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AD9957
The modulation is performed digitally avoiding the phase
offset, gain imbalance, and crosstalk issues commonly
associated with analog modulators. Note that the modulated,
so-called signal is a number stream sampled at the rate of
SYSCLK, the same rate at which the DAC is clocked.
Rev. 0 | Page 24 of 60
The orientation of the modulated signal with respect to the
carrier is controlled by a spectral invert bit. This bit resides in
each of the four profile registers. By default, the time domain
output of the quadrature modulator takes the form
I
(
t
) × cos(
ωt
)
Q
(
t
) × sin(ωt)
(2)
When the spectral invert bit is asserted, it becomes
I
(
t
) × cos(
ωt
) +
Q
(
t
) × sin(ωt)
(3)
DDS CORE
The direct digital synthesizer (DDS) block generates sine
and/or cosine signals. In single tone mode, the DDS generates
either a digital sine or cosine waveform based on the select DDS
sine output bit. In QDUC mode, the DDS generates the quadra-
ture carrier reference signal that digitally modulates the I/Q
baseband signal.
The DDS output frequency is tuned using registers accessed via
the serial I/O port. This allows for both precise tuning and
instantaneous changing of the carrier frequency.
The equation relating output frequency (f
OUT
) of the DDS to the
frequency tuning word (FTW) and the system clock (f
SYSCLK
) is
SYSCLK
OUT
f
FTW
32
2
f
=
(4)
where
FTW
is a decimal number from 0 to 2,147,483,647 (2
31
1).
Solving for FTW yields
=
SYSCLK
OUT
f
f
round
FTW
32
2
(5)
where the
round()
function means to round the result to the
nearest integer. For example, for f
OUT
= 41 MHz and f
SYSCLK
=
122.88 MHz, then FTW = 1,433,053,867 (0x556AAAAB).
In single tone mode, the DDS frequency, phase, and amplitude
are all programmable via the serial I/O port. The amplitude is
controlled by means of a digital multiplier using a 14-bit
fractional scale value called the amplitude scale factor (ASF).
The LSB weight is 2
14
, yielding a multiplier range of 0 to
0.99993896484375 (1 2
14
). The phase offset is controlled by
means of a digital adder that uses a 14-bit offset value called the
phase offset word (POW). The adder is situated between the
phase accumulator and the angle-to-amplitude conversion logic
in the DDS core. The adder applies the POW to the instantaneous
phase values produced by the DDS phase accumulator. The
adder is MSB-aligned with the phase accumulator yielding an
LSB weight of 2
14
(which equates to a resolution of ~0.022° or
~0.000383 radians). Both the ASF and the POW are available
for each of the eight profiles.
INVERSE SINC FILTER
The sampled carrier data stream is the input to the on board
digital-to-analog converter. The DAC output spectrum is
shaped by the characteristic sin(x)/x (or sinc) envelope, due to
the intrinsic zero-order hold effect associated with DAC-
generated signals. The shape of the sinc envelope is well known
and can be compensated for. This compensation is provided by
the inverse sinc filter preceding the DAC.
The inverse sinc filter is implemented as a digital FIR filter. Its
response characteristic very nearly matches the inverse of the
sinc envelope, as shown in Figure 37 (along with the sinc
envelope for comparison).
The inverse sinc filter is enabled through a bit in the register
map. The filter tap coefficients are listed in Table 5. The filter
predistorts the data prior to its arrival at the DAC to compensate
for the sinc envelope that otherwise distorts the spectrum.
When the inverse sinc filter is enabled, it introduces an ~3.0 dB
insertion loss. The inverse sinc compensation is effective for
output frequencies up to 40% (nominally) of the DAC sample rate.
Table 5. Inverse Sinc Filter Tap Coefficients
Tap No.
Tap Value
1
35
2
+134
3
562
4
+6729
Tap No.
7
6
5
4
In Figure 37, it can be seen that the sinc envelope introduces a
frequency dependent attenuation that can be as much as 4 dB at
the Nyquist frequency (half of the DAC sample rate). Without
the inverse sinc filter, the DAC output also suffers from the
frequency dependent droop of the sinc envelope. The inverse
sinc filter effectively flattens the droop to within ±0.05 dB as
shown in Figure 38, which shows the corrected sinc response
with the inverse sinc filter enabled.
1
0
–1
–2
–3
–4
0
0.1
0.2
0.4
0.3
0.5
0
(
FREQUENCY RELATIVE TO DAC SAMPLE RATE
INVERSE
SINC
SINC
Figure 37. Sinc and Inverse Sinc Responses