AD9786 datasheet(33/60 Pages) AD

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AD9786

Rev. 0 | Page 33 of 60

–8

–6

–4

–2

–0

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

NO INTERPOLATION

×4 INTERPOLATION

×2 INTERPOLATION

×8 INTERPOLATION

SINC RESPONSE

fSIN

INTERP[1] = 1

INTERP[0] = 1

INTERP[1] = 1

INTERP[0] = 0

INTERP[1] = 0

INTERP[0] = 1

INTERP[1] = 0

INTERP[0] = 0

Figure 57. Interpolation Modes

REAL AND COMPLEX SIGNALS

A complex signal contains both magnitude and phase

information. Given two signals at the same frequency, if a point

in time can be taken such that the signal leading in phase is

cosinusoidal and the lagging signal is sinusoidal, then

information pertaining to the magnitude and phase of a

combination of the two signals can be derived; the combination

of the two signals can be considered a complex signal. The

cosine and sine can be represented as a series of exponentials;

recalling that a multiplication by j is a counterclockwise rotation

about the Re/Im plane, the phasor representation of a complex

signal, with frequency f, can be shown in Figure 58.

A/2

FREQUENCY

–f

πft

C = Ae2πft = Acos(2

πft) + jAsin(2πft)

Acos(2

πft) = A

[e+j2πft + e–j2πft]

e+j2πft + e–j2πft

Asin(2

πft) = A

[je+j2πft + e–j2πft]

e+j2πft + e–j2πft

Figure 58. Complex Phasor Representation

The cosine term represents a signal on the real plane with

mirror symmetry about dc; this is referred to as the real, in-

phase or I component of a complex signal. The sine term

represents a signal on the imaginary plane with mirror

asymmetry about dc; this term is referred to as the imaginary,

quadrature or Q complex signal component.

The AD9786 has two channels of interpolation filters, allowing

both I and Q components to be shaped by the same filter

transfer function. The interpolation filters’ frequency response

is a real transfer function. Two DACs are required to represent a

complex signal. A single DAC can only synthesize a real signal.

When a DAC synthesizes a real signal, negative frequency

components fold onto the positive frequency axis. If the input to

the DAC is mirror symmetrical about dc, the folded negative

frequency components fold directly onto the positive frequency

components in phase producing constructive signal summation.

If the input to the DAC is not mirror symmetric about dc,

negative frequency components may not be in phase with

positive frequency components and will cause destructive signal

summation. Different applications may or may not benefit from

either type of signal summation.

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