AD9957
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 f
SYMBOL
. If pulse shaping is applied to the symbols,
then the sample rate must be increased by some integer factor,
M (a consequence of the pulse shaping process). This new
sample rate (f
IQ
) is related to the symbol rate by
f
IQ
=
Mf
SYMBOL
Rev. 0 | Page 23 of 60
where
f
IQ
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 f
SYMBOL
/2;
for α = 1, the data bandwidth extends to f
SYMBOL
. Figure 36 shows
the relationship between α, the bandwidth of the raised cosine
response, and the response of the first half-band filter.
f
f
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
f
SYMBOL
f
SYMBOL
2
f
SYMBOL
3
f
SYMBOL
f
SYMBOL
0.4
f
IQ
f
IQ
2
f
IQ
f
IQ
f
SYMBOL
2
f
SYMBOL
4
f
SYMBOL
α
= 1
α
= 0
α
= 0.5
0
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 f
IQ
point on the half-band
response portion of the diagram to the right, as it must remain
aligned with the corresponding Mf
SYMBOL
point on the frequency
axis of the raised cosine spectral diagram. However, if f
IQ
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 f
IQ
) 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,
according 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
H
(1)
where
R
is the programmed interpolation factor, and
f
is the
frequency normalized to f
SYSCLK
.
QUADRATURE MODULATOR
The digital quadrature modulator stage shifts the frequency of
the baseband spectrum of the incoming data stream up to the
desired carrier frequency (a process known as upconversion).
At this point, the baseband data, which was delivered to the
device at an I/Q sample rate of f
IQ
, has been upsampled to a rate
equal to the frequency of SYSCLK, making the data sampling
rate equal to the sampling rate of the carrier signal.
The frequency of the carrier signal is controlled by a direct
digital synthesizer (DDS). The DDS very precisely generates the
desired carrier frequency from the internal reference clock
(SYSCLK). The carrier is applied to the I and Q multipliers in
quadrature fashion (90° phase offset) and summed, yielding a
data stream that represents the quadrature modulated carrier.