AD6623BCSLASHPCB datasheet(22/40 Pages) AD

22 / 40 page

REV. 0

AD6623

–22–

CIC Scaling

The scale factor SCIC is a programmable unsigned integer

between 4 and 32. This is a combined scaler for the CIC5 and

rCIC2 stages. The overall gain of the CIC section is given by

the equation below

CIC Gain

CIC

rCIC

CIC

–

=×

(10)

CIC5

The first CIC filter stage, the CIC5, is a fifth order interpolating

cascaded integrator comb whose impulse response is completely

defined by its interpolation factor, LCIC5. The value LCIC5–1 can

be independently programmed for each channel at location 0xn09.

2–SCIC

MrCIC

LrCIC

LCIC5

CIC_SCALE

rCIC2

CIC5

Figure 26. CIC5

While this control register is 8 bits wide, LCIC5 should be confined

to the range from 1 to 32 to avoid the possibility of internal

overflow for full scale inputs. The output rate of this stage is given

by the equation below.

CIC

=×

(11)

The transfer function of the CIC5 is given by the following

equations with respect to the CIC5 output sample rate, fsamp5.

CIC

()

–









(12)

The SCIC value can be independently programmed for each

channel at Control Register 0xn06. SCIC may be safely calculated

according to equation (13) below to ensure the net gain through

the CIC stages.

SCIC serves to frame which bits of the CIC output are transferred

to the NCO stage. This results in controlling the data out of the

CIC stages in 6 dB Increments. For the best dynamic range, SCIC

should be set to the smallest value possible (lowest attenuation)

without creating an overflow condition. This can be safely

accomplished using the equation below. To ensure the CIC

output data is in range, equation (13) must always be met. The

maximum total interpolation rate may be limited by the amount

of scaling available.

ceil

CIC

≥×

()+ ()

()

log

(13)

058

≤≤

CIC

(14)

This polynomial fraction can be completely reduced as follows

demonstrating a finite impulse response with perfect phase

linearity for all values of LCIC5.

CIC

()

–

∑





















∑

(15)

The frequency response of the CIC5 can be expressed as follows.

The initial 1/LCIC5 factor normalizes for the increased rate,

which is appropriate when the samples are destined for a DAC

with a zero order hold output. The maximum gain is LCIC5

4 at

baseband, but internal registers peak in response to various

dynamic inputs. As long as LCIC5 is confined to 32 or less, there

is no possibility of overflow at any register.

CIC

()





























sin

(16)

The pass band droop of CIC5 should be calculated using this equation

and can be compensated for in the RCF stage. The gain should

be calculated from the CIC scaling section above.

As an example, consider an input from the RCF whose bandwidth

is 0.141 of the RCF output rate, centered at baseband. Interpolation

by a factor of five reveals five images, as shown below.

–10

–30

–33

–2

–1

012

–50

–70

–90

–110

–130

–150

Figure 27. Interpolation Images

The CIC5 rejects each of the undesired images while passing the

image at baseband. The images of a pure tone at channel center

(DC) are nulled perfectly, but as the bandwidth increases the

rejection is diminished. The lower band edge of the first image

always has the least rejection. In this example, the CIC5 is inter-

polating by a factor of five and the input signal has a bandwidth

of 0.141 of the RCF output sample rate. The plot below shows

–110 dBc rejection of the lower band edge of the first image. All

other image frequencies have better rejection.

–10

–30

–33

–2

–1

012

–50

–70

–90

–110

–130

–150

Figure 28. –110 dBc Rejection

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