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Sec. 2–11 Study-Aid Examples 113
2–11 STUDY-AID EXAMPLES
SA2–1 DC and RMS Values for Exponential Signals Assume that v(t) is a periodic voltage
waveform as shown in Fig. 2–25. Over the time interval 0 6 t 6 1, v(t) is described by e t . Find
the DC value and the RMS value of this voltage waveform.
SOLUTION.
For periodic waveforms, the DC value is
V dc = 8v(t)9 = 1 T 0
L0
T 0
1
v(t) dt = e t dt = e 1 - e 0
L
0
or
V dc = e - 1 = 1.72 V
Likewise,
2
V rms
1
= 8v 2 (t)9 = (e t ) 2 dt = 1
L 2 (e2 - e 0 ) = 3.19
0
Thus,
V rms = 13.19 = 1.79 V
SA2–2 Power and dBm Value for Exponential Signals The periodic voltage waveform
shown in Fig. 2–25 appears across a 600-Æ resistive load. Calculate the average power dissipated
in the load and the corresponding dBm value.
v(t)
3
2
1
–2 –1 0
t (sec)
1 2 3
Figure 2–25