CS5317 datasheet(14/32 Pages) CIRRUS

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In some applications additional filtering may be

useful to eliminate any jitter associated with the

discrete current pulses from the phase detector.

In this case a capacitor whose value is no more

than 0.1 C can be placed across the RC filter net-

work (C2 in Figure 5).

Filter Design Example

The following is a step by step example of how to

derive the loop filter components. The CS5317

A/D sampling clock is to be derived from a 9600

Hz clock source. The application requires the sig-

nal passband of the CS5317 to be 4 kHz. The

on-chip digital filter of the CS5317 has a 3 dB

passband of CLKOUT/488.65 (see Note 4 in the

data sheet specifications tables). The 4 kHz pass-

band requirement dictates that the sample clock

(CLKOUT) of the CS5317 be a minimum of

4000 X 488.65 = 1.954 MHz. This requires the

VCO to run at 3.908 MHz. The 3.908 MHz rate is

407 times greater than the 9600 Hz PLL input

clock. Therefore the CS5317 must be set up in

mode CLKG2 with N = 512. If the CLKG1 mode

were used (N = 256), too narrow of a signal band-

width through the A/D would result.

Once the operating mode has been determined

from the system requirements, a value for the

damping factor must be chosen. Figure 6 illus-

trates the dynamic aspects of the system with a

given damping factor. Damping factor is gener-

ally chosen to be between 0.5 and 2.0. The choice

of 0.5 will result in an overshoot of 30 % to a step

response whereas the choice of 2.0 will result in

an overshoot of less than 5 %. For example pur-

poses, let us use a damping factor of 1.0.

So, let us begin with the following variables :

Ko = - 10 Mradians/volt.sec

Kd = - 8

µA/radian

N = 512

ζ = 1.0

To calculate values for the resistor R and capaci-

tor C of the filter, we must first derive a value for

ωn. Using the general rule that the sample clock

should be at least 20 times higher frequency than

the 3dB bandwidth of the PLL control loop:

CLKIN

≥ 20 ω

3dB

where CLKIN = 9600 Hz = 2

π 9600 radians/sec.

So:

3dB = 2π 9600/20 = 3016 radians/sec.

Knowing

3dB and the damping factor of 1.0, we

can calculate the natural frequency,

ωn , of the

control loop:

ωn =

ω3dB

√

ζ2 + 1 +

√

(2ζ2 + 1)2 + 1

ωn = 3016

√

(1)2 + 1 +

√

(2(1)2 + 1)2 + 1

ωn = 1215

⁄ sec

Once the natural frequency,

ωn , is determined,

values for R and C for the loop filter can be cal-

culated:

R = 2

ζωnN/KoKd

R = 2(1)(1215 1/s) 512/(-10Mrad/v.s.)(-8

µA/rad)

R = 15552 v/A = 15.55 k

Ω. Use R = 15 kΩ.

C = KoKd/N

ωn2

C = (-10 Mrad/v.s)(- 8

µA/rad)/512 (1215 1/s)2

C = 105.8 x 10

-9 A.s/v = 105 nF. Use 0.1 µF.

The above example assumed typical values for

Ko and Kd. Your application may require a worst

case analysis which includes the minimum or

maximum values. Table 2 shows some other ex-

ample situations and R and C values.

CS5317

DS27F4

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