AD9856AST datasheet(18/32 Pages) AD

18 / 32 page

AD9856

–18–

REV. B

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

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

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 30. Comparing the passband detail of HBF 1

and 2 with the passband detail of HBF 1, 2 and 3, it becomes

evident that HBF 3 has virtually no impact on frequency re-

sponse from 0 to 1 (where 1 corresponds to fNYQ).

DISPLAYED FREQUENCY IS RELATIVE TO I/Q NYQ. BW

–30

–100

–40

–50

–60

–70

–80

–90

–10

–20

a. Half-Band 1, 2 and 3 Frequency Response

DISPLAYED FREQUENCY IS RELATIVE TO I/Q NYQ. BW

–6

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

–1

–2

–3

–4

–5

0.9

1.0

b. Passband Detail

Figure 30. Combined Frequency Response of HBF 1, 2 and 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 sample rate

at the output relative to the input, depending on the architec-

ture. 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. In fact, it is a pro-

grammable 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 is dependent on three factors:

1. The rate change ratio, R.

2. The order of the filter, N.

3. The number of unit delays per stage, M.

It can be shown that 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 other-

wise identical. The only variable parameter for the AD9856’s 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:

jfR

jfk

()

–

–(

)

–(

)

–

–(

)





















∑

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 corre-

sponds to the frequency of the output sample rate of the CIC

filter. H(f/R) will yield the frequency response with respect to

the input sample of the CIC filter. Figure 31 reveals the CIC

frequency response and passband detail for R = 2 and R = 63

and with HBF 3 bypassed. Figure 32 is similar but with HBF 3

selected. Note the flatter passband response when HBF 3 is

employed.

As with the case of the HBFs, consideration must be given to

the frequency dependent attenuation that the CIC filter intro-

duces over the frequency range of the data to be transmitted.

Note that the CIC frequency response plots have fNYQ as their

reference frequency; i.e., unity (1) on the frequency scale corre-

sponds 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 plots. A look at the 0.5 point on the passband

detail plots 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

α = 1 is used, the bandwidth of the data corresponds to f

NYQ

(the point, 1.0 on the CIC frequency scale). Thus, the worst

case attenuation for

α = 1 is about 0.9 dB.

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