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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
Oversampling ADC
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Nyquist-Rate ADC
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
The black box version of the quantization process
Digitizes the input signal up to the Nyquist frequency (fs/2)
Minimum sampling frequency (fs) for a given input bandwidth
Each sample is digitized to the maximum resolution of the converter
A/Dbn
Digital outputAnalog input
b1.
.
.
Vref
fs
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Anti-Aliasing Filter (AAF)
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
Input signal must be
band-limited prior to
sampling
Nyquist sampling places
stringent requirement on
the roll-off characteristic
of AAF
Often some oversampling
is employed to relax the
AAF design (better phase
response too)
Decimation filter (digital)
can be linear-phase
Mfs
PSD
PSD
f
ffm
fm
PSD
ffm=fs/2
fs
AAF
AAFDF
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Oversampling ADC
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
Sample rate is well beyond the signal bandwidth
Coarse quantization is combined with feedback to provide an accurate
estimate of the input signal on an average sense
Quantization error in the coarse digital output can be removed by the
digital decimation filter The resolution/accuracy of oversampling converters is achieved in a
sequence of samples (average sense) rather than a single sample; the
usual concept of DNL and INL of Nyquist converters are not applicable
OSR
Decimation filter
bn
b1.
.
.
A/D
Digital outputAnalog input
d1
Vref
fs
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Oversampling ADC
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
Predictive type
Delta modulation
Noise-shaping type
Sigma-delta modulation
Multi-level (quantization) sigma-delta modulation Multi-stage (cascaded) sigma-delta modulation (MASH)
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Oversampling
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
PSD
f-fs/2
A/Dbn
b1.
.
. M
Decimation filter
bn
b1.
.
.
fs
A/D
Mfs
fs/2
2/12PSD
f-Mfs/2 Mfs/2
2/12
-fs/2 fs/2
Nyquist Oversampled
Sample rate Noise power Power
Nyquist fs 2/12 P
Oversampled M*fs (2/12)/M M*P
OSR = M
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Noise Shaping
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
PSD
f-Mfs/2 Mfs/2-fs/2 fs/2
Push noise out of signal band
Large gain @ LF, low gain @ HF
Integrator?
A/DH(f)
Mfs
Vi
e
Vi
1 2
H(f)
1 2
e e
H(f)
fMfs/2fs/2
1 H-1(f)
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Sigma-Delta () Modulator
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
A/DVi
D/A
Do
Noise shaping obtained with an integrator
Output subtracted from input to avoid integrator saturation
First-ordermodulator
z-1
A/DVi
D/A
Do
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Linearized Discrete-Time Model
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
H(z)X(z) Y(z)
E(z)
1
1
z1
zH(z)
zEz1zXzzY
zEzH1
1zX
zH1
zHzY
zEzYzXzHzY
11
DelayzzX
zYSTF
:FunctionTransferSignal
1
HPz1zE
zYNTF
:FunctionTransferNoise
1
Caveat: E(z) may be correlated with X(z)not white!
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First-Order Noise Shaping
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
PSD
ffs/2fm
3
f
2f
12
dff
f2
2f
1
12
df
f
f2sin
2f
1
12
dfNTF2f
1
12
N
23
s
m
2
2f
0 ss
2
2f
0 ss
2
2f
0 s
22
e
m
m
m
2 2
2e 3
In - band quantization noise :
N12 3M
Doubling OSR (M) increases SQNR by 9 dB (1.5 bit/oct)
2
sf
f2sin
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SC Implementation
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
SC integrator
1-bit ADC simple, ZX detector
1-bit feedback DAC simple, inherently linear
CI
21
12
ViDo
+VR 1-b
DAC-VR
CS
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Second-Order Modulator
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
INT1 INT2
A/D
D/A
Doz-1
Vi
2
z-1
2zSTF
:FunctionTransferSignal
21z1NTF:FunctionTransferNoise
5
422
e5M
12
N
:noiseonquantizatiband-In
Doubling OSR (M) increases SQNR by 15 dB (2.5 bit/oct)
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2nd-Order Modulator (1-Bit Quantizer)
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
Simple, stable, highly-linear
Insensitive to component mismatch
Less correlation b/t E(z) and X(z)
1-bit
A/D
1-bit
D/A
Doz-1
Vi z-1
2
zE1z
1zzX
1z
zY
2
2
2
jy
z-plane
0 1x
(2) (2)
1
1
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Generalization (Lth-Order Noise Shaping)
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
12L2L2
2
eM12L
12
N
:noiseonquantizatiband-In
zEz1zXzzY:functiontransferModulator
L1n
Doubling OSR (M) increases SQNR by (6L+3) dB, or (L+0.5) bit
Potential instability for 3rd- and higher-order single-loop modulators
2L 12L
2L 1 M
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vs. Nyquist ADCs
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
ADC output (1-bit) Nyquist ADC output
ADC behaves quite differently from Nyquist converters Digital codes only display an average impression of the input
INL, DNL, monotonicity, missing code, etc. do not directly apply in
converters use SNR, SNDR, SFDR instead
+1
-1
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Tones
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
...
...
Vi= 0
Vi= 0.001
T
2000*T
The output spectrum corresponding to Vi= 0 results in a tone atfs/2, andwill get eliminated by the decimation filter
The 2nd output not only has a tone at fs/2, but also a low-frequency tone
fs/2000that cannot be eliminated by the decimation filter
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Cascaded (MASH) Modulator
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
H(z)X(z) Y(z)
E(z)
D/A
A/D DNTFE(z)
Idea: to further quantize E(z) and later subtract out in digital domain
The 2nd quantizer can be a modulator as well
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2-1 Cascaded Modulator
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
INT1 INT2
z-1
X(z)
2
z-1
INT3
z-1
(1-z-1
)2
D/A
D/A
E1(z)
E2(z)
z-1
Y(z)
E1(z)
Y1(z)
Y2(z)
DNTF
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2-1 Cascaded Modulator
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
11212
1 zzEz1zXzzY
zEz1zXz
zEz1zEz1zzEz1zzXzzYzYzY
2
313
2
31
1
211
1
2113
21
2121112 z1zEz1zEzzY
E1(z) completely cancelled assuming perfect matching between themodulator NTF (analog domain) and the DNTF (digital domain)
A 3rd-order noise shaping on E2(z) obtained
No potential instability problem
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Integrator Noise
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Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
231
1
213
212
11 Ez1Ez1Nz1Nz1NXY
INT1 INT2
H(z)X(z)
2
H(z)
INT3
H(z)
D/A
D/A
E1
E2
Y1(z)
Y2(z)
N1 N2
N3
Delay ignored
INT1 dominates
the overall noise
Performance!
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References
23
Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
1. B. E. Boser and B. A. Wooley, JSSC, pp. 1298-1308, issue 6, 1988.
2. B. H. Leung et al., JSSC, pp. 1351-1357, issue 6, 1988.
3. T. C. Leslie and B. Singh, ISCAS, 1990, pp. 372-375.
4. B. P. Brandt and B. A. Wooley, JSSC, pp. 1746-1756, issue 12, 1991.
5. F. Chen and B. H. Leung, JSSC, pp. 453-460, issue 4, 1995.
6. R. T. Baird and T. S. Fiez, TCAS2, pp. 753-762, issue 12, 1995.7. T. L. Brooks et al., JSSC, pp. 1896-1906, issue 12, 1997.
8. A. K. Ong and B. A. Wooley, JSSC, pp. 1920-1934, issue 12, 1997.
9. S. A. Jantzi, K. W. Martin, and A.S. Sedra, JSSC, pp. 1935-1950, issue 12, 1997.
10. A. Yasuda, H. Tanimoto, and T. Iida, JSSC, pp. 1879-1886, issue 12, 1998.
11. A. R. Feldman, B. E. Boser, and P. R. Gray, JSSC, pp. 1462-1469, issue 10, 1998.
12. H. Tao and J. M. Khoury, JSSC, pp. 1741-1752, issue 12, 1999.
13. E. J. van der Zwan et al., JSSC, pp. 1810-1819, issue 12, 2000.
14. I. Fujimori et al., JSSC, pp. 1820-1828, issue 12, 2000.
15. Y. Geerts, M.S.J. Steyaert, W. Sansen, JSSC, pp. 1829-1840, issue 12, 2000.
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References
24
Data Converters Oversampling ADC Professor Y. Chiu
EECT 7327 Fall 2012
16. T. Burger and Q. Huang, JSSC, pp. 1868-1878, issue 12, 2001.
17. K. Vleugels, S. Rabii, and B. A. Wooley, JSSC, pp. 1887-1899, issue 12, 2001.
18. S. K. Gupta and V. Fong, JSSC, pp. 1653-1661, issue 12, 2002.
19. R. Schreier et al., JSSC, pp. 1636-1644, issue 12, 2002.
20. J. Silva et al., CICC, 2002, pp. 183-190.
21. Y.-I. Park et al., CICC, 2003, pp. 115-118.22. L. J. Breems et al., JSSC, pp. 2152-2160, issue 12, 2004.
23. R. Jiang and T. S. Fiez, JSSC, pp. 63-74, issue 12, 2004.
24. P. Balmelli and Q. Huang, JSSC, pp. 2161-2169, issue 12, 2004.
25. K. Y. Nam et al., CICC, 2004, pp. 515-518.
26. X. Wang et al., CICC, 2004, pp. 523-526.
27. A. Bosi et al., ISSCC, 2005, pp. 174-175.
28. N. Yaghini and D. Johns, ISSCC, 2005, pp. 502-503.
29. G. Mitteregger et al., JSSC, pp. 2641-2649, issue 12, 2006.
30. R. Schreier et al., JSSC, pp. 2632-2640, issue 12, 2006.