AD9957SLASHPCBZ datasheet(23/60 Pages) AD

23 / 60 page

AD9957

Rev. 0 | Page 23 of 60

Consider that a complex symbol is represented by a real (I) and

an imaginary (Q) component. Thus, requiring two digital words

to represent a single complex sample of the form I + jQ. The

sample rate associated with a sequence of complex symbols is

referred to as fSYMBOL. If pulse shaping is applied to the symbols,

then the sample rate must be increased by some integer factor,

M (a consequence of the pulse shaping process). This new

sample rate (fIQ) is related to the symbol rate by

fIQ

= MfSYMBOL

where fIQ is the rate at which complex samples must be supplied

to the input of the first half-band filter in both (I and Q) signal

paths. This rate should not be confused with the rate at which

data is supplied to the AD9957.

Typically, pulse shaping is applied to the baseband symbols via

a filter having a raised cosine response. In such cases, an excess

bandwidth factor (α, 0 ≤ α ≤ 1) is used to modify the bandwidth

of the data. For α = 0, the data bandwidth corresponds to fSYMBOL/2;

for α = 1, the data bandwidth extends to fSYMBOL. Figure 36 shows

the relationship between α, the bandwidth of the raised cosine

response, and the response of the first half-band filter.

TYPICAL SPECTRUM OF A RANDOM SYMBOL SEQUENCE

RAISED COSINE

SPECTRAL MASK

SAMPLE RATE FOR

2× OVERSAMPLED

PULSE SHAPING

INPUT SAMPLE

RATE OF FIRST

HALF-BAND

FILTER

HALF-BAND

FILTER

RESPONSE

INPUT SAMPLE

RATE OF FIRST

HALF-BAND

FILTER

NYQUIST

BAND

WIDTH

½fSYMBOL

fSYMBOL

½fSYMBOL

0.4

fIQ

½fIQ

fSYMBOL

α = 1

α = 0

α = 0.5

Figure 36. Effect of the Excess Bandwidth Factor (α)

The responses in Figure 36 reflect the specific case of M = 2 (the

interpolation factor for the pulse shaping operation). Increasing

Factor M shifts the location of the fIQ point on the half-band

response portion of the diagram to the right, as it must remain

aligned with the corresponding MfSYMBOL point on the frequency

axis of the raised cosine spectral diagram. However, if fIQ shifts

to the right, so does the half-band response, proportionally.

The result is that the raised cosine spectral mask always lies

within the flat portion (dc to 0.4 fIQ) of the pass band response

of the first half-band filter, regardless of the choice of α, so long

as M > 2. Therefore, for M > 2, the first half-band filter has

absolutely no negative impact on the spectrum of the baseband

signal when raised cosine pulse shaping is employed. For the

case of M = 2, a problem can arise. This is highlighted by the

shaded area in the tail of the α = 1 trace on the raised cosine

spectral mask diagram. Notice that this portion of the raised

cosine spectral mask extends beyond the flat portion of the

half-band response and causes unwanted amplitude and phase

distortion as the signal passes through the first half-band filter.

To avoid this, simply ensure that α ≤ 0.6 when M = 2.

PROGRAMMABLE INTERPOLATING FILTER

The programmable interpolator is implemented as a low-pass

CCI filter. It is programmable by a 6-bit control word, giving a

range of 2× to 63× interpolation.

The programmable interpolator is bypassed when programmed

for an interpolation factor of 1. When bypassed, power to the

stage is removed and the inverse CCI filter is also bypassed,

because its compensation is not needed.

The output of the programmable interpolator is the data from

the 4× interpolator further upsampled by the CCI filter,

according to the rate chosen by the user. This results in the

upsampling of the input data by a factor of 8× to 252× in steps

of four.

The transfer function of the CCI interpolating filter is

()

⎟

⎠

⎞

⎜

⎝

⎛

∑

−

(1)

where

R is the programmed interpolation factor, and f is the

frequency normalized to fSYSCLK.

QUADRATURE MODULATOR

The digital quadrature modulator stage shifts the frequency of

the baseband spectrum of the incoming data stream up to the

desired carrier frequency (a process known as upconversion).

At this point, the baseband data, which was delivered to the

device at an I/Q sample rate of fIQ, has been upsampled to a rate

equal to the frequency of SYSCLK, making the data sampling

rate equal to the sampling rate of the carrier signal.

The frequency of the carrier signal is controlled by a direct

digital synthesizer (DDS). The DDS very precisely generates the

desired carrier frequency from the internal reference clock

(SYSCLK). The carrier is applied to the I and Q multipliers in

quadrature fashion (90° phase offset) and summed, yielding a

data stream that represents the quadrature modulated carrier.

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