AD9549APCBZ datasheet(38/76 Pages) AD

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AD9549

Rev. D | Page 38 of 76

The measurement error (ε) associated with the frequency

estimator depends on the choice of the measurement interval

parameter (K). These are related by

( )

floor

−

ρK

With a specified fractional error (ε0), only those values of K

for which ε ≤ ε0 results in a frequency estimate that meets the

requirements. A plot of ε vs. K (for a given ρ) takes on the

general form that is shown in Figure 48.

ε BOUNDED

BY ENVELOPE

216

ε < ε

0 FOR

SOME K

(K0 < K < K1)

ε > ε

0 FOR

ALL K < K0

ε < ε

0 FOR

ALL K > K1

KLO

KHI

Figure 48. Frequency Estimator ε vs. K

An iterative technique is necessary to determine the exact values

of K0 and K1. However, a closed form exists for a conservative

estimate of K0 (KLOW) and K1 (KHIGH).

























LOW

ceil

























HIGH

ceil

As an example, consider the following system conditions:

fS = 400 MHz

R = 8

fREF_IN = 155.52 MHz

ε0 = 0.00005 (that is, 50 ppm)

These conditions yield KMAX = 3185, which is the largest K value

that can be programmed without causing the frequency estimator

counter to overflow. With K = KMAX, Tmeas = 163.84 μs, and ε =

30.2 ppm, KMAX generally (but not always) yields the smallest

value of ε, but this comes at the cost of the largest measurement

time (Tmeas).

If the measurement time must be reduced, then KHIGH can be used

instead of KMAX. This yields KHIGH = 1945, Tmeas = 100.05 μs, and

ε = 39.4 ppm.

The measurement time can be further reduced (though

marginally) by using K1 instead of KHIGH. K1 is found by solving

the ε ≤ ε0 inequality iteratively. To do so, start with K = KHIGH

and decrement K successively while evaluating the inequality

for each value of K. Stop the process the first time that the

inequality is no longer satisfied and add 1 to the value of K

thus obtained. The result is the value of K1. For the preceding

example, K1 = 1912, Tmeas = 98.35 μs, and ε = 39.8 ppm.

If a further reduction of the measurement time is necessary,

K0 can be used. K0 is found in a manner similar to K1. Start with

K = KLOW and increment K successively while evaluating the

inequality for each value of K. Stop the process the first time that

the inequality is satisfied. The result is the value of K0. For the

preceding example, K0 = 1005, Tmeas = 51.70 μs, and ε = 49.0 ppm.

If external frequency division exists between the DAC output

and the FDBK_IN pins, the frequency estimator should not be

used because it will calculate the wrong initial frequency.

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