AD9878BSTZ datasheet(22/36 Pages) AD

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AD9878

Rev. A | Page 22 of 36

been pulse shaped, there is an additional concern. Typically,

pulse shaping is applied to the baseband data via a filter with a

raised cosine response. In such cases, an α value is used to modify

the bandwidth of the data, where the value of α is such that

A value of 0 causes the data bandwidth to correspond to the

Nyquist bandwidth. A value of 1 causes the data bandwidth to

be extended to twice the Nyquist bandwidth. Thus, with 2× over-

sampling of the baseband data and α = 1, the Nyquist bandwidth

of the data corresponds with the I/Q Nyquist bandwidth. As stated

earlier, this results in problems near the upper edge of the data

bandwidth due to the frequency response of the filters. The

maximum value of α that can be implemented is 0.45, because the

data bandwidth becomes

(

)

NYQ

725

which puts the data bandwidth at the extreme edge of the flat

portion of the filter response.

If a particular application requires an α value between 0.45 and 1,

the user must oversample the baseband data by at least a factor of

4. Over the frequency range of the data to be transmitted, the

combined HBF 1, HBF 2, and CIC filters introduce a worst-case

droop of less than 0.2 dB.

FREQUENCY RELATIVE TO I/Q NYQ BW

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

–6

–5

–4

–3

–2

–1

1.0

Figure 25. Cascaded Filter Pass Band

DIGITAL UPCONVERTER

The digital quadrature modulator stage following the CIC filters

is used to frequency shift (upconvert) the baseband spectrum of

the incoming data stream to the desired carrier frequency. The

carrier frequency is controlled numerically by a direct digital

synthesizer (DDS). The DDS uses the internal system clock

(fSYSCLK) to generate the desired carrier frequency with a high

degree of precision. The carrier is applied to the I and Q

multipliers in a quadrature fashion (90° phase offset) and

summed to yield a data stream that is the modulated carrier. The

modulated carrier becomes the 12-bit sample sent to the DAC.

Tx SIGNAL LEVEL CONSIDERATIONS

The quadrature modulator itself introduces a maximum gain of

3 dB in signal level. To visualize this, assume that both the I and

Q data are fixed at the maximum possible digital value, x. Then,

the output of the modulator, z, is

( )

[

]

−

sin

cos

Figure 26. 16-Quadrature Modulation

It can be shown that |z| assumes a maximum value of

(a gain of +3 dB). However, if the

same number of bits represent |z| and x, an overflow occurs.

To prevent this, an effective −3 dB attenuation is internally

implemented on the I and Q data path:

The following example assumes a peak rms level of 10 dB:

LSBs

2000

LSBs

2047

−

Value

Input

Component

Symbol

Maximum

()

rms

LSBs

1265

LSBs

2000

−

rms

Peak

Value

RMS

Input

Complex

Maximum

The maximum complex input rms value calculation uses both

I and Q symbol components that add a factor of two (6 dB)

to the formula. Table 10 shows typical I-Q input test signals

with amplitude levels related to 12-bit full scale (FS).

Table 10. I-Q Input Test Signals

Analog

Output

Digital Input

Input Level

Modulator

Output Level

Single Tone

I = cos(f)

FS − 0.2 dB

FS − 3.0 dB

(fC − f)

Q = cos(f + 90°)

= −sin(f)

FS − 0.2 dB

Single Tone

I = cos(f)

FS − 0.2 dB

FS − 3.0 dB

(fC + f)

Q = cos(f + 270°)

= +sin(f)

FS − 0.2 dB

Dual Tone

I = cos(f)

FS − 0.2 dBFS

FS − 0.2 dB

(fC ± f)

Q = cos(f + 180°)

= −cos(f) or

Q = +cos(f)

FS − 0.2 dB

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