Linearization of The Timing Analysis and Optimization of Level-Sensitive Circuits

This thesis describes a linear programming (LP) formulation applicable to the static timing analysis of large scale synchronous circuits with level-sensitive latches. The automatic timing analysis procedure presented here is composed of deriving the connectivity information, constructing the LP model and solving the clock period minimization problem of synchronous digital VLSI circuits. In synchronous circuits with level-sensitive latches, operation at a reduced clock period (higher clock frequency) is possible by takingadvantage of both non-zero clock skew scheduling and time borrowing. Clock skew schedulingis performed in order to exploit the benefits of nonidentical clock signal delays on circuit timing. The time borrowing property of level-sensitive circuits permits higher operating frequencies compared to edge-sensitivecircuits. Considering time borrowing in the timing analysis, however, introduces non-linearity in this timing analysis. The modified big M (MBM) method is defined in order to transform the non-linear constraints arising in the problem formulation into solvable linear constraints. Equivalent LP model problemsfor single-phase clock synchronization of the ISCAS'89 benchmark circuits are generated and these problems are solved by the industrial LP solver CPLEX. Through the simultaneous application of time borrowing and clock skew scheduling, up to 63% improvements are demonstrated in minimum clock period with respect to zero-skew edge-sensitive synchronous circuits. The timing constraints governing thelevel-sensitive synchronous circuit operation not only solve the clock period minimization problem but also provide a common framework for the general timing analysis of such circuits. The inclusion of additional constraints into the problem formulation in order to meet the timing requirements imposed by specific applicationenvironments is discussed

A 32-bit Ultrafast Parallel Correlator using Resonant Tunneling Devices

An ultrafast 32-bit pipeline correlator has been implemented using resonant tunneling diodes (RTD) and hetero-junction bipolar transistors (HBT). The negative differential resistance (NDR) characteristics of RTD's is the basis of logic gates with the self-latching property that eliminates pipeline area and delay overheads which limit throughput in conventional technologies. The circuit topology also allows threshold logic functions such as minority/majority to be implemented in a compact manner resulting in reduction of the overall complexity and delay of arbitrary logic circuits. The parallel correlator is an essential component in code division multi-access (CDMA) transceivers used for the continuous calculation of correlation between an incoming data stream and a PN sequence. Simulation results show that a nano-pipelined correlator can provide and effective throughput of one 32-bit correlation every 100 picoseconds, using minimal hardware, with a power dissipation of 1.5 watts. RTD plus HBT based logic gates have been fabricated and the RTD plus HBT based correlator is compared with state of the art complementary metal oxide semiconductor (CMOS) implementations

Empirical timing analysis of CPUs and delay fault tolerant design using partial redundancy

The operating clock frequency is determined by the longest signal propagation delay, setup/hold time, and timing margin. These are becoming less predictable with the increasing design complexity and process miniaturization. The difficult challenge is then to ensure that a device operating at its clock frequency is error-free with quantifiable assurance. Effort at device-level engineering will not suffice for these circuits exhibiting wide process variation and heightened sensitivities to operating condition stress. Logic-level redress of this issue is a necessity and we propose a design-level remedy for this timing-uncertainty problem. The aim of the design and analysis approaches presented in this dissertation is to provide framework, SABRE, wherein an increased operating clock frequency can be achieved. The approach is a combination of analytical modeling, experimental analy- sis, hardware /time-redundancy design, exception handling and recovery techniques. Our proposed design replicates only a necessary part of the original circuit to avoid high hardware overhead as in triple-modular-redundancy (TMR). The timing-critical combinational circuit is path-wise partitioned into two sections. The combinational circuits associated with long paths are laid out without any intrusion except for the fan-out connections from the first section of the circuit to a replicated second section of the combinational circuit. Thus only the second section of the circuit is replicated. The signals fanning out from the first section are latches, and thus are far shorter than the paths spanning the entire combinational circuit. The replicated circuit is timed at a subsequent clock cycle to ascertain relaxed timing paths. This insures that the likelihood of mistiming due to stress or process variation is eliminated. During the subsequent clock cycle, the outcome of the two logically identical, yet time-interleaved, circuit outputs are compared to detect faults. When a fault is detected, the retry sig- nal is triggered and the dynamic frequency-step-down takes place before a pipe flush, and retry is issued. The significant timing overhead associated with the retry is offset by the rarity of the timing violation events. Simulation results on ISCAS Benchmark circuits show that 10% of clock frequency gain is possible with 10 to 20 % of hardware overhead of replicated timing-critical circuit

Utilizing Magnetic Tunnel Junction Devices in Digital Systems

The research described in this dissertation is motivated by the desire to effectively utilize magnetic tunnel junctions (MTJs) in digital systems. We explore two aspects of this: (1) a read circuit useful for global clocking and magnetologic, and (2) hardware virtualization that utilizes the deeply-pipelined nature of magnetologic. In the first aspect, a read circuit is used to sense the state of an MTJ (low or high resistance) and produce a logic output that represents this state. With global clocking, an external magnetic field combined with on-chip MTJs is used as an alternative mechanism for distributing the clock signal across the chip. With magnetologic, logic is evaluated with MTJs that must be sensed by a read circuit and used to drive downstream logic. For these two uses, we develop a resistance-to-voltage (R2V) read circuit to sense MTJ resistance and produce a logic voltage output. We design and fabricate a prototype test chip in the 3 metal 2 poly 0.5 um process for testing the R2V read circuit and experimentally validating its correctness. Using a clocked low/high resistor pair, we show that the read circuit can correctly detect the input resistance and produce the desired square wave output. The read circuit speed is measured to operate correctly up to 48 MHz. The input node is relatively insensitive to node capacitance and can handle up to 10s of pF of capacitance without changing the bandwidth of the circuit. In the second aspect, hardware virtualization is a technique by which deeply-pipelined circuits that have feedback can be utilized. MTJs have the potential to act as state in a magnetologic circuit which may result in a deep pipeline. Streams of computation are then context switched into the hardware logic, allowing them to share hardware resources and more fully utilize the pipeline stages of the logic. While applicable to magnetologic using MTJs, virtualization is also applicable to traditional logic technologies like CMOS. Our investigation targets MTJs, FPGAs, and ASICs. We develop M/D/1 and M/G/1 queueing models of the performance of virtualized hardware with secondary memory using a fixed, hierarchical, round-robin schedule that predict average throughput, latency, and queue occupancy in the system. We develop three C-slow applications and calibrate them to a clock and resource model for FPGA and ASIC technologies. Last, using the M/G/1 model, we predict throughput, latency, and resource usage for MTJ, FPGA, and ASIC technologies. We show three design scenarios illustrating ways in which to use the model

A Framework for Verification of Signal Propagation Through Sequential Nanomagnet Logic Devices

Nanomagnet Logic is an emerging technology for low-power, highly-scalable implementation of quantum-dot cellular automata. Feedback permits reuse of logical subroutines, which is a desired functionality of any computational device. Determining whether feedback is feasible is essential to assessing the robustness of nanomagnet logic in any pipelined computing design. Therefore, development of a quantitative approach for verification of feedback paths is critical for development of design and synthesis tools for nanomagnet logic structures. In this paper, a framework for verification of sequential nanomagnet logic devices is presented. A set of definitions for canonical alignment and state definitions for NML paths are presented, as well as mathematical operations for determining the resulting states. The simulation results are presented for quantification of the NML magnetization angles for horizontal, vertical, negative-diagonal, and positive diagonal geometric alignments. The presented framework may be used as the basis for defining a representation of signal propagation for design and verification for robust NML devices and preventing deadlock resulting from improper implementation

Advanced Timing and Synchronization Methodologies for Digital VLSI Integrated Circuits

This dissertation addresses timing and synchronization methodologies that are critical to the design, analysis and optimization of high-performance, integrated digital VLSI systems. As process sizes shrink and design complexities increase, achieving timing closure for digital VLSI circuits becomes a significant bottleneck in the integrated circuit design flow. Circuit designers are motivated to investigate and employ alternative methods to satisfy the timing and physical design performance targets. Such novel methods for the timing and synchronization of complex circuitry are developed in this dissertation and analyzed for performance and applicability.Mainstream integrated circuit design flow is normally tuned for zero clock skew, edge-triggered circuit design. Non-zero clock skew or multi-phase clock synchronization is seldom used because the lack of design automation tools increases the length and cost of the design cycle. For similar reasons, level-sensitive registers have not become an industry standard despite their superior size, speed and power consumption characteristics compared to conventional edge-triggered flip-flops.In this dissertation, novel design and analysis techniques that fully automate the design and analysis of non-zero clock skew circuits are presented. Clock skew scheduling of both edge-triggered and level-sensitive circuits are investigated in order to exploit maximum circuit performances. The effects of multi-phase clocking on non-zero clock skew, level-sensitive circuits are investigated leading to advanced synchronization methodologies. Improvements in the scalability of the computational timing analysis process with clock skew scheduling are explored through partitioning and parallelization.The integration of the proposed design and analysis methods to the physical design flow of integrated circuits synchronized with a next-generation clocking technology-resonant rotary clocking technology-is also presented. Based on the design and analysis methods presented in this dissertation, a computer-aided design tool for the design of rotary clock synchronized integrated circuits is developed

Introduction to Logic Circuits & Logic Design with VHDL

The overall goal of this book is to fill a void that has appeared in the instruction of digital circuits over the past decade due to the rapid abstraction of system design. Up until the mid-1980s, digital circuits were designed using classical techniques. Classical techniques relied heavily on manual design practices for the synthesis, minimization, and interfacing of digital systems. Corresponding to this design style, academic textbooks were developed that taught classical digital design techniques. Around 1990, large-scale digital systems began being designed using hardware description languages (HDL) and automated synthesis tools. Broad-scale adoption of this modern design approach spread through the industry during this decade. Around 2000, hardware description languages and the modern digital design approach began to be taught in universities, mainly at the senior and graduate level. There were a variety of reasons that the modern digital design approach did not penetrate the lower levels of academia during this time. First, the design and simulation tools were difficult to use and overwhelmed freshman and sophomore students. Second, the ability to implement the designs in a laboratory setting was infeasible. The modern design tools at the time were targeted at custom integrated circuits, which are cost- and time-prohibitive to implement in a university setting. Between 2000 and 2005, rapid advances in programmable logic and design tools allowed the modern digital design approach to be implemented in a university setting, even in lower-level courses. This allowed students to learn the modern design approach based on HDLs and prototype their designs in real hardware, mainly field programmable gate arrays (FPGAs). This spurred an abundance of textbooks to be authored teaching hardware description languages and higher levels of design abstraction. This trend has continued until today. While abstraction is a critical tool for engineering design, the rapid movement toward teaching only the modern digital design techniques has left a void for freshman- and sophomore-level courses in digital circuitry. Legacy textbooks that teach the classical design approach are outdated and do not contain sufficient coverage of HDLs to prepare the students for follow-on classes. Newer textbooks that teach the modern digital design approach move immediately into high-level behavioral modeling with minimal or no coverage of the underlying hardware used to implement the systems. As a result, students are not being provided the resources to understand the fundamental hardware theory that lies beneath the modern abstraction such as interfacing, gate-level implementation, and technology optimization. Students moving too rapidly into high levels of abstraction have little understanding of what is going on when they click the “compile and synthesize” button of their design tool. This leads to graduates who can model a breadth of different systems in an HDL but have no depth into how the system is implemented in hardware. This becomes problematic when an issue arises in a real design and there is no foundational knowledge for the students to fall back on in order to debug the problem

Emerging Technologies - NanoMagnets Logic (NML)

In the last decades CMOS technology has ruled the electronic scenario thanks to the constant scaling of transistor sizes. With the reduction of transistor sizes circuit area decreases, clock frequency increases and power consumption decreases accordingly. However CMOS scaling is now approaching its physical limits and many believe that CMOS technology will not be able to reach the end of the Roadmap. This is mainly due to increasing difficulties in the fabrication process, that is becoming very expensive, and to the unavoidable impact of leakage losses, particularly thanks to gate tunnel current. In this scenario many alternative technologies are studied to overcome the limitations of CMOS transistors. Among these possibilities, magnetic based technologies, like NanoMagnet Logic (NML) are among the most interesting. The reason of this interest lies in their magnetic nature, that opens up entire new possibilities in the design of logic circuits, like the possibility to mix logic and memory in the same device. Moreover they have no standby power consumption and potentially a much lower power consumption of CMOS transistors. In literature NML logic is well studied and theoretical and experimental proofs of concept were already found. However two important points are not enough considered in the analysis approach followed by most of the work in literature. First of all, no complex circuits are analyzed. NML logic is very different from CMOS technologies, so to completely understand the potential of this technology it is mandatory to investigate complex architectures. Secondly, most of the solutions proposed do not take into account the constraints derived from fabrication process, making them unrealistic and difficult to be fabricated experimentally. This thesis focuses therefore on NML logic keeping into account these two important limitations in the research approach followed in literature. The aim is to obtain a complete and accurate overview of NML logic, finding realistic circuital solutions and trying to improve at the same time their performance. After a brief and complete introduction (Chapter 1), the thesis is divided in two parts, which cover the two fundamental points followed in this three years of research: A circuits architecture analysis and a technological analysis. In the architecture analysis first an innovative VHDL model is described in Chapter 2. This model is extensively used in the analysis because it allows fast simulation of complex circuits, with, at the same time, the possibility to estimate circuit per- formance, like area and power consumption. In Chapter 3 the problem of signals synchronization in complex NML circuits is analyzed and solved, using as benchmark a simple but complete NML microprocessor. Different solutions based on asynchronous logic are studied and a new asynchronous solution, specifically designed to exploit the potential of NML logic, is developed. In Chapter 4 the layout of NML circuits is studied on a more physical level, considering the limitations of fabrication processes. The layout of NML circuits is therefore changed accordingly to these constraints. Secondly CMOS circuits architectures are compared to more simple architectures, evaluating therefore which one is more suited for NML logic. Finally the problem of interconnections in NML technology is analyzed and solutions to improve it are found. In Chapter 5 the problem of feedback signals in heavy pipelined technologies, like NML, is studied. Solutions to improve performances and synchronize signals are developed. Systolic arrays are then analyzed as possible candidate to exploit NML potential. Finally in Chapter 6 ToPoliNano, a simulator dedicated to NML and other emerging technologies, that we are developing, is described. This simulator allows to follow the same top-down approach followed for CMOS technology. The layout generator and the simulation engine are detailed described. In the first chapter of the technological analysis (Chapter 7), the performance of NML logic is explored throughout low level simulations. The aim is to understand if these circuits can be fabricated with optical lithography, allowing therefore the commercial development of NML logic. Basic logic gates and the clock system are there analyzed from a low level perspective. In Chapter 8 an innovative electric clock system for NML technology is shown and the first experimental results are reported. This clock system allows to achieve true low power for NML technology, obtaining a reduction of power consumption of 20 times considering the best CMOS transistors available. This power consumption takes into account all the losses, also the clock system losses. Moreover the solution presented can be fabricated with current technological processes. The research work behind this thesis represents an important breakthrough in NML logic. The solutions here presented allow the design and fabrication of complex NML circuits, considering the particular characteristics of this technology and considerably improving the performance. Moreover the technological solutions here presented allow the design and fabrication of circuits with available fabrication process with a considerable advantage over CMOS in terms of power consumption. This thesis represents therefore a considerable step froward in the study and development of NML technolog

Superconducting Logic Circuits Operating With Reciprocal Magnetic Flux Quanta

Complimentary Medal-Oxide Semiconductor (CMOS) technology is expected to soon reach its fundamental limits of operation. The fundamental speed limit of about 4 GHz has already effectively been sidestepped by parallelization. This increases raw processing power but does nothing to improve power dissipation or latency. One approach for increasing computing performance involves using superconducting digital logic circuits. In this thesis I describe a new kind of superconducting logic, invented by Quentin Herr at Northrop Grumman, which uses reciprocal pairs of quantized single magnetic flux pulses to encode classical bits. In Reciprocal Quantum Logic (RQL) the data is encoded in integer units of the magnetic flux quantum. RQL gates operate without the bias resistors of previous superconducting logic families and dissipate several orders of magnitude less power. I demonstrate the basic operation of key RQL gates (AndOr, AnotB, Set/Reset) and show their self-resetting properties. Together, these gates form a universal logic set and provide memory capabilities. Experiments measuring the bit error rate of the AndOr gate extrapolated a minimum BER of 10-480 and a BER of 10-44 with 30% margins on flux biasing. I describe an analytic timing model for RQL gates which demonstrates the self-correcting timing features. From this model I derive equations for the timing behavior and operating limits. Using this timing model I ran simulations to determine correction factions for more accurate predictions at higher frequencies. Using these results, I also develop Very High Speed Integrated Circuit (VHSIC) Hardware Description Language (VHDL) models to describe the combinational logic of RQL gates. To test the timing predictions of the timing model, I performed three experiments on Nb/AlOx/Nb circuits at 4.2 K. The first measured the time of output. The second measured the operating margins of the circuit. The third measured the maximum frequency of operation for RQL circuits. Together, these three experiments showed quantitative agreement with the model for the timing output, qualitative agreement with the limits of operation, and a projected speed limit of 50 GHz for the Hypres 4.5 kA/cm2 process. To power RQL circuits I describe a new design for power splitters and combiners which minimize standing waves. I describe a new kind of Wilkinson power splitter which required numerical optimization but proved to be adequate. I experimentally tested two new designs of the power splitter. Both showed less than 10% variation in standing waves between power splitter and combiner, making it adequate for RQL circuits. I also compared these results with the S-parameters of the power network, which also indicated that the design was adequate for RQL circuits. Finally, I tested an 8-bit Kogge-Stone architecture carry-look ahead adder designed using VHDL models. The adder contained 815 Josephson junctions and was fully functional at 6.21 GHz with a latency of 1.25 clock cycles. The adder produced the correct logical output, had a measured optimal operating point within 8% of the optimal simulated operating point, and measured power margins of 1 dB. It operated best at the designed clock amplitude of 0.88Ic and dissipated 0.570 mW of power

Introduction to Logic Circuits & Logic Design with Verilog

The overall goal of this book is to fill a void that has appeared in the instruction of digital circuits over the past decade due to the rapid abstraction of system design. Up until the mid-1980s, digital circuits were designed using classical techniques. Classical techniques relied heavily on manual design practices for the synthesis, minimization, and interfacing of digital systems. Corresponding to this design style, academic textbooks were developed that taught classical digital design techniques. Around 1990, large-scale digital systems began being designed using hardware description languages (HDL) and automated synthesis tools. Broad-scale adoption of this modern design approach spread through the industry during this decade. Around 2000, hardware description languages and the modern digital design approach began to be taught in universities, mainly at the senior and graduate level. There were a variety of reasons that the modern digital design approach did not penetrate the lower levels of academia during this time. First, the design and simulation tools were difficult to use and overwhelmed freshman and sophomore students. Second, the ability to implement the designs in a laboratory setting was infeasible. The modern design tools at the time were targeted at custom integrated circuits, which are cost- and time-prohibitive to implement in a university setting. Between 2000 and 2005, rapid advances in programmable logic and design tools allowed the modern digital design approach to be implemented in a university setting, even in lower-level courses. This allowed students to learn the modern design approach based on HDLs and prototype their designs in real hardware, mainly fieldprogrammable gate arrays (FPGAs). This spurred an abundance of textbooks to be authored, teaching hardware description languages and higher levels of design abstraction. This trend has continued until today. While abstraction is a critical tool for engineering design, the rapid movement toward teaching only the modern digital design techniques has left a void for freshman- and sophomore-level courses in digital circuitry. Legacy textbooks that teach the classical design approach are outdated and do not contain sufficient coverage of HDLs to prepare the students for follow-on classes. Newer textbooks that teach the modern digital design approach move immediately into high-level behavioral modeling with minimal or no coverage of the underlying hardware used to implement the systems. As a result, students are not being provided the resources to understand the fundamental hardware theory that lies beneath the modern abstraction such as interfacing, gate-level implementation, and technology optimization. Students moving too rapidly into high levels of abstraction have little understanding of what is going on when they click the “compile and synthesize” button of their design tool. This leads to graduates who can model a breadth of different systems in an HDL but have no depth into how the system is implemented in hardware. This becomes problematic when an issue arises in a real design and there is no foundational knowledge for the students to fall back on in order to debug the problem