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Average, rms, form and peak factor of sawtooth

Short answer

Average = 25 V, rms = 50/√3 ≈ 28.87 V. Form factor = 1.155, peak factor = 1.732.

Calculate the average value, rms value, form factor and peak factor of the saw tooth wave as shown in figure below. [Figure: sawtooth wave rising linearly from 0 to 50 V over each period of 2π; three periods shown up to 6π.]

From the figure: the wave rises linearly from 0 to 50 V over each period 2π, then drops instantly to 0. So in one period v = Vm θ/2π, with Vm = 50 V.

Average value

Vav = (1/2π) ∫₀^{2π} (Vm θ/2π) dθ = (Vm/4π²)(2π)² / 2 = Vm/2

Vav = 25 V

RMS value

Vrms² = (1/2π) ∫₀^{2π} (Vm θ/2π)² dθ = (Vm²/(2π × 4π²)) × (2π)³/3 = Vm²/3

Vrms = Vm/√3 = 50/1.732 = 28.87 V

Form factor

Vrms / Vav = 28.87 / 25 = 1.155

Peak factor

Vm / Vrms = 50 / 28.87 = 1.732

✓ Answer checked by Claude Opus 5.5 (high effort)

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