AD6622AS datasheet(13/28 Pages) AD

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AD6622

–13–

REV. 0

CASCASDED INTEGRATOR COMB (CIC)

INTERPOLATING FILTER

The I and Q outputs of the RCF stage are interpolated in inte-

ger factors by two cascaded integrator comb (CIC) ﬁlters. The

CIC section is separated into three discrete blocks: a ﬁfth order

ﬁlter (CIC5), a second order ﬁlter (CIC2), and a scaling block

(CIC Scaling). The CIC5 and CIC2 blocks each exhibit a gain

that increases with respect to their interpolation factors, LCIC5

and LCIC2. The product of these gains must be compensated for

in a shared CIC Scaling block.

2–CIC_SCALE

LCIC5

LCIC2

CIC_SCALE

CIC5

CIC2

Figure 13. CIC Data Path

CIC Scaling

The CIC5 and CIC2 stages have a baseband gain of LCIC5

LCIC2. The CIC scaling block is used to avoid numeric overflow

in the CIC stages. The CIC scale block reduces the signal level

without truncation or loss of resolution. The overall gain of the

CIC section is given by Equation 9.

CIC Gain

CIC

Scale

–

=×

(9)

The value CIC_Scale may range from 0 to 25, and can be inde-

pendently programmed for each channel at Control Register

0x06. CIC_Scale may be safely calculated according Equation 10

to ensure the net gain through the CIC stages.

CIC Scale

ceil

CIC

(log (

))

=×

(10)

The ceil function is the next highest integer. While this normally

constitutes a small loss, it can be recovered in the RCF scaling.

Likewise, if the RCF output level is known to be less than full

scale, the CIC gain can be increased by reducing CIC_Scale.

CIC5

The CIC5 is a ﬁfth order interpolating cascaded integrator comb

whose impulse response is completely deﬁned by its interpola-

tion factor, LCIC5. The value LCIC5–1 can be independently

programmed for each channel at location 0x09. While this con-

trol 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 transfer function of the CIC5 is given

by the following equations with respect to the CIC5 output

sample rate, fSAMP5.

CIC z

CIC

()

–









(11)

This polynomial fraction can be completely reduced as follows,

demonstrating a ﬁnite impulse response with perfect phase lin-

earity for all values of LCIC5.

CIC

5 1

()

––











 =−













−

∑∑

(12)

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 base-

band, 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





























(13)

As an example, we will consider an input from the RCF whose

bandwidth is 0.141 of the RCF output rate, centered at base-

band. Interpolation by a factor of ﬁve reveals ﬁve images, as

shown in Figure 14.

–150

–2

–1

–130

–110

–90

–70

–50

–30

–10

Figure 14. Unfiltered CIC Interpolation Image

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 interpolating by a factor of ﬁve and the input signal has a band-

width 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.

–150

–2

–1

–130

–110

–90

–70

–50

–30

–10

Figure 15. Filtered CIC5 Interpolation Images

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