EE247 Midterm Exam Statistics

EE247 Lecture 22 Pipelined ADCs (continued) Effect gain stage, sub-dac non-idealities on overall ADC performance Digital calibration (continued) Correction for inter-stage gain nonlinearity Implementation Practical circuits Stage scaling Combining the bits Stage implementation Circuits Noise budgeting How many bits per stage? Algorithmic ADCs utilizing pipeline structure Advanced background calibration techniques Time Interleaved Converters VCO Based ADCs (guest speaker: Rikky Muller) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 1 EE247 Midterm Exam Statistics # of Students 5 4 3 Average: 16 Standard Dev.: 2 Max.: 19 Min.: 12 2 1 0 11 12 13 14 15 16 17 18 19 20 Grade out of 20 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 2

Pipeline ADC Block Diagram ADC DAC - + V in Stage 1 B 1 Bits V res1 Stage 2 B 2 Bits V res2 Stage k B k Bits MSB......LSB Align and Combine Data Digital Output (B 1 +B 2 +..B k ) Bits Idea: Cascade several low resolution stages to obtain high overall resolution (e.g. 10bit ADC can be built with series of 10 ADCs each 1-bit only!) Each stage performs coarse A/D conversion and computes its quantization error, or "residue EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 3 Summary So Far Pipelined A/D Converters V ref V ref V ref V ref T/H+Gain V in B 1 bits 2 B1eff B 2B2 2 2 bits 2 B2eff B 3 bits 2 B3eff ADC Cascade of low resolution stages By adding inter-stage gain= 2 Beff No need to scale down Vref for stages down the pipe Reduced accuracy requirement for stages coming after stage 1 Addition of Track & Hold function to interstage-gain Stages can operate concurrently Throughput increased to as high as one sample per clock cycle Latency function of number of stages & conversion-per-stage Correction for circuit non-idealities Built-in redundancy compensate for sub-adc inaccuracies such as comparator offset (interstage gain: G Bneff, B neff < B n ) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 4

Pipelined ADC Error Correction/Calibration Summary V OS a 3 V 3 V IN1 + - + 2 2 + V RES1 ADC DAC ε gain +ε ADC +ε DAC D 1 Error ε ADC, V os ε gain ε DAC Inter-stage amplifier non-linearity Redundancy either same stage or next stage Digital adjustment Correction/Calibration Either sufficient component matching or digital calibration? EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 5 Inter-stage Gain Nonlinearity Invert gain stage non-linear polynomial Express error as function of V RES1 Push error into digital domain through backend Ref: B. Murmann and B. E. Boser, "A 12-b, 75MS/s Pipelined ADC using Open-Loop Residue Amplification," ISSCC Dig. Techn. Papers, pp. 328-329, 2003 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 6

a 3 V X 3 Inter-stage Gain Nonlinearity V X 2 3 ε gain V RES1 + Backend p 2 D B a = 3 3 3 (2 + ε gain ) (...) D B,corr + - ε(d B, p 2 ) ε(db,p2) = p2db 3p2 DB + 12p2 DB +... Pre-computed & stored in table look-up form p 2 continuously estimated & updated (account for temp. & other variations) Ref: B. Murmann and B. E. Boser, "A 12-b, 75MS/s Pipelined ADC using Open-Loop Residue Amplification," ISSCC Dig. Techn. Papers, pp. 328-329, 2003 3 2 5 3 7 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 7 Inter-stage Gain Nonlinearity Compensation Proof of Concept Evaluation Prototype Re-used 14-bit ADC in 0.35μm from Analog Devices [Kelly, ISSCC 2001] Modified only 1 st stage with 3-b eff open-loop amplifier built with simple diff-pair + resistive load instead of the conventional feedback around high-gain amp Conventional 9-b eff backend, 2-bit redundancy in 1 st stage Real-time post-processor off-chip (FPGA) Ref: B. Murmann and B. E. Boser, "A 12-b, 75MS/s Pipelined ADC using Open-Loop Residue Amplification," ISSCC Dig. Techn. Papers, pp. 328-329, 2003 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 8

Measurement Results 12-bit ADC w Extra 2-bits for Calibration (a) without calibration INL [LSB] 10 0-10 RNG=0 RNG=1 0 1000 2000 3000 4000 Code (b) with calibration 10 1 0.5 (b) with calibration INL [LSB] 0-10 0 1000 2000 3000 4000 Code 0-0.5-1 0 1000 2000 3000 4000 C d EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 9 Combining the Bits Example: Three 2-bit stages, no redundancy B 1 B 1eff B 2 B 2eff B 3 V in Stage 1 Stage 2 Stage 3 6 2 D 2 2 1 D 2 D 3 D out + + 1/2 2 1/2 2 1 1 Dout = D1 + D 1 2 + B eff B1eff B2eff 2 2 2 1 1 Dout = D1 + D2 + D3 4 16 D3 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 10

Combining the Bits D 1 XX D 2 XX D 3 XX ------------ D out DDDDDD Only bit shifts No arithmetic circuits needed B 1 B 1eff B 2 B 2eff B 3 V in Stage 1 Stage 2 Stage 3 D 1 D 2 D 3 MSB LSB D out[5:0] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 11 Combining the Bits Including Redundancy Example: Three 2-bit stages, incorporating 1- bit redundancy in stages 1 and 2 B 1 =3 B 1eff B 2 =3 B 2eff B 3 V in Stage 1 Stage 2 Stage 3 8 Wires??? 6 Wires D out[5:0] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 12

Combining the Bits 1 1 Dout = D1 + D 1 2 + D B eff B1eff B2eff 3 2 2 2 1 1 Dout = D1 + D2 + D3 4 16 B 1 =3 B 1eff B 2 =3 B 2eff B 3 V in Stage 1 Stage 2 Stage 3 D 1 D 2 D 3 Bits overlap Need adders D 1 XXX D 2 XXX D 3 XX ------------ D out DDDDDD HADD HADD FADD HADD HADD D out[5:0] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 13 Combining the Bits Example B 1 =3 B 1eff B 2 =3 B 2eff B 3 V in Stage 1 Stage 2 Stage 3 D 1 D 2 D 3 D 1 001 D 2 111 D 3 10 ------------ D out 011000 HADD HADD FADD HADD HADD D out[5:0] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 14

Pipelined ADC Stage Implementation CLK φ 1 φ 1 φ 2 φ 1... φ 2 acquire convert convert acquire...... V in Stage 1 Stage 2 Stage n V in T/H + - G V res ADC DAC Each stage needs T/H hold function Track phase: Acquire input/residue from previous stage Hold phase: sub-adc decision, compute residue EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 15 Stage Implementation V in T/H T/H +- G V res T/H ADC DAC Usually no dedicated T/H amplifier in each stage (Except first stage in some cases why?) T/H implicitely contained in stage building blocks EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 16

Stage Implementation V in T/H + - G V res T/H ADC DAC MDAC DAC-subtract-gain function can be lumped into a single switched capacitor circuit "MDAC" EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 17 1.5-Bit Stage Implementation Example D1,D0 V DAC Ref: A. Abo, "Design for Reliability of Low- voltage, Switched-capacitor Circuits," UCB PhD Thesis, 1999 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 18

1.5-Bit Stage Implementation Acquisition Cycle Φ 1 D1,D0 V DAC Vc f =Vc s =V i Q Cs =C s xv i Q Cf =C f xv i Ref: A. Abo, "Design for Reliability of Low- voltage, Switched-capacitor Circuits," UCB PhD Thesis, 1999 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 19 Φ 2 1.5-Bit Stage Implementation Conversion Cycle D1,D0 V DAC Ref: A. Abo, "Design for Reliability of Low- voltage, Switched-capacitor Circuits," UCB PhD Thesis, 1999 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 20

1.5 Bit Stage Implementation Example Note: Interstage gain set by C ratios Accuracy better than 0.1% Up to 10bit level no need for gain calibration Ref: A. Abo, "Design for Reliability of Low- voltage, Switched-capacitor Circuits," UCB PhD Thesis, 1999 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 21 1.5-Bit Stage Implementation Timing of Stages V DAC V DAC Conversion Acquisition EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 22

Pipelined ADC Stage Power Dissipation & Noise Typically pipeline ADC noise dominated by inter- stage gain blocks Sub-ADC comparator noise translates into comparator threshold uncertainty and is compensated for by redundancy V in Stage 1 Stage 2 Stage 3 V in V n1 G1 G2 G3 V n2 V n3 2 2 in 2 V n2 V V n3 noise = V n1 + + +... 2 2 2 G1 G1 G2 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 23 Pipelined ADC Stage Scaling Example: Pipeline using 1-bit eff stages V in V n1 G1 G2 G3 V n2 V n3 C 1 /2 C 2 /2 C 3 /2 V in C 1 Gm C 2 Gm C 3 Gm Total input referred noise power: 1 1 1 Ntot kt + + +... C 2 2 2 1 G1 C2 G1 G2 C3 1 1 1 Ntot kt + + +... C1 4C2 16C3 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 24

Pipelined ADC Stage Scaling C 1 /2 C 2 /2 C 3 /2 V in C 1 Gm C 2 Gm C 3 Gm N tot 1 1 1 kt + + +... C1 4C2 16C3 If all caps made the same size, backend stages contribute very little noise Wasteful power-wise, because: Power ~ Gm Speed ~ Gm/C Fixed speed Gm/C filxed Power ~ C EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 25 Pipelined ADC Stage Scaling C 1 /2 C 2 /2 C 3 /2 V in C 1 Gm C 2 Gm C 3 Gm N tot 1 1 1 kt + + +... C1 4C2 16C3 How about scaling caps down by G 2 2 =4x per stage? Same amount of noise from every stage All stages contribute significant noise To keep overall noise the same noise/stage must be reduced Power ~ Gm ~ C goes up! EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 26

Stage Scaling Example: 2-bit eff /stage Optimum capacitior scaling lies approximately midway between these two extremes Ref: D. W. Cline, P.R. Gray "A power optimized 13-b 5MSamples/s pipelined analog-to-digital converter in 1.2um CMOS," JSSC 3/1996 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 27 Pipeline ADC Stage Scaling Power minimum is "shallow Near optimum solution in practice: Scale capacitors by stage gain E.g. for effective stage resolution of 1bit (Gain): C/2 C/4 C/8 V in C Gm C/2 Gm C/4 Gm EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 28

Stage Scaling Example Note: Resolution per stage: 2bits G=4 Ref: D. W. Cline, P.R Gray "A power optimized 13-b 5 MSamples/s pipelined analog-to-digital converter in 1.2um CMOS," JSSC 3/1996 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 29 How Many Bits Per Stage? Many possible architectures E.g. B 1eff =3, B 2eff =1,... vs. B 1eff =1, B 2eff =1, B 3eff =1,... Complex optimization problem, fortunately optimum tends to be shallow... Qualitative answer: Maximum speed for given technology Use small resolution-per-stage (large feedback factor) Maximum power efficiency for fixed, "low" speed Try higher resolution stages Can help alleviate matching & noise requirements in stages following the 1 st stage Ref: Singer VLSI 96, Yang, JSSC 12/01 (14bit ADC w/o calibration) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 30

14 & 12-Bit State-of-the-Art Implementations Reference Bits Architecture SNR/SFDR Speed Power Yang (JSSC 12/2001) 0.35μ/3V 14 3-1-1-1-1-1-1-1-1-3 ~73dB/88dB 75MS/s 340mW Loloee (ESSIRC 2002) 0.18μ/3V 12 1-1-1-1-1-1-1-1-1-1-2 ~66dB/75dB 80MS/s 260mW EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 31 10 & 8-Bit State-of-the-Art Implementations Reference Bits Architecture SNR/SFDR Speed Power Yoshioko et al (ISSCC 2005) 0.18μ/1.8V 10 1.5bit/stage ~55dB/66dB 125MS/s 40mW Kim et al (ISSCC 2005) 0.18μ/1.8V 8 2.8-2.8-4 ~48dB/56dB 200MS/s 30mW EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 32

Algorithmic ADC Digital Output start of conversion Shift Register & Correction Logic Residue V IN T/H sub-adc (1.6 Bit) DAC 2 B Essentially same as pipeline, but a single stage is reused for all partial conversions For overall B overall bits need B overall /B stage clock cycles per conversion Small area, slow Trades conversion time for area EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 33 Least Mean Square Adaptive Digital Background Calibration of Pipelined Analog-to-Digital Converters Slow, but accurate ADC operates in parallel with pipelined (main) ADC Slow ADC samples input signal at a lower sampling rate (f s /n) Difference between corresponding samples for two ADCs (e) used to correct fast ADC digital output via an adaptive digital filter (ADF) based on minimizing the Least-Mean-Squared error Ref: Y. Chiu, et al, Least Mean Square Adaptive Digital Background Calibration of Pipelined Analog-to-Digital Converters, IEEE TRANS. CAS, VOL. 51, NO. 1, JANUARY 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 34

Example: "A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration" Pipelined ADC operates at 20Ms/s @ has 1.5bit/stage Slow ADC Algorithmic type operating at 20Ms/32=625ks/s Digital correction accounts for bit redundancy Digital error estimator minimizes the mean-squared-error Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-Msample/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 35 Algorithmic ADC Used for Calibration of Pipelined ADC (continued from previous page) Uses replica of pipelined ADC stage Requires extra SHA in front to hold residue Undergoes a calibration cycle periodically prior to being used to calibrate pipelined ADC Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 36

12-bit 20-MS/s Pipelined ADC with Digital Background Calibration Sampling capacitors scaled (1B eff /stage): Input SHA: 6pF Pipelined ADC: 2pF,0.9,0.4,0.2, 0.1,0.1 Algorithmic ADC: 0.2pF Chip area: 13.2mm 2 Does not include digital calibration circuitry estimated ~1.7mm 2 Area of Algorithmic ADC <20% Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 37 Measurement Results 12-bit 20-MS/s Pipelined ADC with Digital Background Calibration Without Calibration INL <4.2LSB With Calibration INL <0.5LSB Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 38

Measurement Results 12-bit 20-MS/s Pipelined ADC with Digital Background Calibration Nyquist rate Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 39 Measurement Results 12-bit 20-MS/s Pipelined ADC with Digital Background Calibration Does not include digital calibration circuitry estimated ~1.7mm 2 Alg. ADC SNDR dominated by noise Ref: X. Wang, P. J. Hurst, S. H. Lewis, " A 12-bit 20-MS/s pipelined analog-to-digital converter with nested digital background calibration, IEEE JSSC, vol. 39, pp. 1799-1808, Nov. 2004 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 40

Time Interleaved Converters Example: 4 ADCs operating in parallel at sampling frequency f s Each ADC converts on one of the 4 possible clock phases Overall sampling frequency= 4f s Note T/H has to operate at 4f s! Extremely fast: Typically, limited by speed of T/H V IN 4f s T/H f s ADC f s +T s /4 ADC f s +2T s /4 ADC Output Combiner Digital Output Accuracy limited by mismatch among individual ADCs (timing, offset, gain, ) f s +3T s /4 ADC EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 41 Input signal sampled Time Interleaved Converters Timing T s =1/f s 1/4T s 1/4T s 1/4T s 1/4T s Note: Effective sampling rate 4xf s EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 42

VCO-Based Analog to Digital Conversion Rikky Muller November 17, 2009 EE247 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 43 Picking an ADC At 6 bits you are not limited by thermal noise Pick an architecture which minimizes other errors Can trade off noise efficiency [S. Chen, R. Brodersen, A 6-bit 600-MS/s 5.3-mW Asynchronous ADC in 0.13-µm CMOS: IEEE J. of Solid-State Circuits, Vol. 41, No. 12, December 2006.] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 44

Quantizes tuning voltage Performs an integration Two methods Method 1: count cycles VCO ADC Basics [M. Straayer, Noise Shaping Techniques for Analog and Time to Digital Converters Using Voltage Controlled Oscillator, Ph.D. Thesis, MIT, 6/ 08.] [M. Straayer, M. Perrott, A 12-Bit, 10-MHz Bandwidth, Continuous-Time ADC with a 5-bit, 950MS/s VCO-Based Quantizer IEEE J. of Solid- State Circuits, Vol. 43, No. 4, April 2008.] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 45 Method 2: Sample Phases VCO: High frequency Low frequency [Straayer JSSC 08] Voltage Frequency Frequency Phase Phase Frequency EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 46

Noise Shaping Behavioral Model [Straayer JSSC 08] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 47 Why Use a VCO ADC? Fully digital K vco linearity - Simple - Best for lower resolutions - Scalable - Amplify or integrate - Low-energy Very small area First-order noise shaping - Mismatch whitening and shaping Oversampling - Efficient due to noise shaping EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 48

Segmentation Project: 6-bit,1GS/s, 90nm process Number of digital blocks grows as 2 B (B=bits in ring) Clock frequency grows as 2 (N-B)/1.5 (N=total resolution) Lowest-power solution: Minimize resolution in the ring Maximize oversampling: limited by process [R. Muller, C. Thakkar] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 49 Tuning the VCO ADC: INL as voltage deviation TDC: INL as frequency deviation Multiple ways to tune K vco ex. Linearization resistance, current control, direct V dd modulation or virtual rail Frequency SFDR = 20log 2N INL Control Voltage [Wismar 07] [Alon 05] [Straayer 08] [Xiao 04] [E. Alon, V. Stojanovic, M. Horowitz, Circuits and Techniques for High-Resolution Measurement of On-Chip Power Supply Noise IEEE J. of Solid-State Circuits, Vol. 40, No. 4, April 2005.] [J. Xiao, A. Peterchev, J. Zhang, S. Sanders, A 4-uA Quiescent-Current Dual-Mode Digitally Controlled Buck Converter IC for Cellular Phone Applications IEEE J. of Solid-State Circuits, Vol. 39, No. 12, December 2004.] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 50

Linearization 33dB SFDR [R. Muller, C. Thakkar] V DS = V T δ ln 1 I D I O 63dB SFDR f 2I DS CV DD e VGS / nvt V DD [U. Wismar, D. Wisland, P. Andreani, Linearity of bulk-controlled inverter ring VCO in weak and strong inversion Analog integr Circ Sig Process, 2007, 50:59-67.] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page [R. 51Muller] Energy Efficient Flash ADC 6Bit, 1GS/s Zero Static Power 59fJ/step Potential to be lowest FOM to date for 1GS/s Just a start: other considerations Phase noise, mismatch, range, calibration, input/output interface, putting it in feedback loop (stability), fully differential implementation, etc. This work FOM = Power 2 ENOB f s [A. Ismail, M. Elmastry, A 6-Bit 1.6GS/s Low-Power Wideband Flash ADC Converter in 0.13-µm CMOS Technology IEEE J. of Solid- State Circuits, Vol. 43, No. 9, September 2008.] EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 52

Oversampled ADCs EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 53 Analog-to-Digital Converters Two categories: Nyquist rate ADCs f sig max ~ 0.5xf sampling Maximum achievable signal bandwidth higher compared to oversampled type Resolution limited to max. ~14bits Oversampled ADCs f sig max << 0.5xf sampling Maximum possible signal bandwidth lower compared to nyquist Maximum achievable resolution high (18 to 20bits!) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 54

The Case for Oversampling Nyquist sampling: Signal f s B Freq narrow transition AA-Filter f s >2B +δ Sampler Nyquist ADC DSP Oversampling: Signal f s >> f N?? B Freq wide transition AA-Filter f s = Mf N Sampler Oversampled ADC DSP Nyquist rate f N ~2B Oversampling rate M = f s /f N >> 1 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 55 Nyquist v.s. Oversampled Converters Antialiasing X(f) Input Signal f B frequency Nyquist Sampling f B f s f S ~2f B Anti-aliasing Filter 2f s Oversampling frequency f B f S >> 2f B f s frequency EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 56

Oversampling Benefits No stringent requirements imposed on analog building blocks Takes advantage of the availability of low cost, low power digital filtering Relaxed transition band requirements for analog anti-aliasing filters Reduced baseband quantization noise power Allows trading speed for resolution EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 57 ADC Converters Baseband Noise For a quantizer with quantization step size Δ and sampling rate f s : Quantization noise power distributed uniformly across Nyquist bandwidth ( f s /2) N e (f) N B -f B f s /2 -f s /2 f B Power spectral density: 2 2 e Δ 1 N(f) e = = fs 12 fs Noise is distributed over the Nyquist band f s /2 to f s /2 EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 58

Oversampled Converters Baseband Noise fb fb 2 Δ 1 SB = N e( f )df = df fb fb 12 fs N e (f) 2 Δ 2fB = 12 f N B s where for fb = f s/2 2 Δ SB0 = -f s /2 -f B f B f s /2 12 2fB SB0 SB = SB0 = f s M fs where M = = oversampling ratio 2f B EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 59 B Oversampled Converters Baseband Noise 2fB SB0 SB = SB0 = f s M fs where M = = oversampling ratio 2f 2X increase in M 3dB reduction in S B ½ bit increase in resolution/octave oversampling To further increase the improvement in resolution: Embed quantizer in a feedback loop Noise shaping (sigma delta modulation) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 60

Pulse-Count Modulation V in (kt) /8 Nyquist ADC 010 010 0 t/ts 1 2 2/8 V in (kt) /8 Oversampled ADC, M = 8 0 1 2 t/ts Mean of pulse-count signal approximates analog input! EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 61 Magnitude Pulse-Count Spectrum 2/8 Digital filter f s /4 f Signal: low frequencies, f < B << f s Quantization error: high frequency, B f s / 2 Separate with low-pass filter! EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 62

Oversampled ADC Predictive Coding v IN + _ ADC D OUT 1-bit Digital Filter N-bit Predictor Quantize the difference signal rather than the signal itself Smaller input to ADC Buy dynamic range Only works if combined with oversampling 1-Bit digital output Digital filter computes average N-bit output EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 63 Oversampled ADC Signal B Freq wide transition Analog AA-Filter f s = Mf N Sampler E.g. Pulse-Count Modulator Modulator 1-Bit Digital f s1 = M f N Decimator narrow transition Digital AA-Filter N-Bit Digital f s2 = f N + δ DSP Decimator: Digital (low-pass) filter Removes quantization error for f > B Provides anti-alias filtering for DSP Narrow transition band, high-order 1-Bit input, N-Bit output (essentially computes average ) EECS 247- Lecture 22 Pipelined ADCs and More 2009 Page 64