1
O ylSi CHAPTER 1 INTRODUCTION TO ELECTRONICS
1.3
Find the frequencies/and to of a sine-wave signal with a period of
1
ms.
Ans.
/ ^ 1000 H/:
<o
- In x 10
3
rad/s
1.4
What is the
period
T of
sine
waveforms characterized by
frequencies
of (a):f = 60 Hz? (b)/= IQ~'
}
Hz?
.
(c)/= 1 MHz? \}-]
Ans.
16.7 ms; 1000 s; 1 £is
TiS
; The UHF (Ultra High Frequency) television broadcast band begins
with
channel 14 and extends from
•^.mWJO
MHz lo 806 MHz. If 6 MHz is allocated for each channel, how manytchannels can this band
accommodate?
ssAns.
56; channels 14 to 69
1.6
When the square-wave signal of Fig. 1.4, whose Fourier series is given in Eq. (1.2), is applied to a resistor,
the total power dissipated may be calculated directly using the relationship
JP]
= 1/T
\l{v
1
/R)dl
or indirectly by summing the contribution of each of the harmonic components, that is, P = P,+
P
3
+ P
5
+ • • •, which may be found directly from rms values. Verify that the two approaches are equiv-
alent.
What
iVacumi of
(he
energy of a square wave is in its fundamental? In its first five harmonics'.' In
its first seven? First nine? In what number of harmonics is 90% of the energy? (Note that in counting
harmonies, the fundamental at co
0
is the first, the one at 2ft>„ is the second, etc.)
Ans. 0.81;
0.93; 0.95; 0.96; 3
1.3 ANALOG AND DIGITAL SIGNALS
The voltage signal depicted in Fig. 1.2 is called an analog signal. The name derives from
the fact that such a signal is analogous to the physical signal that it represents. The magni-
tude of an analog signal can take on any value; that is, the amplitude of an analog signal
exhibits a continuous variation over its range of activity. The vast majority of signals in the
world around us are analog. Electronic circuits that process such signals are known as
analog circuits. A variety of analog circuits will be studied in this book.
An alternative form of signal representation is that of a sequence of numbers, each num-
ber representing the signal magnitude at an instant of time. The resulting signal is called a
digital signal. To see how a signal can be represented in this form—that is, how signals can
be converted from analog to digital form—consider Fig.
1.7(a).
Here the curve represents a
voltage signal, identical to that in Fig. 1.2. At equal intervals along the time axis we have
marked the time instants t
0
, t
h
t
2
, and so on. At each of these time instants the magnitude of
the signal is measured, a process known as sampling. Figure
1.7(b)
shows a representation
of the signal of Fig.
1.7(a)
in terms of its samples. The signal of Fig.
1.7(b)
is defined only at
the sampling instants; it no longer is a continuous function of time, but rather, it is a discrete-
time signal. However, since the magnitude of each sample can take any value in a continuous
range,
the signal in Fig.
1.7(b)
is still an analog signal.
Now if we represent the magnitude of each of the signal samples in Fig.
1.7(b)
by a num-
ber having a finite number of digits, then the signal amplitude will no longer be continuous;
rather, it is said to be quantized, discretized, or digitized. The resulting digital signal then is
simply a sequence of numbers that represent the magnitudes of the successive signal samples.
The choice of number system to represent the signal samples affects the type of digital
signal produced and has a profound effect on the complexity of the digital circuits required
1.3 ANALOG AND DIGITAL SIGNALS I 11
v(t) k
h h h h • ' ' X
s
I
t
(a)
v(i)
A
?
,r!N
ll
lllllt
h h h h ' ' ' 1 1
1
(b)
FIGURE
1.7 Sampling the continuous-time analog signal in
(a)
results in the discrete-time signal in (b).
to process the signals. It turns out that the binary number system results in the simplest pos-
sible digital signals and circuits. In a binary system, each digit in the number takes on one of
only two possible values, denoted 0 and 1. Correspondingly, the digital signals in binary
systems need have only two voltage levels, which can be labeled low and high. As an example,
in some of the digital circuits studied in this book, the levels are 0 V and +5 V. Figure 1.8
shows the time variation of such a digital signal. Observe that the waveform is a pulse train
with 0 V representing a 0 signal, or logic 0, and +5 V representing logic 1.
v(t) A
+5
Logic values 5» 10 110 10 0 Time, t
FIGURE
1.8 Variation of a particular binary digital signal with time.