Waveform Factors: Peak factor and form factor of sinusoidal waves

Waveform Factors: Peak factor and form factor of sinusoidal waves

1. Definitions (for any periodic waveform, but exam focuses on sine)

• Form factor ($F$): ratio of RMS to average (half-wave):

• Peak factor (Crest factor, $C$): ratio of peak to RMS:

Sometimes called peak factor or crest factor.

2. For Sine Wave (memorize)

• $V_{rms}=V_m/√2≈0.707V_m$
• $V_{avg}=2V_m/π≈0.637V_m$ (half-wave / rectified)
• Form factor:

• Peak factor:

3. For Other Waveforms (for comparison, often asked)

Waveform	$V_{rms}$	$V_{avg}$ (rectified)	Form $F$	Peak $C$
Sine	$V_m/√2$	$2V_m/π$	1.11	1.414
Half-wave rectified sine	$V_m/2$	$V_m/π$	1.57 ($π/2$)	2
Square (±Vm)	$V_m$	$V_m$	1	1
Triangular (Vm)	$V_m/√3$	$V_m/2$	1.155 ($2/√3$)	√3≈1.732
Sawtooth	$V_m/√3$	$V_m/2$	1.155	1.732

4. Why They Matter

• Form factor indicates shape; used to correct moving-coil meters (which measure average but scale to RMS assuming sine $F=1.11$): reading = $1.11·V_{avg}$. If waveform non-sine, error.
• Peak factor indicates stress on insulation/diodes (needs $V_m$).
• Transformer design: core flux depends on $V_{avg}$ ($V=4.44 f N Φ_m$ uses $F=1.11$).

5. Worked Examples

(a) Sine V_m=10V: V_rms=7.07V, V_avg=6.37V ⇒ F=1.11, C=1.414 ✓

(b) Half-wave rectifier output V_m=325V (mains peak): V_rms=162.5V, V_avg=103.5V ⇒ F=1.57 ✓

(c) Why moving-coil reads low for square? Square F=1, but meter calibrated for 1.11 ⇒ reads 11% high.

(d) Need to find peak from RMS+form: V_m = C·V_rms

6. Exam Points

• Define $F=V_{rms}/V_{avg}$ and $C=V_m/V_{rms}$ — 3-5 marks, very frequent.
• Compute for sine $F=1.11, C=√2$ and derivation — 5-7 marks, very frequent (almost certain to ask sine factors).
• Give table for square, triangular vs sine — 5 marks, frequent.
• Mention meter correction uses $F=1.11$ — 3 marks.