Stochastic Resonance Analog-to-Digital Conversion 1-Bit Signal Acquisition Employing Noise D.P.N. Mul Technische Universiteit Delft Stochastic Resonance Analog-to-Digital Conversion 1-Bit Signal Acquisition Employing Noise by D.P.N. Mul in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering at the Delft University of Technology, to be defended publicly on Wednesday August 22, 2018 at 1:30 PM. Supervisor: Prof. dr. ir. W.A. Serdijn Thesis committee: Dr. ir. J. Weber, TU Delft Dr. M. Alavi, TU Delft Dr. O.C. Akgun, TU Delft An electronic version of this thesis is available at http://repository.tudelft.nl/. “I wanted to make noise, not study theory” – James Hetfield Abstract Stochastic resonance (SR) is a phenomenon in which the presence of noise increases the performance of the system. The phenomenon has first been discovered in a climate change model and is later observed in neuronal systems. In artificial, electronic, systems, stochastic resonance is observed in systems based on Schmitt-Triggers and comparators. The common property of all these systems is the threshold, which, when reached, causes a large transition in the system. The presence of noise in small signals can cause the system to reach the threshold or can increase the number of state transitions, increasing the quality of the output signal. Oversampling and integration are applied to reconstruct the original signal. Biomedical signals are typically affected relative high noise levels. The observations of stochastic resonance in nature, such as biological neural systems, combined with the observations of stochastic resonance in comparator-based circuits formed the inspiration and fundamental of this thesis research. The goal of this project is to investigate the potentials for using stochastic resonance in biomedical signal acquisition. In this thesis, an explorative study on the behavior, the per- formance, and the design of an analog-to-digital (ADC) converter fully based on stochastic resonance in a 1-bit quantizer is presented. The design and application focus on processing ECG measurements. A comprehensive analysis of the behavior, and an analytical method to determine the performance of 1-bit stochastic resonance analog-to-digital conversion in a comparator based circuit is presented. A novel technique using a negative hysteresis is found, showing a potential increase in SNDR up to 6.4 dB. Based on this analysis, a system level design is presented which implements a closed-loop operation of the stochastic resonance ADC. This design comprises a feedback loop to control the noise level, realizing the maximum performance over an input amplitude range from 1-10 mV, independent from noise present in the system. Furthermore, an offset compensation scheme is presented, which controls the threshold of the comparator, and a digital multi-rate filter is implemented to filter the high-frequency noise, and to apply downsampling the highspeed bitstream. IC implementation of the comparator and the noise source is studied. A low-offset comparator, based on a strongARM latch, is proposed, with an offset calibration technique, reducing the offset to below 50 µV. The noise source creates a flat noise spectrum from 20 kHz to 4 MHz, using amplified thermal noise of a resistor combined with the amplifier noise. The proposed system can deliver a 27 dB SNDR in a signal bandwidth of 216 Hz, and an input amplitude range of 10 , using a sampling frequency of 2 MHz. × v vi Acknowledgements Here I would like to show my gratitude to the people who have helped me during my thesis project, and the road leading to this point. First of all, I want to thank Wouter Serdijn, who has been an inspiration to me as a teacher during my Bachelor and my Master. I am thankful for the opportunity to perform my master thesis research under his supervision, and for the great project, I have been able to do. I want to thank him for the freedom I had to give shape to the project. It allowed me to combine my interest in electronics with stochastic processes and signal processing in a biomedical environment. I would like to thank everybody in the Bioelectronics group. It has been an inspiring environment to work in. I have always appreciated the interest in each other’s work, the preparedness to help each other and to share the knowledge. My thanks go out to Can, for the interesting discussions. Your open-minded way of finding solutions has been inspiring and very helpful. Furthermore, I would like to thank Samprajani for her help and the time she took to look at my designs, Ali for his technical support throughout the project, and Marion her support in the administrative work. Finally, I want to show my gratitude to my family and friends. The road has not always been easy, and I want to sincerely thank everybody who supported me on the way. I want to thank my fiancee, Anna Bernard, for her unconditional love and support. My parents, brother, and sister, who have always supported and believed in me. I would not have reached this point without your support. Dieuwert Mul Delft, The Netherlands 30 July 2018 vii viii Contents 1 Introduction 1 1.1 From Current Solutions to Bio-inspired Design . .2 1.2 Stochastic Resonance Analog-to-Digital Conversion . .2 1.3 ECG Measurement . .3 1.4 Goal . .3 1.5 Thesis Outline . .4 2 Background Information on Stochastic Resonance 7 2.1 Stochastic Resonance in Hysteresis Systems . .8 2.2 Stochastic Resonance in Excitable Systems . 10 2.3 Suprathreshold Stochastic Resonance . 10 2.4 Definition . 11 2.5 Conclusions . 12 3 Classification 13 3.1 Definition and Criteria . 14 3.2 Generalized SR-system . 15 3.3 Subthreshold SR – Schmitt-trigger . 16 3.4 Subthreshold SR – Comparator . 18 3.5 Suprathreshold SR – Schmitt-trigger . 21 3.6 Suprathreshold SR – Comparator . 23 3.7 Conclusions . 26 4 Analysis of Stochastic Resonance in Single-bit ADC 29 4.1 System Introduction . 30 4.2 Expected Transfer . 31 4.3 Gain and Harmonic Distortion . 33 4.3.1 Least Square Error . 33 4.3.2 Gain . 36 ix x CONTENTS 4.3.3 Harmonic Distortion . 36 4.4 Noise . 39 4.4.1 Comparator Output Noise Level . 39 4.4.2 Frequency behavior of the noise . 39 4.4.3 Filtered Noise Level . 40 4.5 Signal-to-Noise-and-Distortion Ratio . 44 4.6 Static Performance . 47 4.7 Schmitt-trigger Analysis . 48 4.7.1 Expected Output and Harmonic Distortion . 48 4.7.2 Noise . 50 4.7.3 SNDR . 50 4.8 Negative Hysteresis Comparator . 52 4.8.1 Expected Output and Harmonic Distortion . 52 4.8.2 Noise . 53 4.8.3 SNDR . 54 4.9 Conclusion . 56 5 System Level Design 59 5.1 System Overview . 60 5.2 Digital Filter . 62 5.2.1 IIR/FIR . 62 5.2.2 Filter Window and Transfer Function . 63 5.2.3 Topology . 66 5.2.4 Dataflow . 67 5.2.5 Conclusion . 68 5.3 Dynamic Range Control . 71 5.3.1 Basic Design - Design Approach . 71 5.3.2 Loop Gain and Stability . 74 5.3.3 Exponential Noise Level Control . 76 5.3.4 Noise Adjustment Algorithm . 77 5.4 Offset Compensation . 79 5.4.1 Offline Offset Calibration Accuracy . 79 5.4.2 Dynamic Offset Compensation . 79 5.5 Simulation Results of Complete Control System . 86 5.5.1 Results . 86 5.5.2 Conclusion . 89 CONTENTS xi 6 IC Implementation 91 6.1 Comparator . 92 6.1.1 Topology . 92 6.1.2 Offset Compensation . 95 6.1.3 Comparator Noise and Errors . 97 6.1.4 Common Mode Mismatch . 102 6.2 Noise Source . 103 6.2.1 Noise Source Selection . 103 6.2.2 Passive Thermal Noise . 105 6.2.3 Noise Amplifier . 106 6.2.4 High-Pass Filter . 108 6.2.5 Simulated Output Noise . 109 6.3 Simulation Limitations . 111 6.3.1 Periodic Analysis . 111 6.3.2 Transient Noise Analysis . 111 6.4 Conclusions and Discussion . 113 6.4.1 Comparator . 113 6.4.2 Noise Source . 113 6.4.3 Conclusions on the Combining the Comparator and Noise Source . 114 6.4.4 Discussion . 114 7 Conclusions 115 7.1 Overview . 116 7.2 Conclusions on the SR-ADC . 117 7.3 Contributions . 118 8 Recommendations and Future Work 119 8.1 Recommendations for Implementation . 120 8.1.1 Noise Source and Pre-Amplification . 120 8.1.2 Comparator . 120 8.1.3 Hypothesis . 121 8.2 Negative Hysteresis Implementation . ..