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

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

Fast algorithms for retiming large digital circuits

The increasing complexity of VLSI systems and shrinking time to market requirements demand good optimization tools capable of handling large circuits. Retiming is a powerful transformation that preserves functionality, and can be used to optimize sequential circuits for a wide range of objective functions by judiciously relocating the memory elements. Leiserson and Saxe, who introduced the concept, presented algorithms for period optimization (minperiod retiming) and area optimization (minarea retiming). The ASTRA algorithm proposed an alternative view of retiming using the equivalence between retiming and clock skew optimization;The first part of this thesis defines the relationship between the Leiserson-Saxe and the ASTRA approaches and utilizes it for efficient minarea retiming of large circuits. The new algorithm, Minaret, uses the same linear program formulation as the Leiserson-Saxe approach. The underlying philosophy of the ASTRA approach is incorporated to reduce the number of variables and constraints in this linear program. This allows minarea retiming of circuits with over 56,000 gates in under fifteen minutes;The movement of flip-flops in control logic changes the state encoding of finite state machines, requiring the preservation of initial (reset) states. In the next part of this work the problem of minimizing the number of flip-flops in control logic subject to a specified clock period and with the guarantee of an equivalent initial state, is formulated as a mixed integer linear program. Bounds on the retiming variables are used to guarantee an equivalent initial state in the retimed circuit. These bounds lead to a simple method for calculating an equivalent initial state for the retimed circuit;The transparent nature of level sensitive latches enables level-clocked circuits to operate faster and require less area. However, this transparency makes the operation of level-clocked circuits very complex, and optimization of level-clocked circuits is a difficult task. This thesis also presents efficient algorithms for retiming large level-clocked circuits. The relationship between retiming and clock skew optimization for level-clocked circuits is defined and utilized to develop efficient retiming algorithms for period and area optimization. Using these algorithms a circuit with 56,000 gates could be retimed for minimum period in under twenty seconds and for minimum area in under 1.5 hours

Mix & Latch: An Optimization Flow for High-Performance Designs with Single-Clock Mixed-Polarity Latches and Flip-Flops

Flip-flops are the most used sequential elements in synchronous circuits, but designs based on latches can operate at higher frequencies and occupy less area. Techniques to increase the maximum operating frequency of flip-flop based designs, such as time-borrowing, rely on tight hold constraints that are difficult to satisfy using traditional back-end optimization techniques. We propose Mix & Latch , a methodology to increase the operating frequency of synchronous digital circuits using a single clock tree and a mixed distribution of positive- and negative-edge-triggered flops, and positive- and negative-level-sensitive latches. An efficient mathematical model is proposed to optimize the type and location of the sequential elements of the circuit. We ensure that the initial registers are not moved from their initial location, although they may change type, thus allowing the use of equivalence checking and static timing analysis to verify formally the correctness of the transformation. The technique is validated using a 28nm CMOS FDSOI technology, obtaining 1.33X post-layout average operating frequency improvement on a broad set of benchmarks over a standard commercial design flow. Additionally, the circuit area was also reduced by more than 1.19X on average for the same benchmarks, although the overall area reduction is not a goal of the optimization algorithm. To the best of our knowledge, this is the first work that proposes combining mixed-polarity flip-flops and latches to improve the circuit performance

Design for testability of a latch-based design

Abstract. The purpose of this thesis was to decrease the area of digital logic in a power management integrated circuit (PMIC), by replacing selected flip-flops with latches. The thesis consists of a theory part, that provides background theory for the thesis, and a practical part, that presents a latch register design and design for testability (DFT) method for achieving an acceptable level of manufacturing fault coverage for it. The total area was decreased by replacing flip-flops of read-write and one-time programmable registers with latches. One set of negative level active primary latches were shared with all the positive level active latch registers in the same register bank. Clock gating was used to select which latch register the write data was loaded to from the primary latches. The latches were made transparent during the shift operation of partial scan testing. The observability of the latch register clock gating logic was improved by leaving the first bit of each latch register as a flip-flop. The controllability was improved by inserting control points. The latch register design, developed in this thesis, resulted in a total area decrease of 5% and a register bank area decrease of 15% compared to a flip-flop-based reference design. The latch register design manages to maintain the same stuck-at fault coverage as the reference design.Salpaperäisen piirin testattavuuden suunnittelu. Tiivistelmä. Tämän opinnäytetyön tarkoituksena oli pienentää digitaalisen logiikan pinta-alaa integroidussa tehonhallintapiirissä, korvaamalla valitut kiikut salpapiireillä. Opinnäytetyö koostuu teoriaosasta, joka antaa taustatietoa opinnäytetyölle, ja käytännön osuudesta, jossa esitellään salparekisteripiiri ja testattavuussuunnittelun menetelmä, jolla saavutettiin riittävän hyvä virhekattavuus salparekisteripiirille. Kokonaispinta-alaa pienennettiin korvaamalla luku-kirjoitusrekistereiden ja kerran ohjelmoitavien rekistereiden kiikut salpapiireillä. Yhdet negatiivisella tasolla aktiiviset isäntä-salpapiirit jaettiin kaikkien samassa rekisteripankissa olevien positiivisella tasolla aktiivisten salparekistereiden kanssa. Kellon portittamisella valittiin mihin salparekisteriin kirjoitusdata ladattiin yhteisistä isäntä-salpapireistä. Osittaisessa testipolkuihin perustuvassa testauksessa salpapiirit tehtiin läpinäkyviksi siirtooperaation aikana. Salparekisterin kellon portituslogiikan havaittavuutta parannettiin jättämällä jokaisen salparekisterin ensimmäinen bitti kiikuksi. Ohjattavuutta parannettiin lisäämällä ohjauspisteitä. Salparekisteripiiri, joka suunniteltiin tässä diplomityössä, pienensi kokonaispinta-alaa 5 % ja rekisteripankin pinta-alaa 15 % verrattuna kiikkuperäiseen vertailupiiriin. Salparekisteripiiri onnistuu pitämään saman juuttumisvikamallin virhekattavuuden kuin vertailupiiri

Power Reductions with Energy Recovery Using Resonant Topologies

The problem of power densities in system-on-chips (SoCs) and processors has become more exacerbated recently, resulting in high cooling costs and reliability issues. One of the largest components of power consumption is the low skew clock distribution network (CDN), driving large load capacitance. This can consume as much as 70% of the total dynamic power that is lost as heat, needing elaborate sensing and cooling mechanisms. To mitigate this, resonant clocking has been utilized in several applications over the past decade. An improved energy recovering reconfigurable generalized series resonance (GSR) solution with all the critical support circuitry is developed in this work. This LC resonant clock driver is shown to save about 50% driver power (\u3e40% overall), on a 22nm process node and has 50% less skew than a non-resonant driver at 2GHz. It can operate down to 0.2GHz to support other energy savings techniques like dynamic voltage and frequency scaling (DVFS). As an example, GSR can be configured for the simpler pulse series resonance (PSR) operation to enable further power saving for double data rate (DDR) applications, by using de-skewing latches instead of flip-flop banks. A PSR based subsystem for 40% savings in clocking power with 40% driver active area reduction xii is demonstrated. This new resonant driver generates tracking pulses at each transition of clock for dual edge operation across DVFS. PSR clocking is designed to drive explicit-pulsed latches with negative setup time. Simulations using 45nm IBM/PTM device and interconnect technology models, clocking 1024 flip-flops show the reductions, compared to non-resonant clocking. DVFS range from 2GHz/1.3V to 200MHz/0.5V is obtained. The PSR frequency is set \u3e3× the clock rate, needing only 1/10th the inductance of prior-art LC resonance schemes. The skew reductions are achieved without needing to increase the interconnect widths owing to negative set-up times. Applications in data circuits are shown as well with a 90nm example. Parallel resonant and split-driver non-resonant configurations as well are derived from GSR. Tradeoffs in timing performance versus power, based on theoretical analysis, are compared for the first time and verified. This enables synthesis of an optimal topology for a given application from the GSR

High-Speed and Low-Energy On-Chip Communication Circuits.

Continuous technology scaling sharply reduces transistor delays, while fixed-length global wire delays have increased due to less wiring pitch with higher resistance and coupling capacitance. Due to this ever growing gap, long on-chip interconnects pose well-known latency, bandwidth, and energy challenges to high-performance VLSI systems. Repeaters effectively mitigate wire RC effects but do little to improve their energy costs. Moreover, the increased complexity and high level of integration requires higher wire densities, worsening crosstalk noise and power consumption of conventionally repeated interconnects. Such increasing concerns in global on-chip wires motivate circuits to improve wire performance and energy while reducing the number of repeaters. This work presents circuit techniques and investigation for high-performance and energy-efficient on-chip communication in the aspects of encoding, data compression, self-timed current injection, signal pre-emphasis, low-swing signaling, and technology mapping. The improved bus designs also consider the constraints of robust operation and performance/energy gains across process corners and design space. Measurement results from 5mm links on 65nm and 90nm prototype chips validate 2.5-3X improvement in energy-delay product.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75800/1/jseo_1.pd

Design methodology and productivity improvement in high speed VLSI circuits

2017 Spring.Includes bibliographical references.To view the abstract, please see the full text of the document