Enhancing Variation-aware Analog Circuits Sizing

Today's analog design and verification face significant challenges due to circuit complexity and short time-to-market windows. Moreover, variations in design parameters have an adversely impact on the correctness and performance of analog circuits. Circuit sizing consists in determining the device sizes and biasing voltages and currents such that the circuit satisfies its specifications. Traditionally, analog circuit sizing has been carried out by optimization-based methods, which of course will still be important in the future. Unfortunately, these techniques cannot guarantee an exhaustive coverage of the design search space and hence, are not able to ensure the non-existence of higher quality design solutions. The sizing problem becomes more complicated and computationally expensive under design parameters fluctuation. Indeed, existing yield analysis methods are computationally expensive and still encounter issues in problems with a high-dimensional process parameter space. In this thesis, we present new approaches for enhancing variation-aware analog circuit sizing. The circuit sizing problem is encoded using nonlinear constraints. A new algorithm using Satisfiability Modulo Theory (SMT) solving techniques exhaustively explores the analog design space and computes a continuous set of feasible sizing solutions. Next, a yield optimization stage aims to select the candidate design solution with the highest yield rate in the presence of process parameters variation. For this purpose, a novel method for the computation of parametric yield is proposed. The method combines the advantages of sparse regression and SMT solving techniques. The key idea is to characterize the failure regions as a collection of hyperrectangles in the parameters space. The yield estimation is based on a geometric calculation of probabilistic volumes subtended by the located hyperrectangles. The method can provide very large speed-up over Monte Carlo methods, when a high prediction accuracy is required. A new approach for improving analog yield optimization is also proposed. The optimization is performed in two steps. First, a global optimization phase samples the most potential optimal sub-regions of the feasible design space. The global search locates a design point near the optimal solution. Second, a local optimization phase uses the near optimal solution as a starting point. Also, it constructs linear interpolating models of the yield to explore the basin of convergence and to reach the global optimum. We illustrate the efficiency of the proposed methods on various analog circuits. The application of the yield analysis method on an integrated ring oscillator and a 6T static RAM proves that it is suitable for handling problems with tens of process parameters and can provide speedup of 5X-2000X over Monte Carlo methods. Furthermore, the application of our yield optimization methodology on the examples of a two-stage amplifier and a cascode amplifier shows that our approach can achieve higher quality in analog synthesis and unrivaled coverage of the analog design space when compared to traditional optimization techniques

Clock Generator Circuits for Low-Power Heterogeneous Multiprocessor Systems-on-Chip

In this work concepts and circuits for local clock generation in low-power heterogeneous multiprocessor systems-on-chip (MPSoCs) are researched and developed. The targeted systems feature a globally asynchronous locally synchronous (GALS) clocking architecture and advanced power management functionality, as for example fine-grained ultra-fast dynamic voltage and frequency scaling (DVFS). To enable this functionality compact clock generators with low chip area, low power consumption, wide output frequency range and the capability for ultra-fast frequency changes are required. They are to be instantiated individually per core. For this purpose compact all digital phase-locked loop (ADPLL) frequency synthesizers are developed. The bang-bang ADPLL architecture is analyzed using a numerical system model and optimized for low jitter accumulation. A 65nm CMOS ADPLL is implemented, featuring a novel active current bias circuit which compensates the supply voltage and temperature sensitivity of the digitally controlled oscillator (DCO) for reduced digital tuning effort. Additionally, a 28nm ADPLL with a new ultra-fast lock-in scheme based on single-shot phase synchronization is proposed. The core clock is generated by an open-loop method using phase-switching between multi-phase DCO clocks at a fixed frequency. This allows instantaneous core frequency changes for ultra-fast DVFS without re-locking the closed loop ADPLL. The sensitivity of the open-loop clock generator with respect to phase mismatch is analyzed analytically and a compensation technique by cross-coupled inverter buffers is proposed. The clock generators show small area (0.0097mm2 (65nm), 0.00234mm2 (28nm)), low power consumption (2.7mW (65nm), 0.64mW (28nm)) and they provide core clock frequencies from 83MHz to 666MHz which can be changed instantaneously. The jitter performance is compliant to DDR2/DDR3 memory interface specifications. Additionally, high-speed clocks for novel serial on-chip data transceivers are generated. The ADPLL circuits have been verified successfully by 3 testchip implementations. They enable efficient realization of future low-power MPSoCs with advanced power management functionality in deep-submicron CMOS technologies.In dieser Arbeit werden Konzepte und Schaltungen zur lokalen Takterzeugung in heterogenen Multiprozessorsystemen (MPSoCs) mit geringer Verlustleistung erforscht und entwickelt. Diese Systeme besitzen eine global-asynchrone lokal-synchrone Architektur sowie Funktionalität zum Power Management, wie z.B. das feingranulare, schnelle Skalieren von Spannung und Taktfrequenz (DVFS). Um diese Funktionalität zu realisieren werden kompakte Taktgeneratoren benötigt, welche eine kleine Chipfläche einnehmen, wenig Verlustleitung aufnehmen, einen weiten Bereich an Ausgangsfrequenzen erzeugen und diese sehr schnell ändern können. Sie sollen individuell pro Prozessorkern integriert werden. Dazu werden kompakte volldigitale Phasenregelkreise (ADPLLs) entwickelt, wobei eine bang-bang ADPLL Architektur numerisch modelliert und für kleine Jitterakkumulation optimiert wird. Es wird eine 65nm CMOS ADPLL implementiert, welche eine neuartige Kompensationsschlatung für den digital gesteuerten Oszillator (DCO) zur Verringerung der Sensitivität bezüglich Versorgungsspannung und Temperatur beinhaltet. Zusätzlich wird eine 28nm CMOS ADPLL mit einer neuen Technik zum schnellen Einschwingen unter Nutzung eines Phasensynchronisierers realisiert. Der Prozessortakt wird durch ein neuartiges Phasenmultiplex- und Frequenzteilerverfahren erzeugt, welches es ermöglicht die Taktfrequenz sofort zu ändern um schnelles DVFS zu realisieren. Die Sensitivität dieses Frequenzgenerators bezüglich Phasen-Mismatch wird theoretisch analysiert und durch Verwendung von kreuzgekoppelten Taktverstärkern kompensiert. Die hier entwickelten Taktgeneratoren haben eine kleine Chipfläche (0.0097mm2 (65nm), 0.00234mm2 (28nm)) und Leistungsaufnahme (2.7mW (65nm), 0.64mW (28nm)). Sie stellen Frequenzen von 83MHz bis 666MHz bereit, welche sofort geändert werden können. Die Schaltungen erfüllen die Jitterspezifikationen von DDR2/DDR3 Speicherinterfaces. Zusätzliche können schnelle Takte für neuartige serielle on-Chip Verbindungen erzeugt werden. Die ADPLL Schaltungen wurden erfolgreich in 3 Testchips erprobt. Sie ermöglichen die effiziente Realisierung von zukünftigen MPSoCs mit Power Management in modernsten CMOS Technologien