A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis

Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.Comment: Accepted to American Control Conference (ACC) 2015 (Chicago, USA

Modeling, Optimization and Testing for Analog/Mixed-Signal Circuits in Deeply Scaled CMOS Technologies

As CMOS technologies move to sub-100nm regions, the design and verification for analog/mixed-signal circuits become more and more difficult due to the problems including the decrease of transconductance, severe gate leakage and profound mismatches. The increasing manufacturing-induced process variations and their impacts on circuit performances make the already complex circuit design even more sophisticated in the deeply scaled CMOS technologies. Given these barriers, efforts are needed to ensure the circuits are robust and optimized with consideration of parametric variations. This research presents innovative computer-aided design approaches to address three such problems: (1) large analog/mixed-signal performance modeling under process variations, (2) yield-aware optimization for complex analog/mixedsignal systems and (3) on-chip test scheme development to detect and compensate parametric failures. The first problem focus on the efficient circuit performance evaluation with consideration of process variations which serves as the baseline for robust analog circuit design. We propose statistical performance modeling methods for two popular types of complex analog/mixed-signal circuits including Sigma-Delta ADCs and charge-pump PLLs. A more general performance modeling is achieved by employing a geostatistics motivated performance model (Kriging model), which is accurate and efficient for capturing stand-alone analog circuit block performances. Based on the generated block-level performance models, we can solve the more challenging problem of yield-aware system optimization for large analog/mixed-signal systems. Multi-yield pareto fronts are utilized in the hierarchical optimization framework so that the statistical optimal solutions can be achieved efficiently for the systems. We further look into on-chip design-for-test (DFT) circuits in analog systems and solve the problems of linearity test in ADCs and DFT scheme optimization in charge-pump PLLs. Finally a design example of digital intensive PLL is presented to illustrate the practical applications of the modeling, optimization and testing approaches for large analog/mixed-signal systems

Layout-accurate Ultra-fast System-level Design Exploration Through Verilog-ams

This research addresses problems in designing analog and mixed-signal (AMS) systems by bridging the gap between system-level and circuit-level simulation by making simulations fast like system-level and accurate like circuit-level. The tools proposed include metamodel integrated Verilog-AMS based design exploration flows. The research involves design centering, metamodel generation flows for creating efficient behavioral models, and Verilog-AMS integration techniques for model realization. The core of the proposed solution is transistor-level and layout-level metamodeling and their incorporation in Verilog-AMS. Metamodeling is used to construct efficient and layout-accurate surrogate models for AMS system building blocks. Verilog-AMS, an AMS hardware description language, is employed to build surrogate model implementations that can be simulated with industrial standard simulators. The case-study circuits and systems include an operational amplifier (OP-AMP), a voltage-controlled oscillator (VCO), a charge-pump phase-locked loop (PLL), and a continuous-time delta-sigma modulator (DSM). The minimum and maximum error rates of the proposed OP-AMP model are 0.11 % and 2.86 %, respectively. The error rates for the PLL lock time and power estimation are 0.7 % and 3.0 %, respectively. The OP-AMP optimization using the proposed approach is ~17000× faster than the transistor-level model based approach. The optimization achieves a ~4× power reduction for the OP-AMP design. The PLL parasitic-aware optimization achieves a 10× speedup and a 147 µW power reduction. Thus the experimental results validate the effectiveness of the proposed solution

Metamodeling-based Fast Optimization of Nanoscale Ams-socs

Modern consumer electronic systems are mostly based on analog and digital circuits and are designed as analog/mixed-signal systems on chip (AMS-SoCs). the integration of analog and digital circuits on the same die makes the system cost effective. in AMS-SoCs, analog and mixed-signal portions have not traditionally received much attention due to their complexity. As the fabrication technology advances, the simulation times for AMS-SoC circuits become more complex and take significant amounts of time. the time allocated for the circuit design and optimization creates a need to reduce the simulation time. the time constraints placed on designers are imposed by the ever-shortening time to market and non-recurrent cost of the chip. This dissertation proposes the use of a novel method, called metamodeling, and intelligent optimization algorithms to reduce the design time. Metamodel-based ultra-fast design flows are proposed and investigated. Metamodel creation is a one time process and relies on fast sampling through accurate parasitic-aware simulations. One of the targets of this dissertation is to minimize the sample size while retaining the accuracy of the model. in order to achieve this goal, different statistical sampling techniques are explored and applied to various AMS-SoC circuits. Also, different metamodel functions are explored for their accuracy and application to AMS-SoCs. Several different optimization algorithms are compared for global optimization accuracy and convergence. Three different AMS circuits, ring oscillator, inductor-capacitor voltage-controlled oscillator (LC-VCO) and phase locked loop (PLL) that are present in many AMS-SoC are used in this study for design flow application. Metamodels created in this dissertation provide accuracy with an error of less than 2% from the physical layout simulations. After optimal sampling investigation, metamodel functions and optimization algorithms are ranked in terms of speed and accuracy. Experimental results show that the proposed design flow provides roughly 5,000x speedup over conventional design flows. Thus, this dissertation greatly advances the state-of-the-art in mixed-signal design and will assist towards making consumer electronics cheaper and affordable

Learning Approaches to Analog and Mixed Signal Verification and Analysis

The increased integration and interaction of analog and digital components within a system has amplified the need for a fast, automated, combined analog, and digital verification methodology. There are many automated characterization, test, and verification methods used in practice for digital circuits, but analog and mixed signal circuits suffer from long simulation times brought on by transistor-level analysis. Due to the substantial amount of simulations required to properly characterize and verify an analog circuit, many undetected issues manifest themselves in the manufactured chips. Creating behavioral models, a circuit abstraction of analog components assists in reducing simulation time which allows for faster exploration of the design space. Traditionally, creating behavioral models for non-linear circuits is a manual process which relies heavily on design knowledge for proper parameter extraction and circuit abstraction. Manual modeling requires a high level of circuit knowledge and often fails to capture critical effects stemming from block interactions and second order device effects. For this reason, it is of interest to extract the models directly from the SPICE level descriptions so that these effects and interactions can be properly captured. As the devices are scaled, process variations have a more profound effect on the circuit behaviors and performances. Creating behavior models from the SPICE level descriptions, which include input parameters and a large process variation space, is a non-trivial task. In this dissertation, we focus on addressing various problems related to the design automation of analog and mixed signal circuits. Analog circuits are typically highly specialized and fined tuned to fit the desired specifications for any given system reducing the reusability of circuits from design to design. This hinders the advancement of automating various aspects of analog design, test, and layout. At the core of many automation techniques, simulations, or data collection are required. Unfortunately, for some complex analog circuits, a single simulation may take many days. This prohibits performing any type of behavior characterization or verification of the circuit. This leads us to the first fundamental problem with the automation of analog devices. How can we reduce the simulation cost while maintaining the robustness of transistor level simulations? As analog circuits can vary vastly from one design to the next and are hardly ever comprised of standard library based building blocks, the second fundamental question is how to create automated processes that are general enough to be applied to all or most circuit types? Finally, what circuit characteristics can we utilize to enhance the automation procedures? The objective of this dissertation is to explore these questions and provide suitable evidence that they can be answered. We begin by exploring machine learning techniques to model the design space using minimal simulation effort. Circuit partitioning is employed to reduce the complexity of the machine learning algorithms. Using the same partitioning algorithm we further explore the behavior characterization of analog circuits undergoing process variation. The circuit partitioning is general enough to be used by any CMOS based analog circuit. The ideas and learning gained from behavioral modeling during behavior characterization are used to improve the simulation through event propagation, input space search, complexity and information measurements. The reduction of the input space and behavioral modeling of low complexity, low information primitive elements reduces the simulation time of large analog and mixed signal circuits by 50-75%. The method is extended and applied to assist in analyzing analog circuit layout. All of the proposed methods are implemented on analog circuits ranging from small benchmark circuits to large, highly complex and specialized circuits. The proposed dependency based partitioning of large analog circuits in the time domain allows for fast identification of highly sensitive transistors as well as provides a natural division of circuit components. Modeling analog circuits in the time domain with this partitioning technique and SVM learning algorithms allows for very fast transient behavior predictions, three orders of magnitude faster than traditional simulators, while maintaining 95% accuracy. Analog verification can be explored through a reduction of simulation time by utilizing the partitions, information and complexity measures, and input space reduction. Behavioral models are created using supervised learning techniques for detected primitive elements. We will show the effectiveness of the method on four analog circuits where the simulation time is decreased by 55-75%. Utilizing the reduced simulation method, critical nodes can be found quickly and efficiently. The nodes found using this method match those found by an experienced layout engineer, but are detected automatically given the design and input specifications. The technique is further extended to find the tolerance of transistors to both process variation and power supply fluctuation. This information allows for corrections in layout overdesign or guidance in placing noise reducing components such as guard rings or decoupling capacitors. The proposed approaches significantly reduce the simulation time required to perform the tasks traditionally, maintain high accuracy, and can be automated

Event-Driven Simulation Methodology for Analog/Mixed-Signal Systems

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 김재하.Recent system-on-chip's (SoCs) are composed of tightly coupled analog and digital components. The resulting mixed-signal systems call for efficient system-level behavioral simulators for fast and systematic verifications. As the system-level verifications rely heavily on digital verification tools, it is desirable to build the mixed-signal simulator based on a digital simulator. However, the existing solutions in digital simulators suffer from a trade-off between simulation speed and accuracy. This work breaks down the trade-off and realizes a fast and accurate analog/mixed-signal behavior simulation in a digital simulator SystemVerilog. The main difference of the proposed methodology from existing ones is its way of representing continuous-time signals. Specifically, a clock signal expresses accurate timing information by carrying an additional real-value time offset, and an analog signal represents its continuous-time waveform in a functional form by employing a set of coefficients. With these signal representations, the proposed method accurately simulates mixed-signal behaviors independently of a simulator's time-step and achieves a purely event-driven simulation without involving any numerical iteration. The speed and accuracy of the proposed methodology are examined for various types of analog/mixed-signal systems. First, timing-sensitive circuits (a phase-locked loops and a clock and data recovery loop) and linear analog circuits (a channel and linear equalizers) are simulated in a high-speed I/O interface example. Second, a switched-linear-behavior simulation is demonstrated through switching power supplies, such as a boost converter and a switched-capacitor converter. Additionally, the proposed method is applied to weakly nonlinear behaviors modeled with a Volterra series for an RF power amplifier and a high-speed I/O linear equalizer. Furthermore, the nonlinear behavior simulation is extended to three different types of injection-locked oscillators exhibiting time-varying nonlinear behaviors. The experimental results show that the proposed simulation methodology achieved tens to hundreds of speed-ups while maintaining the same accuracy as commercial analog simulators.ABSTRACT I CONTENTS III LIST OF FIGURES V LIST OF TABLES XII CHAPTER 1 INTRODUCTION 1 1.1 BACKGROUND 1 1.2 MAIN CONTRIBUTION 6 1.3 THESIS ORGANIZATION 8 CHAPTER 2 EVENT-DRIVEN SIMULATION OF ANALOG/MIXED-SIGNAL BEHAVIORS 9 2.1 PROPOSED CLOCK AND ANALOG SIGNAL REPRESENTATIONS 10 2.2 SIGNAL TYPE DEFINITIONS IN SYSTEMVERILOG 14 2.3 EVENT-DRIVEN SIMULATION METHODOLOGY 16 CHAPTER 3 HIGH-SPEED I/O INTERFACE SIMULATION 21 3.1 CHARGE-PUMP PHASE-LOCKED LOOP 23 3.2 BANGBANG CLOCK AND DATA RECOVERY 37 3.3 CHANNEL AND EQUALIZERS 45 3.4 HIGH-SPEED I/O SYSTEM SIMULATION 52 CHAPTER 4 SWITCHING POWER SUPPLY SIMULATION 55 4.1 BOOST CONVERTER 57 4.2 TIME-INTERLEAVED SWITCHED-CAPACITOR CONVERTER 66 CHAPTER 5 VOLTERRA SERIES MODEL SIMULATION 72 5.1 VOLTERRA SERIES MODEL 74 5.2 CLASS-A POWER AMPLIFIER 79 5.3 CONTINUOUS-TIME EQUALIZER 84 CHAPTER 6 INJECTION-LOCKED OSCILLATOR SIMULATION 89 6.1 PPV-BASED ILO MODEL 91 6.2 LC OSCILLATOR 99 6.3 RING OSCILLATOR 104 6.4 BURST-MODE CLOCK AND DATA RECOVERY 109 CONCLUSION 116 BIBLIOGRAPHY 118 초 록 126Docto

System level performance and yield optimisation for analogue integrated circuits

Advances in silicon technology over the last decade have led to increased integration of analogue and digital functional blocks onto the same single chip. In such a mixed signal environment, the analogue circuits must use the same process technology as their digital neighbours. With reducing transistor sizes, the impact of process variations on analogue design has become prominent and can lead to circuit performance falling below specification and hence reducing the yield.This thesis explores the methodology and algorithms for an analogue integrated circuit automation tool that optimizes performance and yield. The trade-offs between performance and yield are analysed using a combination of an evolutionary algorithm and Monte Carlo simulation. Through the integration of yield parameter into the optimisation process, the trade off between the performance functions can be better treated that able to produce a higher yield. The results obtained from the performance and variation exploration are modelled behaviourally using a Verilog-A language. The model has been verified with transistor level simulation and a silicon prototype.For a large analogue system, the circuit is commonly broken down into its constituent sub-blocks, a process known as hierarchical design. The use of hierarchical-based design and optimisation simplifies the design task and accelerates the design flow by encouraging design reuse.A new approach for system level yield optimisation using a hierarchical-based design is proposed and developed. The approach combines Multi-Objective Bottom Up (MUBU) modelling technique to model the circuit performance and variation and Top Down Constraint Design (TDCD) technique for the complete system level design. The proposed method has been used to design a 7th order low pass filter and a charge pump phase locked loop system. The results have been verified with transistor level simulations and suggest that an accurate system level performance and yield prediction can be achieved with the proposed methodology