 5π/4.]
A full-wave rectified sine wave is e = Em |sin θ|, with period π (each hump lasts 0 to π and the next begins at π). Take one hump, 0 to π.
Average value
Eav = (1/π) ∫₀^π Em sin θ dθ = (Em/π) [−cos θ]₀^π = (Em/π)(2)
Eav = 2Em/π = 0.637 Em
RMS value
Erms² = (1/π) ∫₀^π Em² sin²θ dθ = (Em²/π) ∫₀^π (1 − cos 2θ)/2 dθ = (Em²/π)(π/2) = Em²/2
Erms = Em/√2 = 0.707 Em
The rms value of a full-wave rectified wave equals that of the original sine wave. The form factor is 0.707/0.637 = 1.11 and the peak factor is √2 = 1.414.
✓ Answer checked by Claude Opus 5.5 (high effort)
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