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Peak and form factor of triangular wave

Short answer

For the symmetric triangular current wave, half-cycle average = Im/2, RMS = Im/√3. Form factor = 1.155, peak factor = 1.732.

Find the peak factor and form factor of the triangular wave shown in figure below. [Figure: current i versus ωt; rises linearly from 0 to +Im at π/2, falls through zero at π to -Im at 3π/2, and returns to 0 at 2π.]

The current rises linearly from 0 to +Im at π/2, falls through zero at π to −Im at 3π/2, and returns to 0 at 2π. It is a symmetrical alternating triangular wave, so one quarter cycle (0 to π/2) is enough.

In the first quarter, i = Im θ/(π/2) = 2Imθ/π.

Average value (half cycle)

Iav = (1/(π/2)) ∫₀^{π/2} (2Imθ/π) dθ = (2/π)(2Im/π)(π²/8) = Im/2

RMS value

I² = (2/π) ∫₀^{π/2} (2Imθ/π)² dθ = (2/π)(4Im²/π²)(π³/24) = Im²/3

Irms = Im/√3 = 0.577 Im

Factors

  • Form factor = Irms / Iav = 0.577 Im / 0.5 Im = 1.155
  • Peak factor = Im / Irms = 1.732 (= √3)

✓ Answer checked by Claude Opus 5.5 (high effort)

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