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Form and peak factor of triangular wave

Short answer

The triangular wave of peak 100 V has average 50 V, RMS 100/√3 ≈ 57.74 V. Form factor = RMS/average = 1.155, peak factor = peak/RMS = √3 ≈ 1.732.

Calculate the form factor and peak factor of the following triangular waveform. [Figure: train of triangular pulses of peak 100 V; first triangle rises from 0 at 0 to 100 V at π and falls to 0 at 2π; second triangle peaks at 3π and ends at 4π.]

The figure shows triangles of peak 100 V. Each rises linearly from 0 at θ = 0 to 100 V at π and falls to 0 at 2π; the pattern repeats with period 2π. Because the wave is always positive and the rise and fall are symmetrical, one rising slope 0 to π is enough.

Let Vm = 100 V. On the rise, v = Vm θ/π.

Average value

Vav = (1/π) ∫₀^π (Vm θ/π) dθ = (Vm/π²)(π²/2) = Vm/2 = 50 V

RMS value

Vrms² = (1/π) ∫₀^π (Vm θ/π)² dθ = (Vm²/π³)(π³/3) = Vm²/3

Vrms = Vm/√3 = 100/1.732 = 57.74 V

Factors

  • Form factor = Vrms / Vav = 57.74 / 50 = 1.155
  • Peak factor = Vm / Vrms = 100 / 57.74 = 1.732 (= √3)

✓ Answer checked by Claude Opus 5.5 (high effort)

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