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AM, FM, and Digital Modulated Systems Chap. 5
In summary, the circuit of Fig. 5–43 produces an FM signal at 858.0126 MHz that has a
peak deviation of 12.49 kHz. The bandpass filter is centered at (f c ) C sum = 143.0021 MHz and has
a bandwidth sufficient to pass the FM signal with the deviation (∆F) C = 2.08 kHz. Using Carson’s
rule, [Eq. (5–61)], we find that the required bandwidth for the bandpass filter is
or
B T = 2[b C + 1]B = 2[(¢F) C + B]
B T = 2[2.08 + 3.0] = 10.16 kHz
SA5–4 Using an SSB Transmitter to Translate Baseband Data to RF Data are sent by
an amateur radio operator on the 40 meter band by using an SSB transceiver. To accomplish
this, a modem of the Bell 103 type (described in Example 5–9) is connected to the audio
(microphone) input of the SSB transceiver. Assume that the modem is set to the answer mode
and the transceiver is set to transmit a lower SSB signal on a suppressed carrier frequency of
(f c ) SSB = 7.090 MHz. Describe the type of digitally modulated signal that is emitted, and
determine its carrier frequency. For alternating 101010 data, compute the spectrum of the
transmitted signal.
Solution Referring to Sec. 4–5, we note that an LSSB transmitter just translates the spectrum of
the audio input signal up to the suppressed carrier frequency and deletes the upper sideband. From
Table 5–5, the Bell 103 modem (answer mode) has a mark frequency of f 1 = 2,225 Hz, a space
frequency of f 2 = 2,025 Hz, and a carrier frequency of (f c ) Bell 103 = 2,125 Hz. The LSSB transmitter
translates these frequencies to a mark frequency (binary 1) of
a space frequency (binary 0) of
and a carrier frequency of
(f c ) SSB - f 1 = 7090 kHz - 2.225 kHz = 7087.775 kHz
(f c ) SSB - f 2 = 7090 - 2.025 = 7087.975 kHz
(f c ) FSK = (f c ) SSB - (f c ) Bell 103 = 7090 - 2.125 = 7087.875 kHz.
Consequently, the SSB transceiver would produce an FSK digital signal with a carrier frequency
of 7087.875 kHz.
For the case of alternating data, the spectrum of this FSK signal is given by Eqs. (5–85)
and (5–86), where f c = 7087.875 kHz. The resulting spectral plot would be like that of Fig. 5–26a,
where the spectrum is translated from f c = 1,170 Hz to f c = 7087.875 kHz. It is also realized that
this spectrum appears on the lower sideband of the SSB carrier frequency (f c ) SSB = 7090 kHz. If
a DSB-SC transmitter had been used (instead of an LSSB transmitter), the spectrum would be
replicated on the upper sideband as well as on the lower sideband, and two redundant FSK signals
would be emitted.
For the case of random data, the PSD for the complex envelope is given by Eq. (5–90) and
shown in Fig. 5–27 for the modulation index of h = 0.7. Using Eq. (5–2b), we find that the PSD
for the FSK signal is the translation of the PSD for the complex envelope to the carrier frequency
of 7087.875 kHz.