Abstract not found

We propose to use the dominant time constant of a resistor-capacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interesting design problems as convex optimization problems, specifically, semidefinite programs (SDPs). For example, assuming that the conductances and capacitances are affine functions of the design parameters (which is a common model in transistor or interconnect wire sizing), one can minimize the power consumption or the area subject to an upper bound on the dominant time constant, or compute the optimal tradeoff surface between power, dominant time constant, and area. We will also note that, to a certain extent, convex optimization can be used to design the topology of the interconnect wires. This approach has two advantages over methods based on Elmore delay optimization. First, it handles a far wider class of circuits, e.g., those with non-grounded capacitors. Second, it always results in convex optimization problems for which very efficient interiorpoint methods have recently been developed. We illustrate the method, and extensions, with several examples involving optimal wire and transistor sizing.

An algorithm for unifying the techniques of gate sizing and clockskew optimization for acyclic pipelines is presented in this paper. In the design of circuits under very tight timing specifications, the area overhead of gate sizing can be considerable. The procedure utilizes the idea of cycle-borrowing using clock skew optimization to relax the stringency of the timing specification on the critical stages of the pipeline. Experimental results verify that cycle-borrowing using sizing+skew results in a better overall area-delay tradeoff than with sizing alone.

Vdd-programmable FPGAs have been proposed recently to reduce FPGA power, where Vdd levels can be customized for different circuit elements and unused circuit elements can be power-gated. In this paper, we first develop an accurateFPGApowermodelandthendesignnovelVddprogrammable interconnect switches with minimum number of configuration SRAM cells. Applying our power model to placed and routed benchmark circuits, we evaluate Vddprogrammable FPGA architecture using the new switches. The best architecture in our study uses Vdd-programmable logic blocks and Vdd-gateable interconnects. Compared to the baseline architecture similar to the leading commercial architecture, the best architecture reduces the minimal energy-delay product by 44.14 % with 48 % area overhead and 3 % SRAM cell increase. Our evaluation results also show that LUT size 4 always gives the lowest energy consumption while LUT size 7 always leads to the highest performance for all evaluated architectures.

Buffer insertion is a technique that is used either to increase the driving power of a path in a circuit, or to isolate large capacitive loads that lie on noncritical or less critical paths. Gate sizing sets the sizes of gates within a circuit to achieve a given timing specification. Traditional design techniques perform gate sizing and buffer insertion as two separate and independent steps during synthesis. However, until sizing is performed, any information on capacitive loads is incomplete and therefore a buffer insertion algorithm must operate with incomplete information, leading to suboptimal results. Moreover, the insertion of buffers can change the structure of the circuit sufficiently so that it may lead to a different sizing solution from the unbuffered circuit. Therefore, these techniques of buffer insertion and sizing are intimately linked and it makes a lot of sense to integrate them into a single optimization. This work presents strategies to insert buffers in a circuit, combined with gate sizing, to achieve better power-delay and area-delay tradeoffs. The purpose of this work is to examine how combining sizing algorithm with buffer insertion will help us achieve better area-delay or power-delay tradeoffs, and to determine where and when to insert buffers in a circuit. The delay model incorporates placement-based information and the effect of input slew rates on gate delays. The results obtained by using the new method are significantly better than the results

Abstract — We propose a transistor sizing method that downsizes MOSFETs inside a cell to eliminate redundancy of cell-based circuits as much as possible. Our method reduces power dissipation of detail-routed circuits while preserving interconnects. The effectiveness of our method is experimentally evaluated using 5 circuits. The power dissipation is reduced by 77 % maximum and 65 % on average without delay increase. I.

The problem of sizing gates for power-delay tradeoffs is of great interest to designers. In this work, the theoretical basis for gate sizing under delay and power considerations is presented, and results on a practical implementation are presented. The dynamic power as well as the short-circuit power are modeled, using notions of delay and transition density, and the optimization problem is formulated using notions of convex programming. Previous approaches have not modeled the short circuit power, and our experimental results show that the incorporation of this leads to counter-intuitive results where the minimumpower circuit is not necessarily the minimum-sized circuit.

As technology continues to scale beyond 100nm, there is a significant increase in performance uncertainty of CMOS logic due to process and environmental variations. Traditional circuit optimization methods assuming deterministic gate delays produce a flat “wall ” of equally critical paths, resulting in variation-sensitive designs. This paper describes a new method for sizing of digital circuits, with uncertain gate delays, to minimize their performance variation leading to a higher parametric yield. The method is based on adding margins on each gate delay to account for variations and using a new “soft maximum ” function to combine path delays at converging nodes. PSfrag Using replacements analytic models to predict the means and standard deterministic deviations method of gate delays as posynomial functions of the device sizes, PDF we create a simple, computationally efficient heuristic for uncertainty-aware sizing of digital circuits via Geometric Programming. Monte-Carlo simulations on custom 32bit adders and ISCAS’85 benchmarks show that about 10 % to 20 % delay reduction over deterministic sizing methods can be achieved, without any additional cost in area. 1.

Process variations result in a considerable spread in the frequency of the fabricated chips. In high performance applications, those chips that fail to meet the nominal frequency after fabrication are either discarded or sold at a loss which is typically proportional to the degree of timing violation. The latter is called binning. In this paper we present a gate sizing-based algorithm that optimally minimizes the binning yield-loss. We make the following contributions: 1) prove the binning yield function to be convex, 2) do not make any assumptions about the sources of variability, and their distribution model, 3) we integrate our strategy with statistical timing analysis tools (STA), without making any assumptions about how STA is done, 4) if the objective is to optimize the traditional yield (and not binning yield) our approach can still optimize the same to a very large extent. Comparison of our approach with sensitivity-based approaches under fabrication variability shows an improvement of on average 72 % in the binning yield-loss with an area overhead of an average 6%, while achieving a 2.69 times speedup under a stringent timing constraint. Moreover we show that a worstcase deterministic approach fails to generate a solution for certain delay constraints. We also show that optimizing the binning yield-loss minimizes the traditional yield-loss with a 61 % improvement from a sensitivity-based approach.

The problem of power-delay tradeoffs in transistor sizing is examined using a nonlinear optimization formulation. Both the dynamic and the short-circuit power are considered, and a new modeling technique is used to calculate the short-circuit power. The notion of transition density is used, with an enhancement that considers the effect of gate delays on the transition density. When the short-circuit power is neglected, the minimum power circuit is identical to the minimum area circuit. However, under our more realistic models, our experimental results on several circuits show that the minimum power circuit is not necessarily the same as the minimum area circuit.