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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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

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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

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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.