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REV. 0
–28–
AD6635
Both
L
rCIC2
and
M
rCIC2
are unsigned integers. The interpolation
rate (
L
rCIC2
) may be from 1 to 512 and the decimation (
M
rCIC2
)
may be from 1 to 4096. The stage can be bypassed by setting
the decimation/interpolation to 1/1.
The frequency response of the rCIC2 filter is given by the fol-
lowing equations.
H z
L
z
z
SrCIC
2
rCIC
MrCIC
LrCIC
=
¥
¥
ê
á
á
ˉ
1
1
1
2
2
2
2
1
2
–
–
–
–
H f
L
M
f
L
f
f
f
SrCIC
2
rCIC
rCIC
rCIC
ê
SAMP
ˉ
SAMP
=
¥
¥
¥
¥
ê
ˉ
ê
á
á
á
á
ˉ
1
2
2
2
2
2
sin
sin
p
p
The scale factor,
S
rCIC2
is a programmable unsigned 5-bit value
between 0 and 31. This serves as an attenuator that can reduce
the gain of the
rCIC2
in 6 dB increments. For the best dynamic
range,
S
rCIC2
should be set to the smallest value possible (i.e.,
lowest attenuation) without creating an overflow condition.
This can be safely accomplished using the equation below,
where
input_level
is the largest fraction of full scale possible at
the input to the AD6635 (normally 1). The rCIC2 scale factor
is always used, whether or not the rCIC2 is bypassed.
S
ceil
M
floor
M
L
M
L
floor
M
L
rCIC
rCIC
rCIC
rCIC
rCIC
rCIC
rCIC
rCIC
2
2
2
2
2
2
2
2
2
2
1
=
+
ê
ˉ¥
¥
¥
+
ê
ˉ
ê
ˉ
ê
á
á
á
á
ˉ
è
í
í
í
í
í
˙
˙
˙
˙
˙
log
–
OL
M
L
input
level
CIC
rCIC
¥
rCIC
SrCIC
2
2
2
2
2
2
=
(
¥
_
The
ceil
function used above denotes the next whole integer,
and the
floor
function denotes the previous whole integer. For
example,
ceil
(4.5) is 5, while
floor
(4.5) is 4.
There are two scale registers (rCIC2_LOUD[4:0] Bits 4–0 in
0x92), and (rCIC2_QUIET[4:0] Bits 9–5 in 0x92), which are
used to implement the
S
rCIC2
scale factor. The value written into
the these programmable registers is the sum total of
S
rCIC2
, ExpOff
required for floating point ADCs (explained in the Input Port
section), and any compensation for external attenuation that
may be activated using the LI (level indicator) pins. The third
component can have different values when the LI pin is active
and when it is inactive, and hence two registers, rCIC2_LOUD
and rCIC2_QUIET. The sum total of these components is
supplied to the AD6635 as rCIC2_LOUD and rCIC2_QUIET
registers, and these registers can contain a maximum number of
31. It should also be noted that the scaling specified by these
register is applied at only one place in the AD6635 channel
(before the rCIC2 filter).
The gain and passband droop of the rCIC2 should be calculated
by the equations above, as well as the filter transfer equations
mentioned previously. Excessive passband droop can be com-
pensated for in the RCF stage by peaking the pass band by the
inverse of the roll-off.
scaled
scaled
input
input
IN
IN
ExpInv
ExpInv
,
Exp rCIC
Exp rCIC
_
_
,
– mod(
,
– mod( –
,
=
=
¥
¥
2
2
2
7
2
32)
32)
=0
=1
where
IN
is the value of INx[13:0] (x = A, B, C, D),
Exp
is the
value of EXPx[2:0], and
rCIC2
is the value of the 0x92
(rCIC2_QUIET[4:0] or rCIC2_LOUD[4:0], depending on
LI pin) scale register.
rCIC2 Rejection
Table III illustrates the amount of bandwidth in percent of the
data rate into the rCIC2 stage. The data in this table may be
scaled to any other allowable sample rate up to 80 MHz. The
table can be used as a tool to decide how to distribute the deci-
mation between rCIC2, CIC5 and the RCF.
Table III. SSB rCIC2 Alias Rejection Table (f
SAMP
= 1)
Bandwidth Shown as Percentage of f
SAMP.
(input rate)
M
rCIC2
/L
rCIC2
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Example Calculations
Goal: Implement a filter with an input sample rate of 10 MHz
requiring 100 dB of alias rejection for a
±
7 kHz pass band.
Solution: First determine the percentage of the sample rate that
is represented by the pass band.
–50 dB –60 dB –70 dB –80 dB
–90 dB –100 dB
1.790
1.508
1.217
1.006
0.853
0.739
0.651
0.581
0.525
0.478
0.439
0.406
0.378
0.353
0.331
1.007
0.858
0.696
0.577
0.490
0.425
0.374
0.334
0.302
0.275
0.253
0.234
0.217
0.203
0.190
0.566
0.486
0.395
0.328
0.279
0.242
0.213
0.190
0.172
0.157
0.144
0.133
0.124
0.116
0.109
0.318
0.274
0.223
0.186
0.158
0.137
0.121
0.108
0.097
0.089
0.082
0.075
0.070
0.066
0.061
0.179
0.155
0.126
0.105
0.089
0.077
0.068
0.061
0.055
0.050
0.046
0.043
0.040
0.037
0.035
0.101
0.087
0.071
0.059
0.050
0.044
0.038
0.034
0.031
0.028
0.026
0.024
0.022
0.021
0.020
BW
kHz
MHz
FRACTION
=
¥
=
100
7
10
0 07
.
In the –100 dB column on the right of the table, look for a
value greater than or equal to your passband percentage of the
clock rate. Then look across to the extreme left column and
find the corresponding rate change factor (M
rCIC2
/L
rCIC2)
. Referring
to the table, notice that for a M
rCIC2
/L
rCIC2
of 4, the frequency
having –100 dB of alias rejection is 0.071%, which is slightly
greater than the 0.07% calculated. Therefore, for this example,
the maximum bound on rCIC2 rate change is 4. Choosing a
higher M
rCIC2
/L
rCIC2
results in less alias rejection than the
required 100 dB.
An M
rCIC2
/L
rCIC2
of less than 4 would still yield the required
rejection, however the power consumption can be minimized by
decimating as much as possible in this rCIC2 stage. Decimation
in rCIC2 lowers the data rate, and thus reduces power consumed
in subsequent stages. It should also be noted that there is more
than one way to get the decimation of 4. A decimation of 4 is
the same as an L/M ratio of 0.25. Thus, any integer combination