AD9856AST datasheet(22/37 Pages) AD

22 / 37 page

AD9856

Rev. C | Page 21 of 36

In applications requiring both a low data rate and a high output

sample rate, a third HBF is available (HBF 3). Selecting HBF 3

offers an upsampling ratio of eight (8) instead of four (4). The

combined frequency response of HBF 1, 2, and 3 is shown in

Figure 33 and Figure 34. Comparing the pass-band detail of

HBF 1 and 2 with the pass-band detail of HBF 1, 2, and 3,

HBF 3 has virtually no impact on frequency response from

0 to 1 (where 1 corresponds to fNYQ).

–100

–90

–70

–30

–10

–50

–80

–40

–20

–60

DISPLAYED FREQUENCY IS RELATIVE TO I/Q NYQ. BW

Figure 33. Half-Band 1, 2, and 3 Frequency Response

–6

–5

–4

–3

–2

–1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

DISPLAYED FREQUENCY IS RELATIVE TO I/Q NYQ. BW

Figure 34. Pass-Band Detail: Combined Frequency Response of HBF 1 to 3

CASCADED INTEGRATOR COMB (CIC) FILTER

A CIC filter is unlike a typical FIR filter in that it offers the

flexibility to handle differing input and output sample rates

(only in integer ratios, however). In the purest sense, a CIC

filter can provide either an increase or a decrease in the sample

rate at the output relative to the input, depending on the archi-

tecture. If the integration stage precedes the comb stage, the

CIC filter provides sample rate reduction (decimation). When

the comb stage precedes the integrator stage the CIC filter

provides an increase in sample rate (interpolation). In the

AD9856, the CIC filter is configured as an interpolator—

a programmable interpolator—and provides a sample rate

increase, R, such that 2 ≤ R ≤ 63.

In addition to the ability to provide a change in sample rate

between input and output, a CIC filter also has an intrinsic low-

pass frequency response characteristic. The frequency response

of a CIC filter depends on:

•

The rate change ratio, R.

•

The order of the filter, N.

•

The number of unit delays per stage, M.

The system function, H(z), of a CIC filter is given by:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

∑

−

)

(

The form on the far right has the advantage of providing a

result for z = 1 (corresponding to zero frequency or dc). The

alternate form yields an indeterminate form (0/0) for z = 1,

but is otherwise identical. The only variable parameter for

the AD9856 CIC filter is R. M and N are fixed at 1 and 4,

respectively. Thus, the CIC system function for the AD9856

simplifies to:

)

(

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

∑

−

The transfer function is given by:

)

(

)

(

)

(

)

(

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

∑

−

The frequency response in this form is such that f is scaled

to the output sample rate of the CIC filter. That is, f = 1

corresponds to the frequency of the output sample rate of the

CIC filter. H(f/R) yields the frequency response with respect to

the input sample of the CIC filter. Figure 35 to Figure 44 show

the CIC frequency response and pass-band detail for R = 2 and

R = 63, with HBF 3 bypassed. Figure 45 to Figure 50 are similar,

but HBF 3 is selected. Note the flatter pass-band response when

HBF 3 is employed.

As with HBFs, consideration must be given to the frequency-

dependent attenuation that the CIC filter introduces over the

frequency range of the data to be transmitted. Note that the

CIC frequency response figures have fNYQ as their reference

frequency; i.e., unity (1) on the frequency scale corresponds

to fNYQ. If the incoming data that is applied to the AD9856 is

oversampled by a factor of 2 (as required), then the Nyquist

bandwidth of the applied data is one-half fNYQ on the CIC

frequency response figures. A look at the 0.5 point on the pass-

band detail figures reveals a worst-case attenuation of about

0.25 dB (HBF 3 bypassed, R = 63). This, of course, assumes

pulse-shaped data with α = 0 (minimum bandwidth scenario).

When a value of α = 1 is used, the bandwidth of the data

corresponds to fNYQ (the point1.0 on the CIC frequency scale).

Thus, the worst-case attenuation for α = 1 is about 0.9 dB.

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