AD9786BSVRL datasheet(39/56 Pages) AD

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AD9786

Rev. B | Page 39 of 56

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 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.

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

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.

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

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