1
Oversampling ADC
2
Nyquist-Rate ADC

• 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

3
Anti-Aliasing Filter (AAF)

• 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

4
Oversampling ADC

• 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

5
Relaxed AAF Requirement

• Nyquist-rate converters
• Oversampling converters

OSR fs/2fm
Sub-sampling
Band-pass oversampling
6
Oversampling ADC

• Predictive type
• Delta modulation
• Noise-shaping type
• Sigma-delta modulation
• Multi-level (quantization) sigma-delta modulation
• Multi-stage (cascaded) sigma-delta modulation
  (MASH)

7
Oversampling
Nyquist
Oversampled
? OSR M
8
Noise Shaping
Push noise out of signal band
?
Large gain _at_ LF, low gain _at_ HF ? Integrator?
9
Sigma-Delta (S?) Modulator
First-order S? modulator

• Noise shaping obtained with an integrator
• Output subtracted from input to avoid integrator
  saturation

10
Linearized Discrete-Time Model
Caveat E(z) may be correlated with X(z) not
white!
11
First-Order Noise Shaping

• Doubling OSR (M) increases SQNR by 9 dB (1.5
  bit/oct)

12
SC Implementation

• SC integrator
• 1-bit ADC ? simple, ZX detector
• 1-bit feedback DAC ? simple, inherently linear

13
Second-Order S? Modulator

• Doubling OSR (M) increases SQNR by 15 dB (2.5
  bit/oct)

14
2nd-Order S? Modulator (1-Bit Quantizer)

• Simple, stable, highly-linear
• Insensitive to component mismatch
• Less correlation b/t E(z) and X(z)

15
Generalization (Lth-Order Noise Shaping)

• Doubling OSR (M) increases SQNR by (6L3) dB, or
  (L0.5) bit
• Potential instability for 3rd- and higher-order
  single-loop S? modulators

16
S? vs. Nyquist ADCs
S? ADC output (1-bit)
Nyquist ADC output

• S? 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 S? converters ? use SNR, SNDR,
  SFDR instead

17
Tones

• 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

18
Tones

• Origin the quantization error spectrum of the
  low-resolution ADC (1-bit in the previous
  example) in a S? 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 S? modulator. Potentially
  unstable.
• Cascaded (MASH) S? modulator. Sensitive to
  mismatch.

19
Cascaded (MASH) S? Modulator

• Idea to further quantize E(z) and later subtract
  out in digital domain
• The 2nd quantizer can be a S? modulator as well

20
2-1 Cascaded Modulator
DNTF
21
2-1 Cascaded Modulator

• 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

22
Integrator Noise
INT1 dominates the overall noise Performance!
Delay ignored
23
References

• B. E. Boser and B. A. Wooley, JSSC, pp.
  1298-1308, issue 6, 1988.
• B. H. Leung et al., JSSC, pp. 1351-1357, issue 6,
  1988.
• T. C. Leslie and B. Singh, ISCAS, 1990, pp.
  372-375.
• B. P. Brandt and B. A. Wooley, JSSC, pp.
  1746-1756, issue 12, 1991.
• F. Chen and B. H. Leung, JSSC, pp. 453-460, issue
  4, 1995.
• R. T. Baird and T. S. Fiez, TCAS2, pp. 753-762,
  issue 12, 1995.
• T. L. Brooks et al., JSSC, pp. 1896-1906, issue
  12, 1997.
• A. K. Ong and B. A. Wooley, JSSC, pp. 1920-1934,
  issue 12, 1997.
• S. A. Jantzi, K. W. Martin, and A.S. Sedra, JSSC,
  pp. 1935-1950, issue 12, 1997.
• A. Yasuda, H. Tanimoto, and T. Iida, JSSC, pp.
  1879-1886, issue 12, 1998.
• A. R. Feldman, B. E. Boser, and P. R. Gray, JSSC,
  pp. 1462-1469, issue 10, 1998.
• H. Tao and J. M. Khoury, JSSC, pp. 1741-1752,
  issue 12, 1999.
• E. J. van der Zwan et al., JSSC, pp. 1810-1819,
  issue 12, 2000.
• I. Fujimori et al., JSSC, pp. 1820-1828, issue
  12, 2000.
• Y. Geerts, M.S.J. Steyaert, W. Sansen, JSSC, pp.
  1829-1840, issue 12, 2000.

24
References

• T. Burger and Q. Huang, JSSC, pp. 1868-1878,
  issue 12, 2001.
• K. Vleugels, S. Rabii, and B. A. Wooley, JSSC,
  pp. 1887-1899, issue 12, 2001.
• S. K. Gupta and V. Fong, JSSC, pp. 1653-1661,
  issue 12, 2002.
• R. Schreier et al., JSSC, pp. 1636-1644, issue
  12, 2002.
• J. Silva et al., CICC, 2002, pp. 183-190.
• Y.-I. Park et al., CICC, 2003, pp. 115-118.
• L. J. Breems et al., JSSC, pp. 2152-2160, issue
  12, 2004.
• R. Jiang and T. S. Fiez, JSSC, pp. 63-74, issue
  12, 2004.
• P. Balmelli and Q. Huang, JSSC, pp. 2161-2169,
  issue 12, 2004.
• K. Y. Nam et al., CICC, 2004, pp. 515-518.
• X. Wang et al., CICC, 2004, pp. 523-526.
• A. Bosi et al., ISSCC, 2005, pp. 174-175.
• N. Yaghini and D. Johns, ISSCC, 2005, pp.
  502-503.
• G. Mitteregger et al., JSSC, pp. 2641-2649, issue
  12, 2006.
• R. Schreier et al., JSSC, pp. 2632-2640, issue
  12, 2006.