AD9549 datasheet(25/78 Pages) AD

25 / 78 page

Preliminary Technical Data

AD9549

Rev. PrA | Page 25 of 78

The choice of P is important because it controls both the

response of the CCI filter and the sample rate of the loop filter.

In order to understand the method for determining a useful

value for P, it is first necessary to examine the transfer function

of the CCI filter:

[

)

(

)

(

CCI

−

()

)

(

)

cos(

)

cos(

−

ωP

CCI

To evaluate the response in terms of absolute frequency, make

the substitution:

ω 2

(where fS is the DAC sample rate and f is the frequency at which

HCCI is to be evaluated)

Analysis of this function reveals that the CCI magnitude

response follows a low pass characteristic that consists of a

series of P lobes. The lobes are bounded by null points

occurring at frequency multiples of fS/P. The peak of each

successive lobe is lower that its predecessor over the frequency

range between DC and ½fS. For frequencies greater than ½fS,

the response is a reflection about the vertical at ½fS.

Furthermore, the first lobe (which appears between DC and

fS/P) exhibits a monotonically decreasing response. That is, the

magnitude is unity at DC and it steadily decreases with

frequency until it vanishes at the first null point (fS/P).

The null points imply the existence of transmission zeros placed

at finite frequencies. While transmission zeros placed at

infinity yield minimal phase delay, zeros placed closer to DC

result in increased phase delay. Hence, the position of the first

null point has a significant impact on the phase delay

introduced by the CCI filter. This is an important

consideration, because excessive phase delay negatively impacts

the overall closed loop response. As a rule of thumb, choose a

value for P so that the frequency of the first null point (fS/P) is

the greater of:

80 times the desired loop bandwidth, or

1.5 times the frequency of CLK (fR/R)

The value of P thus calculated (PMAX) is the largest usable value

in practice. Since P is programmed as PIO, it is necessary to

define PMAX in terms of PIO, so that PIOMAX may be determined.

The condition, PIO ≤ PIOMAX, ensures that the impact of the

phase delay of the CCI filter on the phase margin of the loop

will not exceed 5°. PIOMAX may be expressed as:

































































REF

LOOP

IOMAX

floor

log

min

max

With a properly chosen value for P, the closed-loop response of

the digital PLL is primarily determined by the response of the

digital loop filter. Flexibility in controlling the loop filter

response translates directly into flexibility in the range of

applications satisfied by the architecture of the AD9549.

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