Page 259 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

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where N is ап integer > О, аге as follows:

ОС а ! а 2 аз а 4 a s а б а 7 аз а 9
-v2
1
1
- - v2 - - 2 О -v2 -1 -- О - v2
-
-
4 7т 7т 3'lТ 51Т 31Т 7Тi 9Тi
Note that every fourth harmonic signal is zero ог missing in а 25 percent duty-cycle
pulse signal QF{f):

Р t) -..!... (2-п .l) + ~ 4-пf t) + "\!? (1 7ff () . . .
"1 .. ' J-rr ~ (15-7)
Thus, if ап input signal .5{ f) is sampledby the 25 percent duty-cycle pulse-train
signal, wehave

х -Z'П --п ' t +

\12 11"" t - \12
'~тr :-'п I 1Т . ...
]
.....
From the preceding two example pulse-train signals, we find that sampling is
indeed а way of multiplying the input signal with pulse-train signals that include а
ОС term and alternating-current (АС) signals, including the fundamental frequency
and harmonics of the sampling signal. Multiplication of the input signal with the
sampling signal then provides а form of harmonic mixing as well.

Figure 15-48 shows the relative spect.rum associated with ап ideal sampling sigпа l
that has а very narrow pulse width, and Figure 15-4С shows the spectrum
associated with а square-wave-sampling waveform. It should Ье noted that when
two sigпаls аге multiplied such as from .5{ f) = Ь 1 соs(2пJfnf) and the fuпdаmепtа l
sampling frequency signal of the square-wave signal S(J.fJ, [b 1 cos(2nfst

- t
1т
I the resulting signal is а doubIe-sidеЬапd-suрргеssеd carrieг signal. That iS, there
аге по signals from the multiplication operation that include а "carrier" frequency of
f 5 • We will find that doubIe-sidеЬапd-suрргеssеd carrier signals аге the building
bIocks for 1 апd Q sigпаls in Chapter 16.