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CS5317

16-Bit, 20 kHz Oversampling A/D Converter

Cirrus Logic 

CS5317

characteristic form in which the damping factor,

ζ, and the natural frequency, ωn , are evident:

CLKIN is approximately 20 times greater than

the 3 dB corner frequency of the control loop.

θ2

θ1

=

2ζωns +

s2 + 2ζωns

ωn 2

+ ωn

2

Both the natur al frequency and the damping fac-

tor are particularly important in determining the

transient response of the phase-locked loop when

subjected to a step input of phase or frequency. A

family of curves are illustrated in Figure 6 that

indicate the overshoot and stability of the loop as

a function of the damping factor. Each response is

plotted as a function of the normalized time, ωn t.

For a given ζ and lock time, t, the ωn required

can be determined. Alternatively, phase lock con-

trol loop bandwidth may be a specified parameter.

In some systems it may be desirable to reduce the

-3dB bandwidth of the PLL control loop to re-

duce the effects of jitter in the phase of the input

clock. The 3 dB bandwidth of the PLL control

loop is defined by the following equation:

Filter Components

Using the equations which describe the transfer

function of the PLL system, the following exter-

nal filter component equations can be determined:

C

=

KoKd

Nωn 2

R

=

2ζωn

N

KoKd

The gain factors (Ko, Kd) are specified in the

Analog Characteristics table. In the event the sys-

tem calls for very low bandwidth, hence a

corresponding reduction in loop gain, the phase

detector gain factor Kd can be reduced. A large

series resistor (R1) can be inserted between the

output of the detector and the filter. Then the

50 µA current sources will saturate to the supplies

and yield the following gain factor:

ω3dB = ωn√2ζ2+1+√(2ζ2+1)2+1

The equations used to describe the PLL and the

3 dB bandwidth are valid only if the frequency of

Kd

≈

−5V

2πR1

20 log(θ2/θ1)

θ2 normalized to θ1

1.3

ζ= 0.5

4

ζ = 0.5

3

ζ = 0.5

1.2

1.1

1.0

0.9

ζ= 10.0

ζ = 0.6

2

ζ = 0.7

1

0

ζ = 0.8 -1

ζ = 10

0.8

ζ = 0.9 -2

0.7

ζ = 1.0 -3

0.6

ζ = 1.5 -4

0.5

0.4

ζ = 2.0 -5

-6

0.3

ζ = 3.0 -7

0.2

ζ = 10.0 -8

0.1

-9

0.0

-10

0 1 2 3 4 5 6 7 8 9 10

ωn t.

Figure 6a. θ2 Unit Step Response

0.1

1

10

ω/ωn

Figure 6b. Second Order PLL Frequency Response

DS27F4

13

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