Trigonometric waveforms 151
waveform using harmonic synthesis over one
cycle of the fundamental waveform.
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⎢
⎣
(a)v=300sin314. 2 t
+90sin( 628. 3 t−π/ 2 )
+30sin( 1256. 6 t+π/ 3 )V
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- A voltage waveform is represented by:
v= 20 +50sinωt
+20sin( 2 ωt−π/ 2 )volts.
Draw thecomplex waveform over one cycle of
the fundamental by using harmonic synthesis.
- Write down an expression representing a
currentihaving a fundamental component of
amplitude 16A and frequency 1kHz, together
withitsthirdand fifthharmonics beingrespec-
tively 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 funda-
mental using harmonic synthesis.
[
i=16sin2π 103 t+ 3 .2sin6π 103 t
+ 1 .6sinπ 104 tA
]
- A voltage waveform is described by
v=200sin377t+80sin
(
1131 t+
π
4
)
+20sin
(
1885 t−
π
3
)
volts
Determine (a) the fundamental and harmonic
frequencies of the waveform (b) the percent-
age third harmonic and (c) the percentage
fifth harmonic. Sketch the voltage waveform
usingharmonic synthesis over one cycle of the
fundamental. ⎡
⎢
⎣
(a)60Hz,180Hz,300Hz
(b)40%
(c)10%
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