-350
-300
-250
-200
-150
-100
-50
0
0
0.25 0.5 0.75
1
Gain (dB)
F/Fs
1.25 1.5 1.75
2
2.25 2.5 2.75
3
3.25
3.5 3.75
4
4.25 4.5
7
7
M
M
M
M
f
f
sinc OSR
sin OSR ×
×
f
f
1
H(f) =
=
×
OSR
f
f
sinc
sin
×
f
f
æ
ö
æ
ö
æ
ö
æ
ö
p
p
ç
÷
ç
÷
ç
÷
ç
÷
ç
÷
ç
÷
è
ø
è
ø
ç
÷
ç
÷
æ
ö
æ
ö
ç
÷
ç
÷
p
p
ç
÷
ç
÷
ç
÷
ç
÷
è
ø
è
ø
è
ø
è
ø
7
–OSR
–1
1
1 – z
H(z) =
×
OSR
1 – z
æ
ö
ç
÷
ç
÷
è
ø
f
S
f
M
f
M
f
M
f
S
f
S
Differentiator
Integrator
Bitstream from
Modulator
Integrator
Integrator
Differentiator
Differentiator
z
-1
z
-1
z
-1
z
-1
z
-1
z
-1
+
+
+
+
+
+
-
-
-
f
M
f
M
f
M
Integrator
Integrator
Integrator
z
-1
z
-1
z
-1
+
+
+
f
M
Integrator
z
-1
+
f
S
f
S
f
S
Differentiator
Differentiator
Differentiator
z
-1
z
-1
z
-1
+
+
+
-
-
-
f
S
Differentiator
z
-1
+
-
SDHS Functional Operation
572
SLAU367P – October 2012 – Revised April 2020
Copyright © 2012–2020, Texas Instruments Incorporated
Sigma-Delta High Speed (SDHS)
Figure 22-4. CIC
7
Filter Structure
The transfer function is described in the z-domain by
(11)
The transfer function is described in the frequency domain by
where
•
OSR = The ratio of the modulator frequency f
M
to the sample frequency f
S
(12)
shows the filter frequency response beyond f
S
(normalized), and
shows the filter
frequency response within f
S
. The first filter notch is always at f
S
= f
M
/ OSR. The digital filter for the SDHS
converter completes the decimation of the digital bit stream and outputs the new conversion result to the
SDHSDT register at the sample frequency, f
S
.
Figure 22-5. SDHS Filter Frequency Response, SDHSCTL1.OSR = 10