ICS673-01

PLL Building Block

MDS 673-01 D

5

Revision 022500

Printed 11/15/00

Integrated Circuit Systems, Inc. • 525 Race Street • San Jose • CA • 95126•(408)295-9800tel • www.icst.com

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,

ωn =

Kv Ic

NC

•

•1

Equation 1

Damping factor,

ζ =

Rz

Kv Ic C

N

2

1

••

Equation 2

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,

ωn, 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.,

ωn ≈ 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

2

π•10,000 =

95 2 4

200

1

•.

• C

and C1 = 289 pF (270 pF nearest std. value).

Choosing a damping factor of 0.7, Equation 2

becomes

0.7 =

Rz

E

2

95 2 4 270 10

12

200

•.•

•

−

and Rz = 79.8 k

Ω (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 k

Ω

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.