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AD9957
Data Sheet
Rev. C | Page 24 of 64
Knowledge of the frequency response of the half-band filters is
essential to understanding their impact on the spectral properties
of the input signal. This is especially true when using the quad-
rature modulator to upconvert a baseband signal containing
complex data symbols that have been pulse shaped.
Consider that a complex symbol is represented by a real (I) and
an imaginary (Q) component, thus requiring two digital words
to represent a single complex sample of the form I + jQ. The
sample rate associated with a sequence of complex symbols is
referred to as fSYMBOL. If pulse shaping is applied to the symbols,
the sample rate must be increased by some integer factor, M
(a consequence of the pulse shaping process). This new sample
rate (fIQ) is related to the symbol rate by
fIQ = MfSYMBOL
where fIQ is the rate at which complex samples must be supplied
to the input of the first half-band filter in both (I and Q) signal
paths. This rate should not be confused with the rate at which
data is supplied to the AD9957.
Typically, pulse shaping is applied to the baseband symbols via
a filter having a raised cosine response. In such cases, an excess
bandwidth factor (α, 0 ≤ α ≤ 1) is used to modify the bandwidth
of the data. For α = 0, the data bandwidth corresponds to fSYMBOL/2;
for α = 1, the data bandwidth extends to fSYMBOL. Figure 36 shows
the relationship between α, the bandwidth of the raised cosine
response, and the response of the first half-band filter.
f
TYPICAL SPECTRUM OF A RANDOM SYMBOL SEQUENCE
RAISED COSINE
SPECTRAL MASK
SAMPLE RATE FOR
2× OVERSAMPLED
PULSE SHAPING
INPUT SAMPLE
RATE OF FIRST
HALF-BAND
FILTER
HALF-BAND
FILTER
RESPONSE
INPUT SAMPLE
RATE OF FIRST
HALF-BAND
FILTER
NYQUIST
BAND
WIDTH
fSYMBOL
2
fSYMBOL
3
fSYMBOL
0.4
fIQ
2
fIQ
fSYMBOL
2
fSYMBOL
4
fSYMBOL
α = 1
α = 0
α = 0.5
06384-
016
Figure 36. Effect of the Excess Bandwidth Factor (α)
The responses in
Figure 36 reflect the specific case of M = 2 (the
interpolation factor for the pulse shaping operation). Increasing
Factor M shifts the location of the fIQ point on the half-band
response portion of the diagram to the right, as it must remain
aligned with the corresponding MfSYMBOL point on the frequency
axis of the raised cosine spectral diagram. However, if fIQ shifts
to the right, so does the half-band response, proportionally.
The result is that the raised cosine spectral mask always lies
within the flat portion (dc to 0.4 fIQ) of the pass band response
of the first half-band filter, regardless of the choice of α so long
as M > 2. Therefore, for M > 2, the first half-band filter has
absolutely no negative impact on the spectrum of the baseband
signal when raised cosine pulse shaping is employed. For the
case of M = 2, a problem can arise. This is highlighted by the
shaded area in the tail of the α = 1 trace on the raised cosine
spectral mask diagram. Notice that this portion of the raised
cosine spectral mask extends beyond the flat portion of the
half-band response and causes unwanted amplitude and phase
distortion as the signal passes through the first half-band filter.
To avoid this, simply ensure that α ≤ 0.6 when M = 2.
PROGRAMMABLE INTERPOLATING FILTER
The programmable interpolator is implemented as a low-pass
CCI filter. It is programmable by a 6-bit control word, giving a
range of 2× to 63× interpolation.
The programmable interpolator is bypassed when programmed
for an interpolation factor of 1. When bypassed, power to the
stage is removed and the inverse CCI filter is also bypassed,
because its compensation is not needed.
The output of the programmable interpolator is the data from
the 4× interpolator further upsampled by the CCI filter, accord-
ing to the rate chosen by the user. This results in the upsampling of
the input data by a factor of 8× to 252× in steps of four.
The transfer function of the CCI interpolating filter is
( )
5
1
0
2
=
∑
=
R
k
fk
π
j
e
f
H
(1)
where R is the programmed interpolation factor, and f is the
frequency normalized to fSYSCLK.
Note that minimum R requirements exist depending on the
mode and frequency of fSYSCLK. The minimum R setting is
defined under the follo wing conditions.
QDUC Mode
If fSYSCLK is between 500 MSPS to 1 GSPS, then the minimum R is 2.
If fSYSCLK is less than 500 MSPS, then the minimum R is 1.
BFI Mode
If fSYSCLK is between 500 MSPS to 750 MSPS, then the minimum
R is 3.
If fSYSCLK is between 250 MSPS to 500 MSPS, then the minimum
R is 2.
If fSYSCLK is less than 250 MSPS, then the minimum R is 1.