Trigonometric waveforms 151
waveform using harmonic synthesis over one
cycle of the fundamental waveform.
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(a) v = 300 sin314.2t
+ 90 sin(628.3t − π/2)
+ 30sin(1256.6t + π/3) V
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3. A voltage waveform is represented by:
v = 20 + 50 sin ωt
+ 20sin(2ωt − π/2) volts.
Draw the complex waveform over one cycle of
the fundamental by using harmonic synthesis.
4. Write down an expression representing a
current i having a fundamental component of
amplitude 16 A and frequency 1 kHz, together
with its third and fifth harmonics being respectively one-fifth and one-tenth the amplitude
of the fundamental, all components being
in phase at zero time. Sketch the complex
current waveform for one cycle of the fundamental using harmonic synthesis.
i = 16 sin 2π10 3 t + 3.2 sin 6π10 3 t
+ 1.6 sin π10
4 t A
5. A voltage waveform is described by
v = 200 sin 377t + 80 sin
1131t +
π
4
+ 20 sin
1885t −
π
3
volts
Determine (a) the fundamental and harmonic
frequencies of the waveform (b) the percentage third harmonic and (c) the percentage
fifth harmonic. Sketch the voltage waveform
using harmonic synthesis over one cycle of the
fundamental. ⎡
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⎣
(a) 60 Hz, 180 Hz, 300 Hz
(b) 40%
(c)10%
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