AD9786 datasheet(40/60 Pages) AD

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AD9786

Rev. 0 | Page 40 of 60

FILTERED INTERPOLATION IMAGES

fS/8 MODULATION

fS/4 MODULATION

Figure 70. Complex Modulation with Negative Frequency Aliasing

Table 35. Dual Channel Complex Modulation with Hilbert

Hilbert

Mode

Hilbert transform off

Hilbert transform on

When complex modulation is performed, the entire spectrum is

translated by the modulation factor. If the resulting modulated

spectrum is not mirror symmetric about dc, when the DAC

synthesizes the modulated signal, negative frequency compo-

nents will 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.

A/2

X = Ae j2π(f + fm)t

Y = Ae j2π(f + fm)t – π/2

Z = HILBERT(Y)

C = X – Z

Figure 71. Negative Frequency Image Rejection

Referring to Figure 71, by performing a second complex

modulation with a modulating signal having a fixed π/2 phase

difference, Figure (Y), relative to the original complex

modulation signal, Figure (X), taking the Hilbert transform of

the new resulting complex modulation, and subtracting it from

the original complex modulation output all negative frequency

components can be folded in phase to the positive frequency

axis before being synthesized by the DAC. 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.

ALIASED NEGATIVE FREQUENCY INTERPOLATION IMAGES

0.5

–0.5

–0.4

–0.3

–0.2

–0.1

0.1

0.2

0.3

0.4

–150

–50

–100

Figure 72. Negative Frequency Aliasing Distortion

Figure 72 shows this effect at the DAC output for a mirror

asymmetric signal about dc produced by complex modulation

without a Hilbert transform. The signal bandwidth was nar-

rowed to show the aliased negative frequency interpolation

images.

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