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Bandpass Signaling Principles and Circuits Chap. 4
equivalent bandpass filtering, as described by Sec. 4–5, or equivalent modulation of another
type, as described by Sec. 4–2. If desired, the original bandpass signal may be reconstructed
with the use of Eq. (4–32).
SA4–6 Frequency Synthesizer Design for a Receiver LO. Design a frequency synthesizer
for use as the local oscillator in an AM superheterodyne radio. The radio has a 455-kHz IF and can
be tuned across the AM band from 530 kHz to 1,710 kHz in 10-kHz steps. The synthesizer uses a
1-MHz reference oscillator and generates a high-side LO injection signal.
Solution. Referring to Eq. (4–59) and Fig. 4–29 for the case of down conversion and highside
injection, we find that the required frequency for the LO is f 0 = f c + f IF . If f c = 530 kHz
and f IF = 455 kHz, the desired synthesizer output frequency is f 0 = 985 kHz. Referring to the
block diagram for the frequency synthesizer (Fig. 4–25), we select the frequency of the
mixer input signal, v in (t), to be 5 kHz, which is one-half the desired 10-kHz step. Then
M = f x f in = 1,000 kHz5 kHz = 200, and an integer value can be found for N to give the
needed LO frequency. Using Eq. (4–112), we obtain N = f 0 f in . For f 0 = 985 kHz and f in = 5
kHz, we get N = 197. Thus, to tune the radio to f c = 530 kHz, the required values of M and N
are M = 200 and N = 197. In a similar way, other values for N can be obtained to tune the
radio to 540, 550, ..., 1,710 kHz. (M remains at 200.) Table 4–6 lists the results. The selected
values for M and N are kept small in order to minimize the spurious sideband noise on the
synthesized LO signal. M and N are minimized by making the size of the step frequency, f in ,
as large as possible.
The spectral sideband noise on the synthesizer output signal is minimized by using a
low-noise reference oscillator and a low-noise VCO and by choosing a small value of N for
the reduction in the number of intermodulation noise components on the synthesized signal.
The bandwidth of the loop filter is also minimized, but if it is too small, the pull-in range will
not be sufficient for reliable locking of the synthesizer PLL when it is turned on. In this
1
example, N can be reduced by a factor of about
2
the IF frequency is chosen to be 450 kHz
instead of 455 kHz. For example, for f IF = 450 kHz and f c = 530 kHz, we need f 0 = 980 kHz.
This LO frequency is attained if M = 100 (for a step size of f in = 10 kHz) and N = 98,
compared with (see Table 4–6) M = 200 and N = 197, which was needed for the case when
f IF = 455 kHz.
TABLE 4–5 SOLUTION TO SA4–6 WITH DIVIDER RATIOS M AND N FOR AN AM RADIO-
FREQUENCYSYNTHESIZER
Reference frequency = 1,000 Hz; IF frequency = 455 kHz
Received frequency, f c
(kHz)
Local oscillator frequency,
f 0 (kHz) M N
530 985 200 197
540 995 200 199
550 1,005 200 201
o o o o
1,700 2,155 200 431
1,710 2,165 200 433