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544 ⏐⏐⏐ SINUSOIDAL ALTERNATING WAVEFORMS
10
0
10 mV
0
v (V)
v (mV)
1 cycle
p
Sine wave
FIG. 13.48
Example 13.17.
FIG. 13.49
Example 13.18.
(a)
2p
� 1
t
EXAMPLE 13.17 Determine the average value of the waveform of
Fig. 13.48.
Solution:
2Am � 0 2(10 V)
G �����3.18 V
2p 2p
EXAMPLE 13.18 For the waveform of Fig. 13.49, determine whether
the average value is positive or negative, and determine its approximate
value.
Solution: From the appearance of the waveform, the average value
is positive and in the vicinity of 2 mV. Occasionally, judgments of this
type will have to be made.
Instrumentation
The dc level or average value of any waveform can be found using a
digital multimeter (DMM) or an oscilloscope. For purely dc circuits,
simply set the DMM on dc, and read the voltage or current levels.
Oscilloscopes are limited to voltage levels using the sequence of steps
listed below:
1. First choose GND from the DC-GND-AC option list associated
with each vertical channel. The GND option blocks any signal to
which the oscilloscope probe may be connected from entering the
oscilloscope and responds with just a horizontal line. Set the
resulting line in the middle of the vertical axis on the horizontal
axis, as shown in Fig. 13.50(a).
Vertical sensitivity = 50 mV/div.
FIG. 13.50
Using the oscilloscope to measure dc voltages: (a) setting the GND condition;
(b) the vertical shift resulting from a dc voltage when shifted to the DC option.
(b)
Shift = 2.5 div.
2. Apply the oscilloscope probe to the voltage to be measured (if
not already connected), and switch to the DC option. If a dc voltage
is present, the horizontal line will shift up or down, as
demonstrated in Fig. 13.50(b). Multiplying the shift by the vertical
sensitivity will result in the dc voltage. An upward shift is a
positive voltage (higher potential at the red or positive lead of the
oscilloscope), while a downward shift is a negative voltage
(lower potential at the red or positive lead of the oscilloscope).