Page 177 - Phase-Locked Loops Design, Simulation, and Applications

DESIGN PROCEDURE FOR MIXED-SIGNAL PLLS Ronald E. Best 109
The design procedure presented here is independent of the type of PLL circuit that will
finally be used to implement the system. The individual steps are described in the following.
As mentioned, most of the formulas used to design the PLL are listed in Tables 3.1 through
3.5. In the procedure explained in the following, the VCO is assumed to be a relaxation
oscillator VCO (as shown in Fig. 2.23). With some slight modifications, however, it can also
be applied to resonant-type VCOs. We add some comments at the end of this chapter
regarding the design of resonant VCOs that use varactor diodes to vary the output frequency.

Step 1. In the first step, the input and output frequencies of the PLL must be specified.
There are cases where both input frequency and output frequency are constant but not
necessarily identical. In other applications (for example, frequency synthesizers), the input
frequency is always the same, but the output frequency is variable. As a last variant, both input
and output frequencies could be variable. Let f and f be the minimum and maximum
1min 1max
input frequencies, and f 2min and f 2max the minimum and maximum output frequencies,

respectively.
Step 2. In this step, the scaler ratio must be determined. In some PLL applications, the
output frequency f always equals the reference frequency f . Here no down-scaler is
2
1
needed—in other words, N = 1. Cases exist where the ratio of output to reference frequency is
greater than 1 but remains fixed. Here, a down scaler with constant divider ratio N is required.
When the PLL is used to build a frequency synthesizer, the ratio of output to reference
frequency is variable; thus, a range for N must be defined (N ≤ N ≤ N ). When N is
min max
variable, natural frequency ω and damping factor ζ will vary with N, as seen from the
n
corresponding equations in Tables 3.1 through 3.5. Both of these parameters will vary
approximately with . Consequently, ω will vary in the range ω < ω < ω , and
n nmin n nmax
ζ will vary in the range ζ < ζ < ζ . For these ranges, we get approximately
min max

(5.1)

and

(5.2)

respectively. As we know, a damping factor between 0.5 and 1 is considered optimum. As
long as the ratio N max /N min is not too large, the variation of the damping factor can be

accepted; if N varies by a factor of 10, for example, ζ varies by about a factor of 3, which can
be tolerated.
Much larger variations of ζ, however, must be avoided, because the loop then would get
oscillatory for the smallest, and become sluggish for the largest damping factor. When N
varies over a large range (for instance, 1 to 100), it is often

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