AD9548 datasheet(108/111 Pages) AD

108 / 111 page

AD9548

Data Sheet

Rev. G | Page 108 of 111

CALCULATING DIGITAL FILTER COEFFICIENTS

The digital loop filter coefficients (, , , and  (see Figure 42))

relate to the time constants (T1, T2, and T3) associated with the

equivalent analog circuit for a third order loop filter (see Figure 69).

Note that AD9548 evaluation software contains a profile

designer that will compute these coefficients for you. The user

should not normally need to use these formulas.

FROM

CHARGE

PUMP

VCO

Figure 69. Third Order Analog Loop Filter

The design process begins by deciding on two design

parameters related to the second order loop filter shown in

Figure 70—the desired open-loop bandwidth (fP) and phase

margin (.

FROM

CHARGE

PUMP

VCO

Figure 70. Second Order Analog Loop Filter

An analysis of the second order loop filter leads to its primary

time constant, T1. It can be shown that T1 is expressible in terms

of fP and  as

)

cos(

)

sin(











where







An analysis of the third order loop filter leads to the definition

of another time constant, T3. It can be shown that T3 is

expressible in terms of the desired amount of additional

attenuation introduced by R3 and C3 at some specified

frequency offset (fOFFSET) from the PLL output frequency.

OFFSET

ATTEN



10 10





where

OFFSET







Note that ATTEN is the desired excess attenuation in decibels.

Furthermore, ATTEN and ωOFFSET should be chosen so that

3 

With an expression for T1 and T3, it is possible to define an

adjusted open-loop bandwidth (fC) that is slightly less than fP. It

can be shown that ωC (fC expressed as a radian frequency) is

expressible in terms of T1, T3, and θ (phase margin) as























)

tan(

)

tan(





It can also be shown that the adjusted open-loop bandwidth

leads to T2 (the secondary time constant of the second order

loop filter) expressed as









Calculation of the digital loop filter coefficients requires a

scaling constant, K (related to the system clock frequency, fS),

and the PLL feedback divide ratio, D.

125

578

517







where S, U, and V are the integer and fractional feedback

divider values that reside in the profile registers. Keep in mind

that the desired integer feedback divide ratio is one more than

the stored value of S (hence, the +1 term in the equation for D

in this equation). This leads to the digital filter coefficients

given by





 



2



























S T







S T





Calculation of the coefficient register values requires the

application of some special functions described as follows:

The if() function

y = if(test_statement, true_value, false_value)

where test_statement is a conditional expression (for example, x

< 3), true_value is what y equals if the conditional expression is

true, and false_value is what y equals if the conditional

expression is false.

The round() function

y = round(x)

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