– 1 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Oversampling ADC

Nyquist-Rate ADC – 2 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 The “black box” version of the quantization process Digitizes the input signal up to the Nyquist frequency (f s /2) Minimum sampling frequency (f s ) for a given input bandwidth Each sample is digitized to the maximum resolution of the converter

Anti-Aliasing Filter (AAF) – 3 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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

Oversampling ADC – 4 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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

Relaxed AAF Requirement – 5 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Nyquist-rate converters Oversampling converters Sub-sampling Band-pass oversampling OSR = f s /2f m

Oversampling ADC – 6 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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 ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 NyquistOversampled Sample rateNoise powerPower Nyquistfsfs Δ 2 /12P OversampledM*f s (Δ 2 /12)/MM*P  OSR = M

Noise Shaping – 8 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Push noise out of signal band Large LF, low HF → Integrator? 

Sigma-Delta (ΣΔ) Modulator – 9 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Noise shaping obtained with an integrator Output subtracted from input to avoid integrator saturation First-order ΣΔ modulator

Linearized Discrete-Time Model – 10 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Caveat: E(z) may be correlated with X(z) – not “white”!

First-Order Noise Shaping – 11 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Doubling OSR (M) increases SQNR by 9 dB (1.5 bit/oct)

SC Implementation – 12 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 SC integrator 1-bit ADC → simple, ZX detector 1-bit feedback DAC → simple, inherently linear

Second-Order ΣΔ Modulator – 13 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Doubling OSR (M) increases SQNR by 15 dB (2.5 bit/oct)

2nd-Order ΣΔ Modulator (1-Bit Quantizer) – 14 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Simple, stable, highly-linear Insensitive to component mismatch Less correlation b/t E(z) and X(z)

Generalization (L th -Order Noise Shaping) – 15 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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

ΣΔ vs. Nyquist ADC’s – 16 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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

Tones – 17 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 The output spectrum corresponding to V i = 0 results in a tone at f s /2, and will get eliminated by the decimation filter The 2nd output not only has a tone at f s /2, but also a low-frequency tone – f s /2000 – that cannot be eliminated by the decimation filter

Tones – 18 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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 ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 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 ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 DNTF

2-1 Cascaded Modulator – 21 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 E 1 (z) completely cancelled assuming perfect matching between the modulator NTF (analog domain) and the DNTF (digital domain) A 3rd-order noise shaping on E 2 (z) obtained No potential instability problem

Integrator Noise – 22 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall 2014 Delay ignored INT1 dominates the overall noise Performance!

References – 23 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall B. E. Boser and B. A. Wooley, JSSC, pp , issue 6, B. H. Leung et al., JSSC, pp , issue 6, T. C. Leslie and B. Singh, ISCAS, 1990, pp B. P. Brandt and B. A. Wooley, JSSC, pp , issue 12, F. Chen and B. H. Leung, JSSC, pp , issue 4, R. T. Baird and T. S. Fiez, TCAS2, pp , issue 12, T. L. Brooks et al., JSSC, pp , issue 12, A. K. Ong and B. A. Wooley, JSSC, pp , issue 12, S. A. Jantzi, K. W. Martin, and A.S. Sedra, JSSC, pp , issue 12, A. Yasuda, H. Tanimoto, and T. Iida, JSSC, pp , issue 12, A. R. Feldman, B. E. Boser, and P. R. Gray, JSSC, pp , issue 10, H. Tao and J. M. Khoury, JSSC, pp , issue 12, E. J. van der Zwan et al., JSSC, pp , issue 12, I. Fujimori et al., JSSC, pp , issue 12, Y. Geerts, M.S.J. Steyaert, W. Sansen, JSSC, pp , issue 12, 2000.

References – 24 – Data ConvertersOversampling ADCProfessor Y. Chiu EECT 7327Fall T. Burger and Q. Huang, JSSC, pp , issue 12, K. Vleugels, S. Rabii, and B. A. Wooley, JSSC, pp , issue 12, S. K. Gupta and V. Fong, JSSC, pp , issue 12, R. Schreier et al., JSSC, pp , issue 12, J. Silva et al., CICC, 2002, pp Y.-I. Park et al., CICC, 2003, pp L. J. Breems et al., JSSC, pp , issue 12, R. Jiang and T. S. Fiez, JSSC, pp , issue 12, P. Balmelli and Q. Huang, JSSC, pp , issue 12, K. Y. Nam et al., CICC, 2004, pp X. Wang et al., CICC, 2004, pp A. Bosi et al., ISSCC, 2005, pp N. Yaghini and D. Johns, ISSCC, 2005, pp G. Mitteregger et al., JSSC, pp , issue 12, R. Schreier et al., JSSC, pp , issue 12, 2006.