AD9857SLASHPCB datasheet(21/41 Pages) AD

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AD9857

Rev. C | Page 20 of 40

Fixed Interpolator (4×)

This block is a fixed 4× interpolator. It is implemented as two

half-band filters. The output of this stage is the original data

upsampled by 4×.

Before presenting a detailed description of the half-band filters,

recall that in the case of the quadrature modulation mode the

input data stream is representative of complex data; i.e., two

input samples are required to produce one I/Q data pair. The

I/Q sample rate is one-half the input data rate. The I/Q sample

rate (the rate at which I or Q samples are presented to the input

of the first half-band filter) is referred to as fIQ. Because the

AD9857 is a quadrature modulator, fIQ represents the baseband

of the internal I/Q sample pairs. It should be emphasized here

that fIQ is not the same as the baseband of the user’s symbol rate

data, which must be upsampled before presentation to the

AD9857 (as explained later). The I/Q sample rate (fIQ) puts a

limit on the minimum bandwidth necessary to transmit the fIQ

spectrum. This is the familiar Nyquist limit and is equal to one-

half fIQ, hereafter referred to as fNYQ.

Together, the two half-band filters provide a factor-of-four

increase in the sampling rate (4 × fIQ or 8 × fNYQ). Their

combined insertion loss is 0.01 dB, so virtually no loss of signal

level occurs through the two half-band filters. Both half-band

filters are linear phase filters, so that virtually no phase

distortion is introduced within the pass band of the filters. This

is an important feature as phase distortion is generally

intolerable in a data transmission system.

The half-band filters are designed so that their composite

performance yields a usable pass band of 80% of the baseband

Nyquist frequency (0.2 on the frequency scale below). Within

that pass band, the ripple does not exceed 0.002 dB. The stop

band extends from 120% to 400% of the baseband Nyquist

frequency (0.3 to 1.0 on the frequency scale) and offers a

minimum of 85 dB attenuation. Figure 24 and Figure 25 show

the composite response of the two half-band filters together.

FREQUENCY

0.2

0.4

–10

–20

–30

–40

–50

–60

–70

–80

–90

–100

–110

–120

–130

–140

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.3

0.2

–85

Figure 24. Half-Band 1 and 2 Frequency Response; Frequency

Relative to HB1 Output Sample Rate

0.05

0.10

0.15

0.20

0.25

0.010

0.008

0.006

0.004

0.002

–0.002

–0.004

–0.006

–0.008

–0.010

RELATIVE FREQUENCY (HB1 OUTPUT SAMPLE RATE = 1)

Figure 25. Combined Half-Band 1 and 2 Pass Band Detail;

Frequency Relative to HB1 Output Sample Rate

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

maximum data rate that can be propagated through the

AD9857. A look at the pass band detail of the half-band filter

response (Figure 25) indicates that in order to maintain an

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

having a bandwidth of no more than about 90% of fNYQ. Thus, to

keep the bandwidth of the data in the flat portion of the filter

pass band, the user must oversample the baseband data by at

least a factor of two prior to presenting it to the AD9857. Note

that without oversampling, the Nyquist bandwidth of the

baseband data corresponds to the fNYQ. Because of this, the

upper end of the data bandwidth suffers 6 dB or more of

attenuation due to the frequency response of the half-band

filters. Furthermore, if the baseband data applied to the AD9857

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 ≤ 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 corresponds with the I/Q

Nyquist bandwidth. As stated earlier, this results in problems

near the upper edge of the data bandwidth due to the roll-off

attenuation of the half-band filters. Figure 26 illustrates the

relationship between α and the bandwidth of raised cosine

shaped pulses. The problem area is indicated by the shading in

the tail of the pulse with α = 1 which extends into the roll-off

region of the half-band filter.

The effect of raised cosine filtering on baseband pulse

bandwidth, and the relationship to the half-band filter response

are shown in Figure 26.

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