AD9873JS datasheet(25/39 Pages) AD

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REV. 0

AD9873

–25–

TxI[11:6]

tHD

tSU

MCLK

Tx SYNC

Tx IQ

TxI[5:0]

TxQ[5:0]

TxQ[11:6]

TxI[11:6]'

TxI[5:0]'

TxQ[5:0]'

TxQ[11:6]'

TxI[5:0]"

TxI[11:6]"

Figure 9. Transmit Timing Diagram

The I/Q sample rate fIQCLK puts a bandwidth limit on the maxi-

mum transmit spectrum. This is the familiar Nyquist limit and is

equal to one-half fIQCLK which hereafter will be referred to as fNYQ.

Half-Band Filters (HBFs)

HBF 1 is a 15-tap filter that provides a factor-of-two increase

in sampling rate. HBF 2 is an 11-tap filter offering an additional

factor-of-two increase in sampling rate. Together, HBF 1 and 2

provide a factor-of-four increase in the sampling rate (4

fIQCLK

or 8

fNYQ).

In relation to phase response, both HBFs are linear phase filters.

As such, virtually no phase distortion is introduced within the

passband of the filters. This is an important feature as phase

distortion is generally intolerable in a data transmission system.

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

architecture. 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

AD9873, the CIC filter is configured as a programmable inter-

polator and provides a sample rate increase by a factor of R = 3

or R = 4. 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 AD9873’s

CIC filter is R; m and n are fixed at 1 and 3, respectively. Thus,

the CIC system function for the AD9873 simplifies to:

()

= 







−









= 







∑









−

The transfer function is given by:

jf R

()

sin(

)

sin(

)

()

= 







−









= 















−

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)

will yield the frequency response with respect to the input sample

of the CIC filter.

Combined Filter Response

The combined frequency response of HBF 1, HBF 2 and CIC is

shown in Figure 10a to 10c and Figure 11a to 11c.

The usable bandwidth of the filter chain puts a limit on the maxi-

mum data rate that can be propagated through the AD9873.

A look at the passband detail of the combined filter response

(Figure 10d and Figure 11d) indicates that in order to maintain

an amplitude error of no more than 1 dB, we are restricted to

signals having a bandwidth of no more than about 60% of fNYQ.

Thus, in order to keep the bandwidth of the data in the flat portion

of the filter passband, the user must oversample the baseband data

by at least a factor of two prior to presenting it to the AD9873.

Note that without oversampling, the Nyquist bandwidth of the

baseband data corresponds to the fNYQ. As such, the upper end

of the data bandwidth will suffer 6 dB or more of attenuation

due to the frequency response of the digital filters. Furthermore, if

the baseband data applied to the AD9873 has been pulse-shaped,

there is an additional concern. Typically, pulse-shaping is applied

to the baseband data via a filter having a raised cosine response.

In such cases, an

α value is used to modify the bandwidth of the

data where the value of

α is such that 0 ≤ α ≤ 1. A value of 0 causes

the data bandwidth to correspond to the Nyquist bandwidth. A

value of 1 causes the data bandwidth to be extended to twice the

Nyquist bandwidth. Thus, with 2

× oversampling of the baseband

data and

α = 1, the Nyquist bandwidth of the data will correspond

with the I/Q Nyquist bandwidth. As stated earlier, this results in

problems near the upper edge of the data bandwidth due to the

frequency response of the filters. The maximum value of

α that

can be implemented is 0.45. This is because the data bandwidth

becomes:

1/2(1+

α) fNYQ = 0.725 fNYQ,

which puts the data bandwidth at the extreme edge of the flat

portion of the filter response.

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