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the equivalent dc value. In the analysis of electronic circuits to be considered
in a later course, both dc and ac sources of voltage will be
applied to the same network. It will then be necessary to know or determine
the dc (or average value) and ac components of the voltage or current
in various parts of the system.
EXAMPLE 13.13 Determine the average value of the waveforms of
Fig. 13.37.
0
v 1
10 V
(Square wave)
1 2 3 4 t (ms)
–10 V
(a)
0
FIG. 13.37
Example 13.13.
v 2
14 V
1 2 3 4 t (ms)
–6 V
Solutions:
a. By inspection, the area above the axis equals the area below over
one cycle, resulting in an average value of zero volts. Using Eq.
(13.26):
(10 V)(1 ms) � (10 V)(1 ms)
G �����
2 ms
0
���0 V
2 ms
b. Using Eq. (13.26):
(14 V)(1 ms) � (6 V)(1 ms)
G ����
2 ms
14 V � 6 V 8 V
��� ���4 V
2 2
as shown in Fig. 13.38.
In reality, the waveform of Fig. 13.37(b) is simply the square wave
of Fig. 13.37(a) with a dc shift of 4 V; that is,
v2 � v1 � 4 V
EXAMPLE 13.14 Find the average values of the following waveforms
over one full cycle:
a. Fig. 13.39.
b. Fig. 13.40.
(b)
14 V
AVERAGE VALUE ⏐⏐⏐ 541
4 V
0 1
–6 V
2 3 4 t (ms)
FIG. 13.38
Defining the average value for the waveform
of Fig. 13.37(b).
3
0
–1
v (V)
1 cycle
4 8
FIG. 13.39
Example 13.14, part (a).
t (ms)