Trigonometric waveforms 147
Voltage v (V)030230
250210050100Time t (s)v 15 100 sin t 1 30 sin 3t
100 sin t30 sin 3tT
12T
4T
23T
4TFigure 14.31
30230
250210050100100 sin t
30 sin
T
4T
2v 25 100 sin t 1 30 sin( 3 t 1 2 )3 T(^4) T
( 3 t 1 2 )
Voltage v (V)
(^0) Time t (s)
Figure 14.32
Problems 17 and 18 demonstrate that whenever
odd harmonics are added to a fundamental waveform,
whether initially in phase witheach other or not, the
positive and negative half-cycles of the resultant com-
plex wave are identical in shape. This is a feature
of waveforms containing the fundamental and odd
harmonics.
Problem 19. Use harmonic synthesis to construct
the complex current given by:
i 1 =10sinωt+4sin2ωtamperes.
Currenti 1 consists of a fundamental compon- ent,
10sinωt, and a second harmonic component, 4sin2ωt,