ICS673-01 Datasheet, PDF (5/9 Pages) Integrated Circuit Systems – PLL Building Block

ICS673-01
PLL Building Block
Determining the Loop Filter Values
The loop filter components consist of C1, C2, and
RZ. Calculating these values is best illustrated by
an example. Using the example in Figure 1, we can
synthesize 40 MHz from a 200 kHz input.
The phase locked loop may be approximately
described by the following equations:
Natural frequency, ω_n =
Kv • Ic
N • C1
Equation 1
Damping factor, ζ = ^{Rz Kv • Ic • C1} Equation 2
2
N
where Kv = VCO gain (MHz/Volt)
Ic = Charge pump current (µA)
N = Total feedback divide
C1 = Loop filter capacitor (Farads)
Rz = Loop filter resistor (Ohms)
The natural frequency, ω_n, is approximately equal
to the bandwidth (in radians/sec). As a general
rule, the bandwidth should be at least 10 times less
than the reference frequency, i.e.,
ω_n ≈ 2π•BW ≤ REFIN/10.
In this example, BW = REFIN/20, giving a
bandwidth of 10 kHz.
Using the first equation, C1 can be determined
since all other variables are known. In the example
of Figure 1, N = 200, comprising a divide-by-2 on
the chip and the external divide-by-100. Therefore,
Equation 1 becomes
Choosing a damping factor of 0.7, Equation 2
becomes
0.7 = ^{Rz 95 • 2.4 • 270 •10E − 12}
2
200
and Rz = 79.8 kΩ (82 kΩ nearest std. value).
The capacitor C2 is used to damp transients from
the charge pump and should be at least 20 times
smaller than C1, i.e.,
C2 ≤ C1/20.
Therefore, C2 = 13.5 pF (13 pF nearest std. value).
To summarize, to generate 40 MHz from 200
kHz with standard values, the loop filter
components are:
C1 = 270 pF
C2 = 13 pF
Rz = 82 kΩ
In general, making C1 larger may give improved
loop performance, since it both lowers the
bandwidth and increases the damping factor.
However, it also increases the time for the loop to
lock since the charge pump current has to charge a
larger capacitance.
When choosing either CLK1 or CLK2 to drive the
feedback divider, CLK2 should be used whenever
possible. See the following section, “Avoiding
PLL Lockup”, for additional explanations.
2π•10,000 =
95 • 2.4
200 • C1
and C1 = 289 pF (270 pF nearest std. value).
MDS 673-01 D
5
Revision 022500
Printed 11/15/00
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