Sigma-Delta ADC Tutorial and Latest Development in 90 nm CMOS for SoC Jinseok Koh Wireless Analog Technology Center Texas Instruments Inc. Dallas, TX
Outline Fundamentals for ADCs Over-sampling and Noise shaping Sigma-Delta ADC Double Sampling Technique 2nd Order Single Amplifier Sigma-Delta ADC Implementation in 90nm CMOS for SoC Conclusions 1
Modeling of Quantizer Quantizer is non-linear building block Need modeling for simplifying the analysis White additive noise assumptions It is not fulfilled in many applications, However It makes analysis easy and makes possible the use of z-tansformation 2
Quantization Noise Quantity of in-band noise depends on the over-sampling ratio SNR = 10log(σ x2 ) -10log(σ n2 ) +3.01r(dB), where σ x 2 and σ n 2 are input signal power and in-band noise power respectively, and r is defined by over-sampling ratio, f s /2f b =2 r Pervez M. Aziz, An overview of sigma-delta converters, IEEE Signal processing Magazine, pp 61-84, Jan. 1996 3
Nyquist Rate vs. Oversampled Digital Filter Anti-Aliasing Filter Any unwanted signals Fs/2 to Fs are folded into band of 0 to Fs/2 Signal Band Fs/2 Fs 4
Over-sampling and Noise Shaping Noise Every doubling of sampling frequency leads approximately 3 db enhancement in SNR Band of Interest f s 2f s 4f s Noise Noise shaping pushes quantization noise to higher frequency resulting in suppressing Q. noise in the band of interest f s 2f s 4f s 5
How to Shape the noise? Y(z) = H(z) 1 X(z) + E(z) 1+ H(z)G(z) 1+ H(z)G(z) STF NTF If H(z) = z -1 /1-z -1 and G(z)=1, NTF and STF will be: NTF = Y(z) E(z) = 1 Z 1 STF = Y(z) X(z) = Z 1 6
Example, 2 nd order Sigma-Delta ADC 7
Summary Sigma-delta ADC provide trade-offs between: Power consumption, Over-sampling ratio (OSR) System performance (SNR) High OSR implies: Lower number of quantization levels Lower modulator order, but More demanding settling requirements for the analog building blocks 8
Objectives For a given performance requirement, power consumption and area are optimized by: Increasing sampling frequency Double sampling technique Increasing modulator order Single Amplifier topology Higher number of levels in Quantizer 5-level quantizer with ILA 9
Advantages: Double sampling Efficient technique to double the OSR Doesn t need faster op-amp settling Provides improvement of SQNR by 6n+3 db (n=order) Disadvantage: Mismatch between capacitors creates noise folding in P 1 P 2 D1 P 2 P 1 u Noise Folding Alternating Gain Effect P 2 D2 P 1 P 1 P 2 Inherent Capacitor Mismatch 10
Noise Folding In Double Sampling Alternating gain effect Noise at F s /2 is folded into Signal bandwidth Noise folding (Input sampling circuit) Noise folding (DAC in feedback path) ΔC gain : C D2 gain :1 gain : ΔC C D2 gain :1 Noise at F s /2 is suppressed by - Anti-aliasing filter - Pre-filtering No filtering on quantization noise 11
Conventional Double Sampling DAC V refp P 1 P 2 C D1 P 1 SB SA C U On P1 phase, Stored charge in C D1 : C D1 (V refp -V refm ) P 1 P 2 C D1 P 1 SA SB C U On P2 phase, Stored charge in C D2 : C D2 (V refp -V refm ) P 2 C D2 SB SA Requires two sets of switched capacitor DACs P 1 P 2 V refm P 2 P 1 C D2 P 2 SA SB Mismatch on stored charge causes alternating gain effect 12
Proposed SC DAC element for double sampling Advantages of this approach vs. conventional approach: Only one pair of capacitors needed No alternating-gain effect No additional circuitry needed for matching purposes 13
Operation of Proposed SC DAC element On P 1 Phase: On P 2 Phase: On phase P 1 the charge transferred to Integrating Capacitor is: Q u = C d (V refp -V refm ) Q u is equal to the charge stored into C d This charge will be used during next integration phase 14
Conventional 2 nd Order Sigma-Delta ADC b1 b2 Each Summing Node requires an Amplifier Conventional Sigma-delta ADC: Needs an amplifier per summing node Poles and zeros are chosen by a i and b i,where i=1,2 15
Single Amplifier 2nd Order Sigma-Delta ADC Summing node 1 z STF = 1 2 1 1 p z q z + z G(z) 1 p z 1 q z 2 NTF = 1 p z 1 q z 2 + z 1 G(z) 16
Q-path Operation H(z): Forward path Filter P4 p z -1 z -1 p-path q-path U P5 P4 P3 q2 P5 P4 q3 P5 q P3 q1 P3 P4 P5 P3 Rotating to do sampling, holding and integrating functions The first SC circuit samples the output v o (n) while the second one holds the previous output v o (n-1) and the third one transfers v o (n-2) to the integrating capacitor, C U 17
Full Filter implementation 18
Amplifier design (SR, GBW) SNR[dB] 70 65 60 55 50 45 40 SNR vs. Amplifier DC gain 35 45 55 65 75 Gain [db] SNR [db] 69 68 67 66 65 64 63 62 61 60 59 58 SNR vs. GBW (SR=100V/usec) 0.2 0.4 0.6 0.8 1 1.2 GBW [Hz] x10 7 GBW and SR were simulated in Matlab behavioral model Amplifier was designed to have: - DC Gain>60dB, SR>100V/µsec and GBW > 50MHz Single amplifier topology has a benefit since settling requirement is lower than conventional one 19
Amplifier implementation Load Capacitance 1.6 pf GBW 100 MHz Input referred Noise* 70 uvrms Slew Rate 200 V/usec Current Consumption 700 ua 20
Measured Power Spectral Density Power Spectral Density [db] 1.94MHz WCDMA BAND Frequency [Hz] Input signal: -6 dbfs sine at 448 khz 3 rd harmonic shows up at -91 dbv Noise floor shows no noticeable noise folding 21
SNDR vs. Input power 70 SNDR vs. Input 60 50 SNDR [db] 40 30 20 10 0-70 -60-50 -40-30 -20-10 0 Input Amplitude [dbfs] 63dB peak SNDR happens at -3dBFS input sinusoidal 22
Die Photography for dual channel ADCs I-channel Q-channel Implemented in 90nm 5 metal digital CMOS process 23
Performance Summary Technology Signal Bandwidth Clock Frequency Sampling Frequency Peak SNDR Dynamic Range Input Range Voltage Supply Power Consumption Core Area 90 nm Digital CMOS 1.94 MHz 38.4 MHz 76.8 MHz 63 db 66 db 1.5 V pp (differential) 1.2 V 1.2 mw per ADC 0.2 mm 2 per ADC 24
Conclusions Second order 5 level Single Amplifier Sigma-Delta ADC with double sampling technique was realized in 90 nm CMOS. By using double sampling technique, OSR is doubled with no increase of power consumption and silicon area. Single-capacitor double-sampling DAC solved alternatinggain error effect. 2 nd order modulator is implemented using a Single-amplifier architecture. Higher order modulator is feasible. Low power consumption: 1.2mW for WCDMA, measured with a 1.2V power supply. 66dB dynamic range was achieved in 1.94MHz bandwidth. 25