– 1 – Data Converters Oversampling ADC Professor Y. Chiu EECT 7327 Fall 2012 Oversampling ADC
Mar 29, 2015
– 1 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
Oversampling ADC
Nyquist-Rate ADC
– 2 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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
Anti-Aliasing Filter (AAF)
– 3 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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
Oversampling ADC
– 4 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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
Relaxed AAF Requirement
– 5 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
• Nyquist-rate converters
• Oversampling converters
|X(jf)|
f2fs 3fsfm=fs/2 fs/2
|X(jf)|
ffm
|X(jf)|
f2fs 3fs
Sub-sampling Band-pass oversampling
fs/2
|X(jf)|
f
OSR = fs/2fm
Oversampling ADC
– 6 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
• Predictive type– Delta modulation
• Noise-shaping type– Sigma-delta modulation– Multi-level (quantization) sigma-delta modulation– Multi-stage (cascaded) sigma-delta modulation (MASH)
Oversampling
– 7 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
PSD
f-fs/2
A/Dbn
b1
... M
Decimation filter
bn
b1
...
fs
A/D
Mfs
fs/2
Δ2/12PSD
f-Mfs/2 Mfs/2
Δ2/12
-fs/2 fs/2
Nyquist Oversampled
Sample rate Noise power Power
Nyquist fs Δ2/12 P
Oversampled M*fs (Δ2/12)/M M*P
OSR = M
Noise Shaping
– 8 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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 2H(f)
1 2
e e
― H(f)
fMfs/2fs/2
1― H-1(f)
Sigma-Delta (ΣΔ) Modulator
– 9 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
A/D∫Vi
D/A
Do
Δ
• Noise shaping obtained with an integrator
• Output subtracted from input to avoid integrator saturation
First-orderΣΔ modulator
z-1Σ
A/D∫Vi
D/A
Do
Δ
Linearized Discrete-Time Model
– 10 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
H(z)X(z) Y(z)
E(z)
1
1
z1
zH(z)
zEz1zXzzY
zEzH1
1zX
zH1
zHzY
zEzYzXzHzY
11
DelayzzX
zYSTF
:Function Transfer Signal
1
HPz1zE
zYNTF
:Function Transfer Noise
1
Caveat: E(z) may be correlated with X(z) – not “white”!
First-Order Noise Shaping
– 11 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
PSD
ffs/2fm
3
π
f
2f
12
Δ
dff
f2π
2f
1
12
Δ
dff
fπ2sin
2f
1
12
Δ
dfNTF2f
1
12
ΔN
23
s
m2
2f
0 ss
2
2f
0 ss
2
2f
0 s
22e
m
m
m
2 2
2e 3
In - band quantization noise :
Δ πN
12 3M
Doubling OSR (M) increases SQNR by 9 dB (1.5 bit/oct)
2
sf
fπ2sin
SC Implementation
– 12 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
• SC integrator
• 1-bit ADC → simple, ZX detector
• 1-bit feedback DAC → simple, inherently linear
CI
Ф2Ф1
Ф1Ф2
Vi
Do
+VR 1-b DAC-VR
CS
Second-Order ΣΔ Modulator
– 13 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
INT1 INT2
A/D
D/A
Doz-1Vi
2
z-1
2zSTF
:Function Transfer Signal
21z1NTF
:Function Transfer Noise
5
422e 5M
π
12
ΔN
:noise onquantizati band-In
Doubling OSR (M) increases SQNR by 15 dB (2.5 bit/oct)
2nd-Order ΣΔ Modulator (1-Bit Quantizer)
– 14 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
• Simple, stable, highly-linear
• Insensitive to component mismatch
• Less correlation b/t E(z) and X(z)
1-bitA/D
1-bitD/A
Doz-1Vi z-1 βα
2
zE1αz
1zzX
1αz
αzY
2
2
2
jy
z-plane
0 1x
(2) (2)
1β
1α
Generalization (Lth-Order Noise Shaping)
– 15 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
12L
2L22e M12L
π
12
ΔN
:noise onquantizati band-In
zEz1zXzzY
:function transfer ModulatorL1n
• Doubling OSR (M) increases SQNR by (6L+3) dB, or (L+0.5) bit
• Potential instability for 3rd- and higher-order single-loop ΣΔ modulators
2L 1
2L
2L 1 M
π
ΣΔ vs. Nyquist ADC’s
– 16 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
ΣΔ ADC output (1-bit) Nyquist ADC output
• ΣΔ 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 ΣΔ converters → use SNR, SNDR, SFDR instead
+1
-1
Tones
– 17 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
...
...
Vi = 0
Vi = 0.001
T
2000*T
• The output spectrum corresponding to Vi = 0 results in a tone at fs/2, and will get eliminated by the decimation filter
• The 2nd output not only has a tone at fs/2, but also a low-frequency tone – fs/2000 – that cannot be eliminated by the decimation filter
Tones
– 18 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
• Origin – the quantization error spectrum of the low-resolution ADC (1-bit in the previous example) in a ΣΔ modulator is NOT white, but correlated with the input signal, especially for idle (DC) inputs.
(R. Gray, “Spectral analysis of sigma-delta quantization noise”)
• Approaches to “whitening” the error spectrum– Dither – high-frequency noise added in the loop to randomize the
quantization error. Drawback is that large dither consumes the input dynamic range.
– Multi-level quantization. Needs linear multi-level DAC.– High-order single-loop ΣΔ modulator. Potentially unstable.– Cascaded (MASH) ΣΔ modulator. Sensitive to mismatch.
Cascaded (MASH) ΣΔ Modulator
– 19 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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 ΣΔ modulator as well
2-1 Cascaded Modulator
– 20 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
INT1 INT2
z-1X(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
2-1 Cascaded Modulator
– 21 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
11
2121 zzEz1zXzzY
zEz1zXz
zEz1zEz1zzEz1zzXz
zYzYzY
2
313
2
311
2111
2113
21
212
11
12 z1zEz1zEzzY
• E1(z) completely cancelled assuming perfect matching between the modulator NTF (analog domain) and the DNTF (digital domain)
• A 3rd-order noise shaping on E2(z) obtained
• No potential instability problem
Integrator Noise
– 22 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 2012
2
311
213
212
11 Ez1Ez1δNz1Nz1NXY
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 dominatesthe overall noise
Performance!
References
– 23 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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.
References
– 24 –
Data Converters Oversampling ADCProfessor Y. Chiu
EECT 7327Fall 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.