FPGA Architecture Optimization Using Geometric Programming

Volume 4 No 13 of the periodical Progression. Published November, February, May and August by The Radiant Healing Centre. SPCL PER BT 732 P76 V.1,1932-V.5,193

Yield-driven power-delay-optimal CMOS full-adder design complying with automotive product specifications of PVT variations and NBTI degradations

We present the detailed results of the application of mathematical optimization algorithms to transistor sizing in a full-adder cell design, to obtain the maximum expected fabrication yield. The approach takes into account all the fabrication process parameter variations specified in an industrial PDK, in addition to operating condition range and NBTI aging. The final design solutions present transistor sizing, which depart from intuitive transistor sizing criteria and show dramatic yield improvements, which have been verified by Monte Carlo SPICE analysis

Robust Resource Allocations in Temporal Networks

Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper, we study a robust resource allocation problem where the functional relationship between task durations and resource assignments is uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically NP-hard. We then develop convergent bounds for the optimal objective value, as well as feasible allocations whose objective values are bracketed by these bounds. Numerical results provide empirical support for the proposed method.Robust Optimisation, Temporal Networks, Resource Allocation Problem

Technology Independent Synthesis of CMOS Operational Amplifiers

Analog circuit design does not enjoy as much automation as its digital counterpart. Analog sizing is inherently knowledge intensive and requires accurate modeling of the different parametric effects of the devices. Besides, the set of constraints in a typical analog design problem is large, involving complex tradeoffs. For these reasons, the task of modeling an analog design problem in a form viable for automation is much more tedious than the digital design. Consequently, analog blocks are still handcrafted intuitively and often become a bottleneck in the integrated circuit design, thereby increasing the time to market. In this work, we address the problem of automatically solving an analog circuit design problem. Specifically, we propose methods to automate the transistor-level sizing of OpAmps. Given the specifications and the netlist of the OpAmp, our methodology produces a design that has the accuracy of the BSIM models used for simulation and the advantage of a quick design time. The approach is based on generating an initial first-order design and then refining it. In principle, the refining approach is a simulated-annealing scheme that uses (i) localized simulations and (ii) convex optimization scheme (COS). The optimal set of input variables for localized simulations has been selected by using techniques from Design of Experiments (DOE). To formulate the design problem as a COS problem, we have used monomial circuit models that are fitted from simulation data. These models accurately predict the performance of the circuit in the proximity of the initial guess. The models can also be used to gain valuable insight into the behavior of the circuit and understand the interrelations between the different performance constraints. A software framework that implements this methodology has been coded in SKILL language of Cadence. The methodology can be applied to design different OpAmp topologies across different technologies. In other words, the framework is both technology independent and topology independent. In addition, we develop a scheme to empirically model the small signal parameters like \u27gm\u27 and \u27gds\u27 of CMOS transistors. The monomial device models are reusable for a given technology and can be used to formulate the OpAmp design problem as a COS problem. The efficacy of the framework has been demonstrated by automatically designing different OpAmp topologies across different technologies. We designed a two-stage OpAmp and a telescopic OpAmp in TSMC025 and AMI016 technologies. Our results show significant (10–15%) improvement in the performance of both the OpAmps in both the technologies. While the methodology has shown encouraging results in the sub-micrometer regime, the effectiveness of the tool has to be investigated in the deep-sub-micron technologies

Discrete Gate Sizing Methodologies for Delay, Area and Power Optimization

The modeling of an individual gate and the optimization of circuit performance has long been a critical issue in the VLSI industry. In this work, we first study of the gate sizing problem for today\u27s industrial designs, and explore the contributions and limitations of all the existing approaches, which mainly suffer from producing only continuous solutions, using outdated timing models or experiencing performance inefficiency. In this dissertation, we present our new discrete gate sizing technique which optimizes different aspects of circuit performance, including delay, area and power consumption. And our method is fast and efficient as it applies the local search instead of global exhaustive search during gate size selection process, which greatly reduces the search space and improves the computation complexity. In addition to that, it is also flexible with different timing models, and it is able to deal with the constraints of input/output slew and output load capacitance, under which very few previous research works were reported. We then propose a new timing model, which is derived from the classic Elmore delay model, but takes the features of modern timing models from standard cell library. With our new timing model, we are able to formulate the combinatorial discrete sizing problem as a simplified mathematical expression and apply it to existing Lagrangian relaxation method, which is shown to converge to optimal solution. We demonstrate that the classic Elmore delay model based gate sizing approaches can still be valid. Therefore, our work might provide a new look into the numerous Elmore delay model based research works in various areas (such as placement, routing, layout, buffer insertion, timing analysis, etc.)

Nanometer VLSI placement and optimization for multi-objective design closure

In a VLSI physical synthesis flow, placement directly defines the interconnection, which affects many other design objectives, such as timing, power consumption, congestion, and thermal issues. With the scaling of technology, the relative interconnect delay increases dramatically. As a result, placement has become a bottleneck in deep sub-micron physical synthesis. In this dissertation, I propose several optimization algorithms from global placement, placement migration, timing driven placements, to incremental power optimizations for multi-objective VLSI design closure. The first work is DPlace, a new global placement algorithm that scales well to the modern large-scale circuit placement problems. DPlace simulates the natural diffusion process to spread cells smoothly over the placement region, and uses both analytical and discrete techniques to improve the wire length. However, global placement is never sufficient for multi-objective design closure, a variety of design objectives have to be improved incrementally, such as timing, routing congestion, signal integrity, and heat distribution. Placement migration is a critical step to address the cell overlaps appearing during incremental optimizations. To achieve high placement stability, I propose a computational geometry based placement migration flow to cope with placement changes, and a new stability metric to measure the “similarity” between two placements accurately. Our placement migration algorithm has clear advantage over conventional legalization algorithms such that the neighborhood characteristics of the original placement are preserved. For timing closure in high performance designs, I present a linear programming based incremental timing driven placement to improve the timing on critical paths directly. I further present an efficient timing driven placement algorithm (Pyramids). Two formulations of Pyramids are proposed, which are suitable for different optimization stages in a physical synthesis flow. Both approaches find the optimal location for timing of a cell in constant time, through computational geometry based approaches. For fast convergence of design closure, placement should be integrated with other optimization techniques. I propose to combine placement, gate sizing and Vt swapping techniques to reduce the total power consumption, especially the leakage power, which is becoming increasingly critical for nanometer VLSI design closure.Electrical and Computer Engineerin

Diseño de circuitos analógicos y de señal mixta con consideraciones de diseño físico y variabilidad

Advances in microelectronic technology has been based on an increasing capacity to integrate transistors, moving this industry to the nanoelectronics realm in recent years. Moore’s Law [1] has predicted (and somehow governed) the growth of the capacity to integrate transistors in a single IC. Nevertheless, while this capacity has grown steadily, the increasing number of design tasks that are involved in the creation of the integrated circuit and their complexity has led to a phenomenon known as the ``design gap´´. This is the difference between what can theoretically be integrated and what can practically be designed. Since the early 2000s, the International Technology Roadmap of Semiconductors (ITRS) reports, published by the Semiconductor Industry Association (SIA), alert about the necessity to limit the growth of the design cost by increasing the productivity of the designer to continue the semiconductor industry’s growth. Design automation arises as a key element to close this ”design gap”. In this sense, electronic design automation (EDA) tools have reached a level of maturity for digital circuits that is far behind the EDA tools that are made for analog circuit design automation. While digital circuits rely, in general, on two stable operation states (which brings inherent robustness against numerous imperfections and interferences, leading to few design constraints like area, speed or power consumption), analog signal processing, on the other hand, demands compliance with lots of constraints (e.g., matching, noise, robustness, ...). The triumph of digital CMOS circuits, thanks to their mentioned robustness, has, ultimately, facilitated the way that circuits can be processed by algorithms, abstraction levels and description languages, as well as how the design information traverse the hierarchical levels of a digital system. The field of analog design automation faces many more difficulties due to the many sources of perturbation, such as the well-know process variability, and the difficulty in treating these systematically, like digital tools can do. In this Thesis, different design flows are proposed, focusing on new design methodologies for analog circuits, thus, trying to close the ”gap” between digital and analog EDA tools. In this chapter, the most important sources for perturbations and their impact on the analog design process are discussed in Section 1.2. The traditional analog design flow is discussed in 1.3. Emerging design methodologies that try to reduce the ”design gap” are presented in Section 1.4 where the key concept of Pareto-Optimal Front (POF) is explained. This concept, brought from the field of economics, models the analog circuit performances into a set of solutions that show the optimal trade-offs among conflicting circuit performances (e.g. DC-gain and unity-gain frequency). Finally, the goals of this thesis are presented in Section 1.5

Statistical timing analysis via modern optimization lens

We formulate statistical static timing analysis (SSTA) as a mixed-integer program and as a geometric program, utilizing histogram approximations of the random variables involved. The geometric-programming approach scales linearly with the number of gates and quadratically with the number of bins in the histogram. This translates, for example, to solving the SSTA for a circuit of 400 gates with 30 bins per each histogram approximation of a random variable in 440 seconds.Comment: 23 pages, 7 figure

Analog circuit optimization using evolutionary algorithms and convex optimization

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 83-88).In this thesis, we analyze state-of-art techniques for analog circuit sizing and compare them on various metrics. We ascertain that a methodology which improves the accuracy of sizing without increasing the run time or the designer effort is a contribution. We argue that the accuracy of geometric programming can be improved without adversely influencing the run time or increasing the designer's effort. This is facilitated by decomposition of geometric programming modeling into two steps, which decouples accuracy of models and run-time of geometric programming. We design a new algorithm for producing accurate posynomial models for MOS transistor parameters, which is the first step of the decomposition. The new algorithm can generate posynomial models with variable number of terms and real-valued exponents. The algorithm is a hybrid of a genetic algorithm and a convex optimization technique. We study the performance of the algorithm on artificially created benchmark problems. We show that the accuracy of posynomial models of MOS parameters is improved by a considerable amount by using the new algorithm. The new posynomial modeling algorithm can be used in any application of geometric programming and is not limited to MOS parameter modeling. In the last chapter, we discuss various ideas to improve the state-of-art in circuit sizing.by Varun Aggarwal.S.M