ET^2: A Metric For Time and Energy Efficiency of Computation

We investigate an efficiency metric for VLSI computation that includes energy, E, and time, t, in the form E t^2. We apply the metric to CMOS circuits operating outside velocity saturation when energy and delay can be exchanged by adjusting the supply voltage; we prove that under these assumptions, optimal Et^2 implies optimal energy and delay. We give experimental and simulation evidences of the range and limits of the assumptions. We derive several results about sequential, parallel, and pipelined computations optimized for E t^2, including a result about the optimal length of a pipeline. We discuss transistor sizing for optimal Et^2 and show that, for fixed, nonzero execution rates, the optimum is achieved when the sum of the transistor-gate capacitances is twice the sum of the parasitic capacitances-not for minimum transistor sizes. We derive an approximation for E t^n (for arbitrary n) of an optimally sized system that can be computed without actually sizing the transistors; we show that this approximation is accurate. We prove that when multiple, adjustable supply voltages are allowed, the optimal Et^2 for the sequential composition of components is achieved when the supply voltages are adjusted so that the components consume equal power. Finally, we give rules for computing the Et^2 of the sequential and parallel compositions of systems, when the Et^2 of the components are known

Algorithms for Circuit Sizing in VLSI Design

One of the key problems in the physical design of computer chips, also known as integrated circuits, consists of choosing a  physical layout  for the logic gates and memory circuits (registers) on the chip. The layouts have a high influence on the power consumption and area of the chip and the delay of signal paths.  A discrete set of predefined layouts  for each logic function and register type with different physical properties is given by a library. One of the most influential characteristics of a circuit defined by the layout is its size. In this thesis we present new algorithms for the problem of choosing sizes for the circuits and its continuous relaxation,  and  evaluate these in theory and practice. A popular approach is based on Lagrangian relaxation and projected subgradient methods. We show that seemingly heuristic modifications that have been proposed for this approach can be theoretically justified by applying the well-known multiplicative weights algorithm. Subsequently, we propose a new model for the sizing problem as a min-max resource sharing problem. In our context, power consumption and signal delays are represented by resources that are distributed to customers. Under certain assumptions we obtain a polynomial time approximation for the continuous relaxation of the sizing problem that improves over the Lagrangian relaxation based approach. The new resource sharing algorithm has been implemented as part of the BonnTools software package which is developed at the Research Institute for Discrete Mathematics at the University of Bonn in cooperation with IBM. Our experiments on the ISPD 2013 benchmarks and state-of-the-art microprocessor designs provided by IBM illustrate that the new algorithm exhibits more stable convergence behavior compared to a Lagrangian relaxation based algorithm. Additionally, better timing and reduced power consumption was achieved on almost all instances. A subproblem of the new algorithm consists of finding sizes minimizing a weighted sum of power consumption and signal delays. We describe a method that approximates the continuous relaxation of this problem in polynomial time under certain assumptions. For the discrete problem we provide a fully polynomial approximation scheme under certain assumptions on the topology of the chip. Finally, we present a new algorithm for timing-driven optimization of registers. Their sizes and locations on a chip are usually determined during the clock network design phase, and remain mostly unchanged afterwards although the timing criticalities on which they were based can change. Our algorithm permutes register positions and sizes within so-called  clusters  without impairing the clock network such that it can be applied late in a design flow. Under mild assumptions, our algorithm finds an optimal solution which maximizes the worst cluster slack. It is implemented as part of the BonnTools and improves timing of registers on state-of-the-art microprocessor designs by up to 7.8% of design cycle time. </div

Metodologia Per la Caratterizzazione di amplificatori a basso rumore per UMTS

In questo lavoro si presenta una metodologia di progettazione elettronica a livello di sistema, affrontando il problema della caratterizzazione dello spazio di progetto dell' amplificatore a basso rumore costituente il primo stadio di un front end a conversione diretta per UMTS realizzato in tecnologia CMOS con lunghezza di canale .18u. La metodologia è sviluppata al fine di valutare in modo quantititativo le specifiche ottime di sistema per il front-end stesso e si basa sul concetto di Piattaforma Analogica, che prevede la costruzione di un modello di prestazioni per il blocco analogico basato su campionamento statistico di indici di prestazioni del blocco stesso, misurati tramite simulazione di dimensionamenti dei componenti attivi e passivi soddisfacenti un set di equazioni specifico della topologia circuitale. Gli indici di prestazioni vengono successivamente ulizzati per parametrizzare modelli comportamentali utilizzati nelle fasi di ottimizzazione a livello di sistema. Modelli comportamentali atti a rappresentare i sistemi RF sono stati pertanto studiati per ottimizzare la scelta delle metriche di prestazioni. L'ottimizzazione dei set di equazioni atti a selezionare le configurazione di interesse per il campionamento ha al tempo stesso richiesto l'approfondimento dei modelli di dispositivi attivi validi in tutte le regioni di funzionamento, e lo studio dettagliato della progettazione degli amplificatori a basso rumore basati su degenerazione induttiva. Inoltre, il problema della modellizzazione a livello di sistema degli effetti della comunicazione tra LNA e Mixer è stato affrontato proponendo e analizzando diverse soluzioni. Il lavoro ha permesso di condurre un'ottimizzazione del front-end UMTS, giungendo a specifiche ottime a livello di sistema per l'amplificatore stesso

Transistor sizing analysis of regular fabrics

This paper presents an extensive transistor sizing analysis for regular transistor fabrics. Several evaluation methods have been exploited, such as DC simulations, ring oscillators and single-gate open chain structures. Different design aspects are addressed taking into account stacked transistors, cells with drive strengths and circuit critical paths. The performance degradation of using regular fabrics in comparison to standard cells is naturally expected, but it is quite important to evaluate the dimension of such impact. The results were obtained for predictive PTM45 CMOS parameters, and the conclusions can be easily extrapolated to other technology nodes and fabrication processesPostprint (published version

Optimizing CMOS circuits for low power using transistor reordering

This paper addresses the optimization of a circuit for low power using transistor reordering. The optimization algorithm relies on a stochastic model of a static CMOS gate that includes the power internal nodes of the gate. This power consumption depends on the switching activity and the equilibrium probabilities of the inputs of the gate. The model allows an exploration of the different configurations of a gate that are obtained by recording its transistors. Thus, the best configuration of each gate is selected and the overall power consumption of the circuit is reduced.Peer ReviewedPostprint (published version

Two-phase RTD-CMOS pipelined circuits

MOnostable-BIstable Logic Element (MOBILE) networks can be operated in a gate-level pipelined fashion (nanopipeline) allowing high through output. Resonant tunneling diode (RTD)-based MOBILE nanopipelined circuits have been reported using different clock schemes including a four-phase strategy and a single-phase clock scheme. In particular, significant power advantages of single-phase RTD-CMOS MOBILE circuits over pure CMOS have been shown. This letter compares the RTD-CMOS realizations using a single clock and a novel two-phase clock solution. Significant superior robustness and performance in terms of power and area are obtained for the two-phase implementations

Design and analysis of a high-efficiencyv high-voltage class-D power output stage

The analysis and design of a highly-efficient 80 V class-D power stage design in a 0.14 μm SOI-based BCD process is described. It features immunity to the on-chip supply bounce, realized by internally regulated floating supplies, variable driving strength for the gate driver, and an efficient 2-step level shifter design. Fast switching transition and low switching loss are achieved with 94% peak efficiency for the complete class-D power stage in the realized chip

Low energy digital circuits in advanced nanometer technologies

The demand for portable devices and the continuing trend towards the Internet ofThings (IoT) have made of energy consumption one of the main concerns in the industry and researchers. The most efficient way of reducing the energy consump-tion of digital circuits is decreasing the supply voltage (Vdd) since the dynamicenergy quadratically depends onVdd. Several works have shown that an optimumsupply voltage exists that minimizes the energy consumption of digital circuits. This optimum supply voltage is usually around 200 mV and 400 mV dependingon the circuit and technology used. To obtain these low supply voltages, on-chipdc-dc converters with high efficiency are needed.This thesis focuses on the study of subthreshold digital systems in advancednanometer technologies. These systems usually can be divided into a Power Man-agement Unit (PMU) and a digital circuit operating at the subthreshold regime.In particular, while considering the PMU, one of the key circuits is the dc-dcconverter. This block converts the voltage from the power source (battery, supercapacitor or wireless power transfer link) to a voltage between 200 mV and 400mV in order to power the digital circuit. In this thesis, we developed two chargerecycling techniques in order to improve the efficiency of switched capacitors dc-dcconverters. The first one is based on a technique used in adiabatic circuits calledstepwise charging. This technique was used in circuits and applications wherethe switching consumption of a big capacitance is very important. We analyzedthe possibility of using this technique in switched capacitor dc-dc converters withintegrated capacitors. We showed through measurements that a 29% reductionin the gate drive losses can be obtained with this technique. The second one isa simplification of stepwise charging which can be applied in some architecturesof switched capacitors dc-dc converters. We also fabricated and tested a dc-dcconverter with this technique and obtained a 25% energy reduction in the drivingof the switches that implement the converter.Furthermore, we studied the digital circuit working in the subthreshold regime,in particular, operating at the minimum energy point. We studied different modelsfor circuits working in these conditions and improved them by considering thedifferences between the NMOS and PMOS transistors. We obtained an optimumNMOS/PMOS leakage current imbalance that minimizes the total leakage energy per operation. This optimum depends on the architecture of the digital circuitand the input data. However, we also showed that important energy reductionscan be obtained by operating at a mean optimum imbalance. We proposed two techniques to achieve the optimum imbalance. We used aFully Depleted Silicon on Insulator (FD-SOI) 28 nm technology for most of the simulations, but we also show that these techniques can be applied in traditionalbulk CMOS technologies. The first one consists in using the back plane voltage of the transistors (or bulk voltage in traditional CMOS) to adjust independently theleakage current of the NMOS and PMOS transistor to work under the optimum NMOS/PMOS leakage current imbalance. We called this approach the OptimumBack Plane Biasing (OBB). A second technique consists of using the length of the transistors to adjust this leakage current imbalance. In the subthreshold regimeand in advanced nanometer technologies a moderate increase in the length has little impact in the output capacitance of the gates and thus in the dynamic energy.We called this approach an Asymmetric Length Biasing (ALB). Finally, we use these techniques in some basic circuits such as adders. We show that around 50% energy reduction can be obtained, in a wide range of frequency while working near the minimum energy point and using these techniques. The main contributions of this thesis are: • Analysis of the stepwise charging technique in small capacitances. •Implementation of stepwise charging technique as a charge recycling tech-nique for efficiency improvement in switched capacitor dc-dc converters. • Development of a charge sharing technique for efficiency improvement inswitched capacitor dc-dc converters. • Analysis of minimum operating voltage of digital circuits due to intrinsicnoise and the impact of technology scaling in this minimum. • Improvement in the modeling of the minimum energy point while considering NMOS and PMOS transistors difference. • Demonstration of the existence of an optimum leakage current imbalance be-tween the NMOS and PMOS transistors that minimizes energy consumptionin the subthreshold regiion. • Development of a back plane (bulk) voltage strategy for working in this optimum.• Development of a sizing strategy for working in the aforementioned optimum. • Analysis of the impact of architecture and input data on the optimum im-balance. The thesis is based on the publications [1–8]. During the Ph.D. program, other publications were generated [9–16] that are partially related with the thesis butwere not included in it.La constante demanda de dispositivos portables y los avances hacia la Internet de las Cosas han hecho del consumo de energía uno de los mayores desafíos y preocupación en la industria y la academia. La forma más eficiente de reducir el consumo de energía de los circuitos digitales es reduciendo su voltaje de alimentación ya que la energía dinámica depende de manera cuadrática con dicho voltaje. Varios trabajos demostraron que existe un voltaje de alimentación óptimo, que minimiza la energía consumida para realizar cierta operación en un circuito digital, llamado punto de mínima energía. Este óptimo voltaje se encuentra usualmente entre 200 mV y 400 mV dependiendo del circuito y de la tecnología utilizada. Para obtener estos voltajes de alimentación de la fuente de energía, se necesitan conversores dc-dc integrados con alta eficiencia. Esta tesis se concentra en el estudio de sistemas digitales trabajando en la región sub umbral diseñados en tecnologías nanométricas avanzadas (28 nm). Estos sistemas se pueden dividir usualmente en dos bloques, uno llamado bloque de manejo de potencia, y el segundo, el circuito digital operando en la region sub umbral. En particular, en lo que corresponde al bloque de manejo de potencia, el circuito más crítico es en general el conversor dc-dc. Este circuito convierte el voltaje de una batería (o super capacitor o enlace de transferencia inalámbrica de energía o unidad de cosechado de energía) en un voltaje entre 200 mV y 400 mV para alimentar el circuito digital en su voltaje óptimo. En esta tesis desarrollamos dos técnicas que, mediante el reciclado de carga, mejoran la eficiencia de los conversores dc-dc a capacitores conmutados. La primera es basada en una técnica utilizada en circuitos adiabáticos que se llama carga gradual o a pasos. Esta técnica se ha utilizado en circuitos y aplicaciones en donde el consumo por la carga y descarga de una capacidad grande es dominante. Nosotros analizamos la posibilidad de utilizar esta técnica en conversores dc-dc a capacitores conmutados con capacitores integrados. Se demostró a través de medidas que se puede reducir en un 29% el consumo debido al encendido y apagado de las llaves que implementan el conversor dc-dc. La segunda técnica, es una simplificación de la primera, la cual puede ser aplicada en ciertas arquitecturas de conversores dc-dc a capacitores conmutados. También se fabricó y midió un conversor con esta técnica y se obtuvo una reducción del 25% en la energía consumida por el manejo de las llaves del conversor. Por otro lado, estudiamos los circuitos digitales operando en la región sub umbral y en particular cerca del punto de mínima energía. Estudiamos diferentes modelos para circuitos operando en estas condiciones y los mejoramos considerando las diferencias entre los transistores NMOS y PMOS. Mediante este modelo demostramos que existe un óptimo en la relación entre las corrientes de fuga de ambos transistores que minimiza la energía de fuga consumida por operación. Este óptimo depende de la arquitectura del circuito digital y ademas de los datos de entrada del circuito. Sin embargo, demostramos que se puede reducir el consumo de manera considerable al operar en un óptimo promedio. Propusimos dos técnicas para alcanzar la relación óptima. Utilizamos una tecnología FD-SOI de 28nm para la mayoría de las simulaciones, pero también mostramos que estas técnicas pueden ser utilizadas en tecnologías bulk convencionales. La primer técnica, consiste en utilizar el voltaje de la puerta trasera (o sustrato en CMOS convencional) para ajustar de manera independiente las corrientes del NMOS y PMOS para que el circuito trabaje en el óptimo de la relación de corrientes. Esta técnica la llamamos polarización de voltaje de puerta trasera óptimo. La segunda técnica, consiste en utilizar los largos de los transistores para ajustar las corrientes de fugas de cada transistor y obtener la relación óptima. Trabajando en la región sub umbral y en tecnologías avanzadas, incrementar moderadamente el largo del transistor tiene poco impacto en la energía dinámica y es por eso que se puede utilizar. Finalmente, utilizamos estas técnicas en circuitos básicos como sumadores y mostramos que se puede obtener una reducción de la energía consumida de aproximadamente 50%, en un amplio rango de frecuencias, mientras estos circuitos trabajan cerca del punto de energía mínima. Las principales contribuciones de la tesis son: • Análisis de la técnica de carga gradual o a pasos en capacidades pequeñas. • Implementación de la técnica de carga gradual para la mejora de eficiencia de conversores dc-dc a capacitores conmutados. • Simplificación de la técnica de carga gradual para mejora de la eficiencia en algunas arquitecturas de conversores dc-dc de capacitores conmutados. • Análisis del mínimo voltaje de operación en circuitos digitales debido al ruido intrínseco del dispositivo y el impacto del escalado de las tecnologías en el mismo. • Mejoras en el modelado del punto de energía mínima de operación de un circuito digital en el cual se consideran las diferencias entre el transistor PMOS y NMOS. • Demostración de la existencia de un óptimo en la relación entre las corrientes de fuga entre el NMOS y PMOS que minimiza la energía de fugas consumida en la región sub umbral. • Desarrollo de una estrategia de polarización del voltaje de puerta trasera para que el circuito digital trabaje en el óptimo antes mencionado. • Desarrollo de una estrategia para el dimensionado de los transistores que componen las compuertas digitales que permite al circuito digital operar en el óptimo antes mencionado. • Análisis del impacto de la arquitectura del circuito y de los datos de entrada del mismo en el óptimo antes mencionado