Higher Engineering Mathematics, Sixth Edition

Trigonometric waveforms 147

Voltage v (V)

0

30

230

250

2100

50

100

Time t (s)

v 15 100 sin t 1 30 sin 3t

100 sin t

30 sin 3t

T

12

T

4

T

2

3T

4

T

Figure 14.31

30

230

250

2100

50

100

100 sin t

30 sin

T

4

T

2

v 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,