Cascaded Noise-Shaping Modulators for Oversampled Data Conversion Bruce A. Wooley Stanford University B. Wooley, Stanford, 2004 1
Outline Oversampling modulators for A/D conversion Cascaded noise-shaping architectures Embedded quantization Distributed noise shaping zeros Bandpass cascaded modulator Digital cascaded modulators with semi-digital reconstruction for D/A conversion B. Wooley, Stanford, 2004 2
Analog-to-Digital Conversion 00001011 11000011 01001000 Digital Processor Filtering Sampling Quantization Processing Quantization Model: e Q [n] p(e Q ) Σ 1/ - /2 /2 B. Wooley, Stanford, 2004 3
Noise Shaping N B S Q (f) -f S /2 -f B f B f S /2 Quantizer resolution increased by 3 db per octave of OVERSAMPLING N B S Q (f) Quantizer resolution increased through NOISE SHAPING -f S /2 -f B f B f S /2 B. Wooley, Stanford, 2004 4
Oversampling Modulators Embed quantizer in a feedback loop to achieve larger improvement in resolution with increasing M Feedback used for PREDICTION ( Modulation) or NOISE SHAPING (Σ Modulation) Noise shaping modulators are more robust and easier to implement than predictive modulators B. Wooley, Stanford, 2004 5
Sigma-Delta (Delta-Sigma) Modulation E Q (z) Integrator X(z) Σ z -1 1 z -1 A/D Y(z) D/A Yz ( ) = z 1 Xz ( ) ( 1 z 1 )E Q ( z) B. Wooley, Stanford, 2004 6
Σ Modulator Response (w/ 1-bit Quantization) 0.6 Modulator Input, Quantizer Output 0.4 0.2 0-0.2-0.4-0.6 0 50 100 150 200 250 Time (t/t) B. Wooley, Stanford, 2004 7
Noise Shaping Noise Shaping Function Ideal Digital Lowpass Filter First-Order Noise Shaping f B f N f S /2 Frequency B. Wooley, Stanford, 2004 8
Noise Differencing Modulators (of order L) Yz ( ) = z 1 Xz ( ) ( 1 z 1 ) L E Q ( z) Noise Shaping LP Filter L=3 L=2 L=1 f B f N f S /2 Frequency B. Wooley, Stanford, 2004 9
Sigma-Delta Modulator Dynamic Range 140 120 Dynamic Range (db) 100 80 60 40 L=3 L=2 L=1 20 0 4 8 16 32 64 128 256 512 Oversampling Ratio B. Wooley, Stanford, 2004 10
Higher-Order Noise Shaping Modulators The order of the noise shaping can be increased using either or Single quantizer modulators Multi-loop noise differencing Single-loop with multi-order filter Cascaded (multistage) modulators B. Wooley, Stanford, 2004 11
Single-Quantizer Σ Modulation E(z) X(z) A(z) Y(z) F(z) Yz ( ) = H X ( z)xz ( ) H E ( z)ez ( ) where and H X ( z) Az ( ) Az ( ) = ---------------------------------, H 1 A( z)fz ( ) E ( z) H X ( z) = ---------------, Fz ( ) H E ( z) = = 1 H E ( z) ------------------------ H X ( z) 1 --------------------------------- 1 A( z)fz ( ) B. Wooley, Stanford, 2004 12
Noise Differencing Modulators Class of modulators where: H X ( z) = z 1 and H E ( z) = ( 1 z 1 ) L L = 1: H E ( z) = ( 1 z 1 ) Az ( ) L = 2: H E ( z) = ( 1 z 1 ) 2 Az ( ) = Fz ( ) = 1 = z 1 ----------------- 1 z 1 z 1 ------------------------- ( 1 z 1 ) 2 Fz ( ) = 2 z 1 ( 1 ) B. Wooley, Stanford, 2004 13
Second-Order Implementation X Σ Σ z 1 A(z) Σ z 1 E Σ Y F(z) Σ Σ z 1 E X Σ Σ z 1 Σ Σ z 1 Σ Y Unity Transfer Function z 1 Σ Σ z 1 B. Wooley, Stanford, 2004 14
B. Wooley, Stanford, 2004 15 X Y E Σ Σ Σ z 1 Σ z 1 Σ 2 X Y E Σ Σ Σ z 1 Σ 2 1 Σ z 1 2 Second-Order Σ Modulator
Second-Order Noise Differencing Σ Modulator (with 1-bit quantization) Can scale only w/ 1-bit quantizer x(nt) Σ 1 2 INTEGRATOR 1 Σ DELAY Σ 1 2 INTEGRATOR 2 Σ DELAY QUANTIZER 1-bit A/D y(nt) q(nt) D/A Key building block for cascaded modulators B. Wooley, Stanford, 2004 16
Cascaded Σ Modulators Quantizer error quantized by subsequent stage and then filtered and subtracted digitally Cancellation of lower-order noise shaping terms depends on matching of analog and digital paths No potential instability B. Wooley, Stanford, 2004 17
Cascaded Oversampling ADC Analog In x Σ e y Delay Σ Digital Out ADC Digital Difference Matches noise shaping of quantization error in first stage B. Wooley, Stanford, 2004 18
Maximum Dynamic Range Improvement 80.0 Dynamic Range Improvement (db) 60.0 40.0 20.0 0.0 0.01 Simulation Closed form equation Independent of OSR 0.1 1 10 Coefficient Mismatch (%) B. Wooley, Stanford, 2004 19
Third-Order (2-1) Cascaded Modulator x 2 nd order Σ y 1 Error Cancellation y e 1 1 st order Σ y 2 Y 1 =z 2 X (1 z 1 ) 2 E 1 Y 2 =z 1 E 1 (1 z 1 ) E 2 Y=z 1 Y 1 (1 z 1 ) 2 Y 2 =z 3 X (1 z 1 ) 3 E 2 B. Wooley, Stanford, 2004 20
Matching Error in 2-1 Cascade 10 Loss in Dynamic Range (db) 8 6 4 2 0 Calculated Simulated -2-10 -5 0 5 10 Matching Error (%) B. Wooley, Stanford, 2004 21
2-1 Spectrum with Mismatch 0 Spectral Power (db) -50-100 -150-200 0 5 10 15 20 25 Frequency (khz) B. Wooley, Stanford, 2004 22
Advantages of 2-1 Cascade Low sensitivity to precision of analog path Suppression of spurious noise tones resulting from correlation of quantization noise with input Considerable design flexibility No potential instability B. Wooley, Stanford, 2004 23
Digitizing MHz-Bandwidth Signals Oversampling modulators dominate precision A/D conversion at modest signal bandwidths e.g. digital audio exploit large oversampling ratios Challenge is to digitize signals where the oversampling ratio is constrained by technology (MHz bandwidths) Possible approaches based on cascade architectures include multibit quantization in second stage merged quantization distributed noise shaping zeros multilevel quantization with digital linearization B. Wooley, Stanford, 2004 24
Lowpass Cascade Architecture X(z) 0.4 z 1 z 1 0.5 1 z 1 1 z 1 Y 1 (z) Y 2 (z) ADC Y 1 (z) Y 2 (z) Digital Error Cancellation Y(z) B. Wooley, Stanford, 2004 25
Embedded Quantization * X(z) 0.4 z -1 z -1 0.5 1 z -1 1 z -1 1-bit DAC Y(z) ADC X(z) 0.4 z -1 z -1 0.5 1 z -1 m bit ADC Y(z) 1 z -1 1-bit DAC * A. Tabatabaei, 99 VLSI Ckt Symp B. Wooley, Stanford, 2004 26
Model of Merged Quantizer Modulator Y 2 (z) X(z) 0.4 z 1 z 1 0.5 1 z 1 1 z 1 Y 1 (z) B. Wooley, Stanford, 2004 27
Implementation of Embedded ADC m-bit DAC z -1 1 z -1 m-bit ADC Noise Shaped Error e z -1 B. Wooley, Stanford, 2004 28
Lowpass Modulator with Embedded ADC * 4-bit DAC z -1 1 1 - z -1 0.4 0.5 1 z -1 z -1 1 - z -1 4-bit ADC 1-bit DAC Delay unaltered Stability maintained by 4-bit quantization B. Wooley, Stanford, 2004 29
2-2 Cascaded Modulator Analog input Quantization noise Lowpass Σ Modulator Lowpass Σ Modulator Digital output Quantization Error Cancellation Input 2.5 Σ Σ 1-bit output Σ Quantization noise B. Wooley, Stanford, 2004 30
Noise Transfer Function for 2-2 Lowpass Cascade 0 Signal Band NTF (db) 40 OSR = 16 80 f s /32 0 f s /32 NTF for a two-stage lowpass cascade (2-2): NTF = N 1 N 2 = (N LP ) 2 NTF > 0 db for OSR < 8 B. Wooley, Stanford, 2004 31
Distribute Zeros Across the Signal Band 0 Signal Band NTF (db) 40 80 f s /32 0 f s /32 Cascade lowpass and bandpass stages: Reduces inband noise NTF = N 1 N 2 = N LP N BP B. Wooley, Stanford, 2004 32
Lowpass-Bandpass Cascaded Modulator * X(n) NTF (db) 0 20 40 Lowpass Σ Modulator Y 1 (n) NTF (db) 0 40 80 f s /32 0 f s /32 fs/32 0 f s /32 Q(n) Bandpass Σ Modulator Y 2 (n) Digital Error Cancellation Y(n) = 0 NTF (db) 40 80 f s/32 0 f s/32 * A. Tabatabaei, JSSC 12/00 B. Wooley, Stanford, 2004 33
Bandpass Second Stage ω s cos ------- nt 2M s ω s cos ------- nt 2M s Lowpass Σ Modulator Lowpass Filter ω s sin ------- nt 2M s ω s sin ------- nt 2M s Lowpass Σ Modulator Lowpass Filter 0 Analog Digital -40-80 -fs/32 0 f s /32 B. Wooley, Stanford, 2004 34
2-2-2/2 Lowpass Modulator Analog input 2nd-order Σ 1-bit Output Quantization noise 2nd-order Σ ω s sin ------- nt 2M s ω s cos ------- nt 2M s 2nd-order Σ 2nd-order Σ B. Wooley, Stanford, 2004 35
Bandpass Stage Mixer Φ1 f LO = f s /32 CK8 CK8 Φ2 Φ2 C8 Vcm Φ1 Φsin CK1 Φ2 C1 Vin Φsin CK1 Φ2 Φ2 Vcm Vout Φsin CK1 Φ2 Φ2 Φsin CK1 Φ2 C1 Vcm Φ1 Φ1 CK8 Φ2 CK1 CK2 CK3 CK8 Φ2 C8 Φ1 CK8 Φsin B. Wooley, Stanford, 2004 36
f s /4 Two-Path Bandpass Modulator IF signal Φ 1 Φ 2 1, 1,1, 1,... 1, 1,1, 1,... 2nd-order Σ 2nd-order Σ 2nd-order Σ 2nd-order Σ ω s sin ------- nt 2M s ω s cos ------- nt 2M s ω s sin ------- nt 2M s 2nd-order Σ 2nd-order Σ 2nd-order Σ 2nd-order Σ B. Wooley, Stanford, 2004 37
Chip Micrograph Third Stage (I) Third Stage (Q) First Stage Second Stage Mixers Clock generator Second Stage Mixers First Stage Third Stage (I) Third Stage (Q) B. Wooley, Stanford, 2004 38
Measured SNR and SNDR 80.0 Signal-to-NoiseDistortion (db) 60.0 40.0 20.0 SNR SNDR 0.0-80.0-60.0-40.0-20.0 0.0 Input Signal Level (db) B. Wooley, Stanford, 2004 39
Measured Output Spectrum First Two Stages All Stages Output Spectrum (db) Output Spectrum (db) 0-50 -100 0-50 -100 40 db Quantization Noise Mirror Input Signal -2.8 db @ 16.2 MHz -1-0.5 0 0.5 1 Frequency (MHz) B. Wooley, Stanford, 2004 40
Performance Summary Sampling rate Passband Oversampling ratio Dynamic range Max SNDR Power supply Power dissipation Technology Area 64 MS/s 2 MHz centered at 16 MHz 16 75 db 70 db 2.5 V 140 mw 0.24-µm, 5-metal CMOS 2 mm 1.7 mm B. Wooley, Stanford, 2004 41
Bandpass Oversampling D/A Conversion * Consider the use of bandpass oversampling D/A conversion in wireless communications transmitters Move IF into the digital domain to eliminate dc offset I & Q mismatch Merge D/A conversion, noise shaping, reconstruction and IF mixing Explore the use of cascaded digital noise shaping for D/A conversion * D. Barkin, 03 VLSI Ckt Symp B. Wooley, Stanford, 2004 42
Traditional Transmitter Architecture cos ωt I M FIR/ROM DAC LPF Out Q M FIR/ROM DAC LPF sin ωt Digital Analog B. Wooley, Stanford, 2004 43
Cascaded Bandpass Oversampling DAC cos(ωt) = [ 1, 0, -1, 0,... ] I M Noise Shaping DAC Filtering Analog IF Output Q M Noise Shaping Digital Analog sin(ωt) = [ 0, 1, 0, -1,... ] Mix to IF (at f s /4) following cascaded noise shapers Error cancellation performed at IF B. Wooley, Stanford, 2004 44
Lowpass Cascaded Noise Shaping Digital Input 2 nd Order Σ Modulator 1 Signal Stage 1 Error 3 rd Order Σ Modulator Noise Estimate 4 (1 - z -1 ) 2 2 nd order differentiator matches noise shaping in first stage B. Wooley, Stanford, 2004 45
DAC Architecture I Cascaded Σ Modulator 1 4 (1 - z -1 ) 2-1,1 φ 1 φ 1 DAC Filtering Q Cascaded Σ Modulator 1 4 (1 - z -1 ) 2 1,-1 φ 2 φ 2 f s /2 f s I & Q modulators operate at f s /2, saving power B. Wooley, Stanford, 2004 46
Discrete Time Continuous Time Interface Signal 1-1,1 Semi-Digital Filter Noise Estimate -1,1 Digital (1 - z -1 ) Filter 2 4 11 6 Control 1 2 64 Digital Analog Semi-digital filtering for reconstruction of signal Digital filter reduces out-of-band quantization noise Digital filter transfer function matches that of semi-digital filter B. Wooley, Stanford, 2004 47
Semi-Digital Filter * Digital Input 1 z -1 z -1 z -1 a 1 a 2 a N Mismatch among current sources alters the transfer function but doesn t introduce nonlinearity Area limits number of taps and precision of coefficients Analog Output Good for 1-bit signal path but not multi-bit noise estimation path * D.Su, et al., JSSC, 1993 B. Wooley, Stanford, 2004 48
Bandpass Data Weighted Averaging 1 Semi-Digital Filter -1,1-1,1 Digital (1 - z -1 ) 2 4 Filter 11 6 BP DWA Pointer Calc Control 1 2 64 f s /2 Notch f s /4 Notch I & Q pointer calculations are independent 7 5 3 8 2 I 7 5 3 8 2 Q 6 4 2 6 3 Time --> * T. Shui, et al., ISCAS, 1998 B. Wooley, Stanford, 2004 49
Bandpass DAC Die Photo Noise Shapers Digital Filters Decoder Current Source Array Semi-digital Bias B. Wooley, Stanford, 2004 50
DAC Output Spectrum Power Spectral Density (db) 0-50 2-3 (4 bit) Digital Noise Shaper Output Measured DAC Output 46 db -100 0 20 40 60 80 100 Frequency (MHz) B. Wooley, Stanford, 2004 51
SNDR and SFDR 100 SFDR & SNDR (db) 80 60 40 20 0 Measured SFDR Measured SNDR -20-100 - 80-60 - 40-20 0 Signal Power (db) B. Wooley, Stanford, 2004 52
DAC Performance Technology Supply: Modulators and Filters Other Center Frequency Bandwidth Peak SNDR Dynamic Range Peak Out-of-Band Noise Suppression 1-p, 5-m 0.25-µm CMOS 1.5 V 2.5 V 50 MHz 6.25MHz 76 db 85 db 46 db Mirror for -6dB input 90 db down Active Area 2.1 mm 2 Power: Modulators and Filters Thermometer Decoders Current Source Array 30 mw 70 mw 115 mw B. Wooley, Stanford, 2004 53
Summary Cascades of first- and second-order noise-shaping modulator stages can be used for A/D and D/A conversion lowpass and bandpass data conversion dynamic range enhancement at low oversampling ratios If properly designed, advantages include no potential instability decorrelation of quantization noise and input low sensitivity to analog precision B. Wooley, Stanford, 2004 54
What s ahead? Challenges in data conversion interface design Impact of technology scaling on analog; ITRS presents problems w.r.t. leakage, output resistance and gain Demand for increased performance driven by increased use of digital signal processing Still room for innovation in architecture and circuits Some ongoing research Very low voltage (V DD 1.2V) oversampling A/D and D/A conversion Oversampling D/A conversion for DSL Continuous-time oversampling modulators for broadband applications B. Wooley, Stanford, 2004 55