Page 269 - Phase-Locked Loops Design, Simulation, and Applications

Source : Phase-Locked Loops: Design, Simulation, and Applications, Sixth
Edition Ronald E. Best 159

Mixed-Signal PLL Applications Part 2:

Fractional-N Frequency Synthesizers

Realization of Fractional Divider Ratios

In the design example of Sec. 6.5, we realized a PLL frequency synthesizer capable of
creating output frequencies that are an integer multiple of the reference frequency (10
kHz). The synthesizer had a lock-in time of about 2 ms. This is not extremely fast.
Actually, there is an empirical relation between lock-in time T and reference frequency
L
f , which says that the lock-in time T equals a number of reference periods, typically 10
ref
L
to 20 reference periods (a reference period has the duration 1/f ). 10,48 Where does that
ref
range stem from?
In most practical PLL designs, the down-scaled center frequency ω ′ is much larger
0
than the natural frequency ω of the PLL. Typically, ω ′ is about 20 times the natural
n 0
frequency. Note that in a PLL frequency synthesizer the down-scaled center frequency
ω ′ is identical with 2πf —in other words, the reference period equals one period of
0 ref
down-scaled center frequency. Also remember that the lock-in time is approximately
equal to one period of natural frequency—that is

[cf. Eq. (3.62)]. Because the down-scaled center frequency is larger by a factor of 20 than
the natural frequency, the lock-in time corresponds to roughly 20 reference periods.
When the channel spacing of a frequency synthesizer must be narrow (for example, on
the order of 1 kHz), we are forced—at least in conventional synthesizer circuits—to
choose a low reference frequency. As we have seen, this results in a slow lock-in time. In
a conventional synthesizer (that is, in the type of synthesizer we considered hitherto) the
output frequency has always been an integer multiple of the reference frequency—for
example, 10 · f , 11 · f ref, 12 · f , and so on. Assuming f ref = 10 kHz, we could
ref
ref
create frequencies of 100 kHz, 110 kHz,

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