Datasheet

AD9786
Rev. B | Page 39 of 56
FILTERED INTERPOLATION IMAGES
f
S
/8 MODULATION
f
S
/4 MODULATION
–
f
DAC
–7
f
DAC
/8
–3
f
DAC
/4
–5
f
DAC
/8
–
f
DAC
/2
–3
f
DAC
/8
–
f
DAC
/8
000
f
DAC
/8
f
DAC
/4
3f
DAC
/8
f
DAC
/2
5f
DAC
/8
3f
DAC
/4
7f
DAC
/8
f
DAC
–
f
DAC
/4
–
f
DAC
–7
f
DAC
/8
–3
f
DAC
/4
–5
f
DAC
/8
–
f
DAC
/2
–3
f
DAC
/8
–
f
DAC
/8
f
DAC
/8
f
DAC
/4
3f
DAC
/8
f
DAC
/2
5f
DAC
/8
3f
DAC
/4
7f
DAC
/8
f
DAC
–
f
DAC
/4
–
f
DAC
–7
f
DAC
/8
–3
f
DAC
/4
–5
f
DAC
/8
–
f
DAC
/2
–3
f
DAC
/8
–
f
DAC
/8
f
DAC
/8
f
DAC
/4
3f
DAC
/8
f
DAC
/2
5f
DAC
/8
3f
DAC
/4
7f
DAC
/8
f
DAC
–
f
DAC
/4
03152-070
Figure 70. Complex Modulation with Negative Frequency Aliasing
Table 35. Dual Channel Complex Modulation with Hilbert
Hilbert Mode
0 Hilbert transform off
1 Hilbert transform on
When complex modulation is performed, the entire spectrum is
translated by the modulation factor. If the resulting modulated
spectrum is not mirrored symmetrically about dc when the
DAC synthesizes the modulated signal, negative frequency
components fall on the positive frequency axis and can cause
destructive summation of the signals, as shown in Figure 70. For
some applications, this can distort the modulated output signal.
Re
Im
f
Re
Im
f
Re
Im
f
Re
Im
f
0000
A/2 A/2
A/2
A/2
A
A
A/2
A/2A/2
A/2
A/2
A/2 A/2
A/2
X = Ae
j2π(f + fm)t
Y = Ae
j2π(f + fm)t – π/2
Z = HILBERT(Y) C = X – Z
03152-071
Figure 71. Negative Frequency Image Rejection
In Figure 71, Figure X represents a complex signal typically
found in the AD9786 signal path. Figure Y is identical to Figure X,
but it is shifted by π/2. The phase shifting in the AD9786 occurs
because the digital LO driving the digital quadrature modulator
in the Hilbert transform path is phase shifted by π/2.
The operation of the Hilbert transform (Figure Z) rotates the
negative frequency components of Figure Y by +π/2, and the
positive frequency components of Figure Y by −π/2. The result
of the Hilbert transform output is then summed with the complex
signal in the main signal path. The result is that negative frequen-
cies are cancelled and, therefore, do not fold back into the
positive side of the frequency spectrum. The Δt block in the main
signal path offsets the delay inherent in the Hilbert transform
(nine DAC clock cycle delay). When the DAC synthesizes the
modulated output, there are no negative frequency components to
fold onto the positive frequency axis out of phase; consequently,
no distortion is produced as a result of the modulation process.
03152-072
ALIASED NEGATIVE FREQUENCY INTERPOLATION IMAGES
0.5–0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4
dBFS
–150
0
–50
–100
Figure 72. Negative Frequency Aliasing Distortion