Micromechanical resonator based bandpass sigma delta modulator

MICROMECHANICAL RESONATOR BASED BANDPASS SIGMA- DELTA MODULATOR WANG XIAOFENG (B of Eng., Northwestern Polytechnical University) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 Abstract In modern RF receivers, high-speed and high-resolution ADCs are needed for IF or RF digitization Bandpass Σ∆ modulator is seen as a potential candidate to fulfill this requirement However, the speed of discrete-time bandpass Σ∆ modulator implemented with switched-capacitor circuit is limited by the settling time of the opamps, while the continuous-time bandpass modulator can operate at much high sampling frequency, but suffers from the degradation of dynamic range due to the low-Q LC or GmC resonators This work is to investigate the possibility of employing micromechanical resonators in bandpass Σ∆ modulator design The design of a newly proposed 2nd-order bandpass Σ∆ modulator based on micromechanical resonator is presented The micromechanical resonator is used to replace its electronic counterpart for its high Q value The design is based on pulse-invariant transform and multi-feedback technique A compensation circuit is proposed to cancel the anti-resonance in the micromechanical resonator in order to obtain the desired transfer function The proposed modulator is implemented in a 0.6-µm CMOS process with an external clamped-clamped beam micromechanical resonator Due to the lack of qualified micromechanical resonator, the testing with the only micromechanical resonator did not give expected results The test was subsequently carried out with crystal resonators and successfully demonstrated a 2nd-order ii bandpass Σ∆ modulator, which proves that the proposed idea is feasible The test results have shown that when sampled at 4MHz the peak SNR in 200-kHz signal bandwidth is measured to be 22dB while the Matlab simulated value is 25dB The modulator is also functional at the sampling frequency of 32MHz iii Acknowledgements I would like to express my sincere appreciation to my supervisor Professor Xu Yong Ping for his guidance and support of my research in the past two years I would also like to thank my co-supervisor Professor Tan Leng Seow for admitting me into NUS which makes my research possible Many thanks go to my co-supervisor Dr Wang Zhe of the Institute of Microelectronics (IME) for providing me the micromechanical resonators and the opportunity to access the equipment at IME I would like to thank Mr Sun Wai Hoong He generously shared his S-function programs with me A numerous discussions with him are also very valuable I would also like to thank Mr Saxon Liw of IME for his generous assistance and support in testing the resonator He also helped me solve many practical problems I would like to express my gratitude to Miss Qian Xinbo, Mr Su Zhenjiang, and Ms Xu Lianchun for their help on circuit design and using Cadence Xinbo also helped me a lot in using test equipment I would like to thank Miss Yu Yajun for providing me her past designs as reference Thanks also go to Mr Luo Zhenying, Mr Liang Yunfeng, and Mr Zhou Xiangdong for their advices on circuit design, and Mr Francis Boey for his support on equipment and electronic components Very special thanks go to all my friends at the Laboratory of Signal Processing and VLSI Design for making my years in NUS a wonderful experience I would like to thank the National University of Singapore for providing me with the financial support iv Finally, I would like to thank my parents and my grandparents for their consistent support v Table of Contents ABSTRACT II ACKNOWLEDGEMENTS IV TABLE OF CONTENTS VI LIST OF FIGURES VIII LIST OF TABLES XI CHAPTER 1.1 1.2 INTRODUCTION .1 MOTIVATION .1 THESIS OUTLINE CHAPTER SIGMA-DELTA MODULATION 2.1 NYQUIST-RATE A/D CONVERTER 2.1.1 Anti-aliasing 2.1.2 Sampling .7 2.1.3 Quantization 2.2 OVERSAMPLING A/D CONVERTER 10 2.3 SIGMA-DELTA MODULATION .11 2.3.1 The Noise-shaping Technique .12 2.3.2 High-order Sigma-Delta Modulation 17 2.3.3 Multi-bit Quantization 19 2.4 CONTINUOUS-TIME BANDPASS SIGMA-DELTA MODULATOR .19 2.4.1 Discrete-time and Continuous-time Sigma-Delta Modulators 19 2.4.2 Design Methodology of Continuous-time Bandpass Sigma-Delta Modulator 20 2.4.3 Review of Continuous-time Bandpass Sigma-Delta Modulators 22 2.4.4 Micromechanical Resonators 24 CHAPTER 3.1 3.2 3.3 3.4 3.5 MICROMECHANICAL RESONATORS 27 MEMS TECHNOLOGY 27 STRUCTURES OF MICROMECHANICAL RESONATORS 28 RESONATOR MODEL 32 SENSING CIRCUITS 35 MICROMECHANICAL RESONATOR VERSUS LC AND GMC RESONATORS 36 CHAPTER BANDPASS SIGMA-DELTA MODULATOR BASED ON MICROMECHANICAL RESONATOR 37 4.1 4.2 4.3 DESIGN METHODOLOGY 37 ANTI-RESONANCE AND ITS CANCELLATION 40 MODULATOR ARCHITECTURE 43 vi 4.4 4.5 PERFORMANCE OF THE PROPOSED SIGMA-DELTA MODULATOR 44 CIRCUIT IMPLEMENTATION 47 CHAPTER 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 CIRCUIT LEVEL DESIGN .49 FUNCTION BLOCKS 49 OPERATIONAL AMPLIFIER 50 COMPARATOR 53 ONE-BIT DACS 55 VOLTAGE LEVEL SHIFTER 56 RESONATOR INTERFACE CIRCUITS .58 PERFORMANCE OF THE BANDPASS SIGMA-DELTA MODULATOR 60 LAYOUT DESIGN AND POST-LAYOUT SIMULATION 62 CHAPTER TESTING 65 6.1 TESTING SETUP 65 6.2 TESTING RESULT .67 6.2.1 Modulator with Micromechanical Resonator 67 6.2.2 Modulator with Crystal Resonators .67 6.2.3 Signal-to-Noise Ratio 72 6.3 DISCUSSION .73 CHAPTER 7.1 7.2 CONCLUSIONS AND FUTURE WORK 75 CONCLUSION .75 FUTURE WORK 76 REFERENCES .77 APPENDIX A A.1 A.2 A.3 MATLAB PROGRAMS 82 PROGRAM FOR PULSE-INVARIANT TRANSFORM 82 PROGRAM FOR POWER SPECTRUM ESTIMATION 84 PROGRAM FOR SNR CALCULATION 86 APPENDIX B SIMULINK MODELS 88 B.1 B.2 SIMULINK MODEL FOR RETURN-TO-ZERO DAC 88 SIMULINK MODEL FOR HALF-RETURN-TO-ZERO DAC .90 APPENDIX C CHIP LAYOUT .92 APPENDIX D CHIP PHOTOGRAPH 93 vii List of Figures Figure Superheterodyne receiver with dual IF and baseband ADC Figure Direct-conversion receiver Figure Direct-IF conversion receiver Figure The operation of Nyquist-rate A/D converter .6 Figure A/D conversion process .8 Figure Linear model for quantization Figure Σ∆ modulator 11 Figure Linear model of Σ∆ modulator 12 Figure Lowpass Σ∆ modulator 13 Figure 10 Gain of NTF and STF of the lowpass Σ∆ modulator 13 Figure 11 Simulated output spectrum 14 Figure 12 Structure of baseband Σ∆ A/D converter 15 Figure 13 Bandpass Σ∆ modulator 15 Figure 14 Magnitude responses of NTF and STF of a 2nd-order bandpass Σ∆ modulator 16 Figure 15 Output power spectrum of a 2nd-order bandpass Σ∆ modulator 16 Figure 16 2nd-order single-stage lowpass Σ∆ modulator 18 Figure 17 2nd-order lowpass MASH Σ∆ modulator 19 Figure 18 Equivalence between continuous and discrete-time modulators 21 Figure 19 Forward loops of (a) continuous-time and (b) discrete-time Σ∆ modulators 21 Figure 20 Noise shapes of the resonators of different Q 25 Figure 21 SNR degradation due to Q .25 Figure 22 Cantilever-beam resonator .29 Figure 23 Comb-transduced resonator 30 Figure 24 Clamped-clamped beam resonator .30 Figure 25 Free-free beam resonator .31 Figure 26 Disk resonator .31 Figure 27 Equivalent circuit of the micromechanical resonator 32 Figure 28 Equivalent circuit with resistive load 32 Figure 29 Simulated frequency response of the resonator (With 10 times amplification) 34 Figure 30 Measured frequency response of the micromechanical resonator 34 Figure 31 Resistive sensing circuit 35 Figure 32 Trans-impedance sensing circuit 35 Figure 33 Equivalence between discrete-time and continuous-time modulators 38 Figure 34 Broken loops of (a) continuous-time and (b) discrete-time Σ∆ modulators 38 Figure 35 Continuous-time modulator with two feedbacks 39 viii Figure 36 DAC waveforms 39 Figure 37 Linear model of Σ∆ modulator 40 Figure 38 Anti-resonance cancellation scheme 41 Figure 39 Frequency response of the resonator with anti-resonance cancellation 42 Figure 40 Frequency response of the micromechanical resonator with anti-resonance cancellation .42 Figure 41 Frequency response of the micromechanical resonator with imperfect anti-resonance cancellation .42 Figure 42 Proposed micromechanical resonator based bandpass Σ∆ modulator 44 Figure 43 Simulink model of the continuous-time modulator 45 Figure 44 Output power spectrum (Matlab simulation) 45 Figure 45 In-band power spectrum (OSR = 80, Matlab simulation) .46 Figure 46 SNR against Input magnitude (Matlab simulation) 47 Figure 47 Circuit structure of the modulator 47 Figure 48 Modulator circuit structure 50 Figure 49 OTA schematic 50 Figure 50 Basing circuit schematic 51 Figure 51 Frequency response of the OTA .52 Figure 52 Schematic of the differential comparator .53 Figure 53 Transient response of the differential comparator .54 Figure 54 Schematic of the DAC .55 Figure 55 Transient simulation results of the return-to-zero DAC 56 Figure 56 Schematic of the differential voltage level shifter .57 Figure 57 VLS transient response 57 Figure 58 Amplification circuit 58 Figure 59 Cancellation circuit 59 Figure 60 Frequency response of the micromechanical resonator .59 Figure 61 Frequency response of the resonator with anti-resonance cancellation 59 Figure 62 Output Spectrum with high insertion loss 60 Figure 63 Output power spectrum at fs = 32 MHz .61 Figure 64 In-band output spectrum at fs = 32MHz 61 Figure 65 SNR against input magnitude at fs = 32MHz .61 Figure 66 Layout floor plan .62 Figure 67 Output power spectrum at fs = 32 MHz from post-layout simulation 64 Figure 68 In-band output power spectrum at fs = 32 MHz from post-layout simulation 64 Figure 69 Test setup 65 Figure 70 Differential clock generation circuit 66 Figure 71 Off-chip bias circuit 66 Figure 72 Reference voltage generation circuit 67 Figure 73 Frequency response of the crystal resonator with resonant frequency of 1MHz 68 Figure 74 Frequency response of the crystal resonator with resonant frequency of 8MHz 68 ix Figure 75 Frequency response of the 1-MHz crystal resonator with anti-resonance cancellation .69 Figure 76 Output power spectrum of the bandpass Σ∆ modulator with 1-MHz crystal resonator 70 Figure 77 In-band spectrum of the modulator with 1-MHz crystal resonator 70 Figure 78 Output spectrum of the modulator with 8-MHz crystal resonator 71 Figure 79 Output power spectrum (1-MHz crystal resonator with anti-resonance cancellation) 71 Figure 80 SNR vs input signal level (1-MHz crystal resonator, OSR = 10) 72 x Solid-State Circuits, vol 31, pp 1981-1986, Dec 1996 [Hay86] T Hayashi, Y Inabe, K Uchimura, and T Kimura “A multi-stage delta-sigma modulator without double integration loop” Int Solid-State Circuits Conf Technical Digest, pp 182-183, 1986 [Hsu00] I Hsu, and H C Luong “A 70-MHz continuous-time CMOS band-pass Σ∆ modulator for GSM receivers” Int Symp On Circuits and Systems 2000, vol 3, pp 750-753, May, 2000 [Inos62] H Inose, Y Yasuda, and J Murakami “A telemetering system by code modulation –∆-Σ modulation” IRE Trans Space Electron Telemetry, vol SET-8, pp 204-209, Sep 1962 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resonators” IEEE J of MEMS, vol 9, no 3, September 2000 [Widr56] B Widrow “A study of rough amplitude quantization by means of Nyquist sampling theory” IRE Trans Circuit Theory, vol CT-3, pp 266-276, December 1956 81 Appendix A Matlab Programs A.1 Program for Pulse-invariant Transform % -% Program: Ct2Dt.m % Author: Xiaofeng Wang % Date: 02/25/2002 % Last Update: 12/29/2002 % Descritption: To design the equivalent continuous-time modulator % Only for 2nd order bandpass Have to revise the % calculation part for other modulators % % - Clear working space and window clear all; clc; % - Clear working space and window end - % - Macro definition % Normalized transfer function of the continuous modulator num = [1 0]; den = [1 (pi/2)^2]; % - Macro definition end - % - System creation SysC = tf(num,den); % Continuous system in the form of transfer function [ac,bc,cc,dc] = tf2ss(num,den); % Continuous system in the form of state space SysCSs = ss(ac,bc,cc,dc); % Create a state space obeject based on the continuous system SysDSs = c2d(SysCSs,1); % Discrete state space form % - System creation end - 82 % Return-to-Zero -SysDRSs = SysDSs; % Syshss is a temp variable % DAC output pulse TB = 0; % DAC beginning point TE = 0.5; % DAC ending point SysDRSs.b = inv(SysCSs.a)*(expm(SysCSs.a*(1-TB)) - expm(SysCSs.a*(1-TE)))*SysCSs.b; fprintf('\n R-return-to-zero: '); TfRz = tf(SysDRSs) % - Return-to-Zero end % - Half-Return-to-Zero SysDHSs = SysDSs; % syshss is a temp variable % DAC output pulse TB = 0.5; % DAC beginning point TE = 1; % DAC ending point SysDHSs.b = inv(SysCSs.a)*(expm(SysCSs.a*(1-TB)) - expm(SysCSs.a*(1-TE)))*SysCSs.b; fprintf('\n Half-return-to-zero: '); TfHrz = tf(SysDHSs) % - Half-Return-to-Zero end - % - Coefficients calculation % The following section is used to calculate the feedback coefficients CoB = [TfRz.num{1}(2:3); TfHrz.num{1}(2:3)] CoC = [0 -1]; % CoC is the desired numerator % The DAC coefficients in the sequence of the DACs CoA = CoC*inv(CoB) % - Coefficients calculation end - % (The end) % - 83 A.2 Program for Power Spectrum Estimation % % Program: OutAnalyse.m % Author: Xiaofeng Wang % Date: 12/26/2001 % Last Updated: 12/29/2002 % Description: Analyze the spectrum of the bit stream % The program must work together with Simulink simulation % - % Notice: N = 2^m, m is an integer % fsignal = Fs/N*p, p is an integer, to alleviate leakage % - Initialization % Clear figure window clf; % Receive the data from the work space % insig is the input signal sequence inp=insig'; % outsig is the output signal sequence of the modulator outp=outsig'; % N is the length of the sequence N=length(outp); % - Initialization end - % - Input and output display % Comparison between the input analog signal and the output digital signal figure(1); clf; t = 0:100; % Demonstrate 100 points stairs(t, inp(t+1)); hold on; stairs(t,outp(t+1)); % Plot label xlabel('sample number'); ylabel('input, output'); title('Modulator Input & Output'); 84 % - Input and output display end - % - Spectrum analysis figure(2); clf; Fs = 1; w = hanning(N); % Hanning windowing [Pxx,f] = psd(outp,N,Fs,w,N/2); % [magnitude,frequency] = % (signal,sample number,sampling frequency,window,overlap number) Pyy = Pxx*norm(w)^2/sum(w)^2; % De-normalization Pn = 10*log10(2*Pyy); % Sum of positive and negative frequency % Plot plot(f/Fs,Pn); xlabel('Frequency (f/fs)'); ylabel('Output Spectral Density (dB)'); title('Power Sepctrum Estimation'); grid; % - Spectrum analysis end - % (The end) % - 85 A.3 Program for SNR Calculation % % Program: BpSnrCalculate.m % Author: Xiaofeng Wang % Date: 12/30/2001 % Last Updated: 12/29/2002 % Description: Calculate the SNR of a bandpass Sigma-Delta modulator % - % - Macro definition % Receive the data from the work space % outsig is the output signal sequence of the modulator outp=outsig'; N = length(outp); % N is the number of the samples; it should be power of OSR = 80; % OSR is the oversampling ratio BW = N/2/OSR; % BW is the interest bandwidth Fs = 1; % Fs is the sampling frequency It should be after normalization BWbb = round(0.25*N-BW/2); % BW beginning bin BWeb = round(0.25*N+BW/2); % BW ending bin % - Macro definition end - % - Power spectrum calculation w = hanning(N); % Hanning windowing [Pxx,f] = psd(outp,N,Fs,w,N/2); % [magnitude,frequency] = % (signal,sample number,sampling frequency,window,overlap number) Pyy = Pxx*norm(w)^2/sum(w)^2*2; % De-normalization of the hanning windowing % - Power spectrum calculation end - % - SNR calculation - 86 total_power = sum(Pyy(BWbb:BWeb)); % Total power of the interest bandwidth [sigpw,fsigbintmp] = max(Pyy(BWbb:BWeb)); fsigbin = fsigbintmp + BWbb -1; % Find the signal bin fsigbin % Find the signal beginning bin sbb = fsigbin; while (Pyy(sbb-1) < Pyy(sbb)) & (sbb>BWbb); sbb = sbb-1; end % Find the signal ending bin seb = fsigbin; while (Pyy(seb+1) < Pyy(seb)) & (seb[...]... multi-bit quantizer modulators [Galt96] 2.4 Continuous-time Bandpass Sigma- Delta Modulator 2.4.1 Discrete-time and Continuous-time Sigma- Delta Modulators Discrete-time Σ∆ modulators refer to the Σ∆ modulators which are implemented 19 with discrete-time switched-capacitor circuits [Sing95] [Baza98] If the loop filter is realized with continuous-time circuit, such as LC or GmC form, the modulator is called... Review of Continuous-time Bandpass Sigma- Delta Modulators The idea of bandpass Σ∆ modulator was first proposed by R Schreier and M Snelgrove [Schr89] The bandpass Σ∆ modulator was realized by putting the zeros of the noise transfer function at a certain frequency instead of DC The modulator was implemented using switched-capacitor circuits Since then, many discrete-time bandpass Σ∆ modulators have been... also pointed out in the paper that the low Q of resonators would affect the performance of the modulator Low Q will lead to a SNR loss A continuous-time bandpass Σ∆ modulator was designed and implemented with GmC resonator A LC resonator based continuous-time bandpass Σ∆ modulator was later reported in [Shoa95] Due to the substrate loss, the on-chip LC resonator suffers from low Q factor A Q-enhancement... factor Many continuous-time bandpass Σ∆ modulators with different structures and technologies were reported later The resonators used in the modulators were either LC or GmC resonators Table 1 lists the details of some reported continuous-time bandpass Σ∆ modulators 23 Table 1 Continuous-time bandpass Σ∆ modulators published Reference Fsampling OSR Order SNRmax (dB) DR (dB) Resonator Process [Shoa97]... DC Bandpass decimation circuit is used after the bandpass modulator to remove the out-of-band noise, so that high SNR can be obtained in the band of interest In bandpass Σ∆ modulator, the sampling frequency is generally selected to be four times of the resonant frequency to simplify the design [Sing95] A bandpass Σ∆ modulator is shown in Figure 13 −1 z +1 x y 2 - Quantizer Figure 13 Bandpass Σ∆ modulator. .. provides better noise shaping and hence better performance Therefore micromechanical resonator is a good candidate to replace conventional LC and GmC resonators in high-speed bandpass Σ∆ ADC design The research carried out in this thesis is to investigate the possibility of realizing 4 bandpass Σ∆ modulator using micromechanical resonator The intended application is IF digitization in modern RF receivers... 100MHz Continuous-time bandpass Σ∆ modulators are not constrained by the settling time problem and suitable for high-speed applications The continuous-time modulators also have the advantage of inherent anti-aliasing [Shoa94], which alleviates the constraints on the anti-aliasing filter 2.4.2 Design Methodology of Continuous-time Bandpass Sigma- Delta Modulator Lowpass continuous-time Σ∆ modulators can be... fundamentals of Nyquist-rate A/D converter The theory of oversampling A/D conversion and different modulator structures are then introduced The previous work on continuous-time bandpass Σ∆ modulator is reviewed and their limitations are analyzed Finally the idea of micromechanical resonator based continuous-time bandpass Σ∆ modulator is proposed 2.1 Nyquist-rate A/D Converter A/D conversion is a process of sampling... possible to integrate micromechanical devices with CMOS circuit on a single chip Different types of micromechanical resonators have been reported [Nguy01] The major advantage of the micromechanical resonator is its high Q value (typically greater than 1000), which cannot be matched by its electronic counterpart, especially at high frequencies In bandpass Σ∆ modulators, high-Q resonator provides better... 2nd-order bandpass modulator is the same as the 1st-order low-pass modulator 2.3.2 High-order Sigma- Delta Modulation In the last section, the noise transfer function has been introduced Generally, the order of the modulator is defined according to the order of its noise transfer function High-order modulators will lead to better noise-shaping It has been proven that, for an Lth-order lowpass modulator, ... micromechanical resonators in bandpass Σ∆ modulator design The design of a newly proposed 2nd-order bandpass Σ∆ modulator based on micromechanical resonator is presented The micromechanical resonator. .. MICROMECHANICAL RESONATORS 28 RESONATOR MODEL 32 SENSING CIRCUITS 35 MICROMECHANICAL RESONATOR VERSUS LC AND GMC RESONATORS 36 CHAPTER BANDPASS SIGMA-DELTA MODULATOR BASED ON MICROMECHANICAL. .. micromechanical resonator is a good candidate to replace LC and GmC resonators in continuous-time bandpass Σ∆ modulators 36 Chapter Bandpass Sigma-Delta Modulator Based on Micromechanical Resonator