AD9856SLASHPCB datasheet(21/37 Pages) AD

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AD9856

Rev. C | Page 20 of 36

HALF-BAND FILTERS (HBFS)

Before presenting a detailed description of the HBFs, recall that

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

AD9856 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

AD9856 (as is 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, which is referred to as fNYQ.

HBF 1 is a 47-tap filter that provides a factor-of-two increase in

the sampling rate. HBF 2 is a 15-tap filter offering an additional

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

and HBF 2 provide a factor-of-four increase in the sampling

rate (4 × fIQ or 8 × fNYQ). Their combined insertion loss is a mere

0.01 dB, so virtually no loss of signal level occurs through the

first two HBFs. HBF 3 is an 11-tap filter and, if selected,

increases the sampling rate by an additional factor of two. Thus,

the output sample rate of HBF 3 is 8 × fIQ or 16 × fNYQ. HBF 3

exhibits 0.03 dB of signal-level loss. As such, the loss in signal

level through all three HBFs is only 0.04 dB and may be ignored

for all practical purposes.

In relation to phase response, all three HBFs are linear phase

filters. As such, 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.

In addition to knowledge of the insertion loss and phase

response of the HBFs, some knowledge of the frequency

response of the HBFs is useful as well. The combined frequency

response of HBF 1 and 2 is shown in Figure 31 and Figure 32.

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

maximum data rate that can be propagated through the device.

A look at the pass-band detail of the HBF 1 and HFB 2 response

indicates that to maintain an amplitude error of no more than

1 dB, users are restricted to signals having a bandwidth of no

more than about 90% of fNYQ. To keep the bandwidth of the data

in the flat portion of the filter pass band, users must oversample

the baseband data by at least a factor of two prior to presenting

it to the AD9856. Without over-sampling, the Nyquist band-

width of the baseband data corresponds to the fNYQ. As such,

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

attenuation due to the frequency response of HBF 1 and HBF 2.

Furthermore, if the baseband data applied to the AD9856 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 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 frequency

response of HBF 1 and 2.

–100

–90

–70

–30

–10

–50

–80

–40

–20

–60

2.0

1.5

0.5

1.0

2.5

3.0

3.5

4.0

DISPLAYED FREQUENCY IS RELATIVE TO I/Q NYQ. BW

Figure 31. Half-Band 1 and 2 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 32. Pass-Band Detail: Combined Frequency Response of HBF 1 and 2

To reiterate, the user must oversample the baseband data by at

least a factor of two (2). In addition, there is a further restriction

on pulse shaping—the maximum value of α that can be imple-

mented is 0.8. This is because the data bandwidth becomes

1/2(1 + α) fNYQ = 0.9 fNYQ, which puts the data bandwidth at the

extreme edge of the flat portion of the filter response. If a

particular application requires an α value between 0.8 and 1,

then the user must oversample the baseband data by at least a

factor of four (4).

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