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Technology scaling in the nanometer era has increased the transistor's susceptibility to process variations. The effects of such variations are having a huge impact on the yield of the integrated circuits and need to be considered early in the design flow. Traditional corner based deterministic methods are no longer effective and circuit optimization methods require reinvention with a statistical perspective. In this paper, we propose a new gate sizing algorithm using fuzzy linear programming in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay which is a function of the gate sizes and the fan-outs of the gates are represented using triangular fuzzy numbers with linear membership functions. Initially, as a preprocessing step for fuzzy optimization, we perform deterministic optimizations by fixing the fuzzy parameters to the worst and the average case values, the results of which are used to convert the fuzzy optimization problem into a crisp nonlinear problem. The crisp problem with delay and power as constraints is then formulated to maximize the robustness, i.e., the variation resistance of the circuit. The fuzzy optimization approach was tested on ITC'99 benchmark circuits and the results were validated for timing yield using Monte Carlo simulations. The proposed approach is shown to achieve better power reduction than the worst case deterministic optimization as well as the stochastic programming based gate sizing methods, while having comparable runtimes.

In the nanometer era, process, voltage, and temperature variations are dominating circuit performance, power, and yield. Over the past few years, statistical optimization methods have been effective in improving yield in the presence of uncertainty due to process variations. However, statistical methods overconsume resources, even in the absence of variations. Hence, to facilitate a better performance-power-yield trade-off, techniques that can dynamically enable variation compensation are becoming necessary. In this article, we propose a dynamic technique that controls the instance of data capture in critical path memory flops, by delaying the clock edge trigger. The methodology employs a dynamic delay detection circuit to identify the uncertainty in delay due to variations and stretches the clock in the destination flip-flops. The delay detection circuit uses a latch and set of combinational gates to dynamically detect and create the slack needed to accommodate the delay due to variations. The Clock Stretching Logic (CSL) is added only to paths, which have a high probability of failure in the presence of variations. The proposed methodology improves the timing yield of the circuit without significant overcompensation. The methodology approach was simulated using Synopsys design tools for circuit synthesis and Cadence tools for placement and routing of the design. Extraction of parasitic of timing information was parsed using Perl scripts and simulated using a simulation program generated in C++. Experimental results based on Monte-Carlo simulations on benchmark circuits indicate considerable improvement in timing yield with negligible area overhead.

Logarithmic Number Systems (LNS) offer a viable alternative in terms of area, delay and power to binary number systems for multiplication and division operations in signalprocessing. The Mitchell Algorithm (MA) proposed in [9], is a simple and low cost approach commonly used for logarithmic multiplication. However, the method involves high error due to piecewise straight line approximation of the logarithm curve. Several methods have been proposed in the literature for improving the accuracy of Mitchell's Algorithm. In this paper, we propose a new method for improving the accuracy of MA using Operand Decomposition (OD). The OD process decreases the number of bits with the value of '1' in the multiplicands and reduces the amount of approximation. The proposed method decreases the error percentage of the Mitchell Algorithm by 44.7% on the average. Since the proposed method does not require any correction term it can be used in combination with other methods for improving the accuracy of the MA based multiplier. Experimental results are presented for random input data, signal and image processing applications, which clearly indicate that the proposed method significantly outperforms previous methods proposed in the literature.