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An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization
 IEEE Transactions on ComputerAided Design
, 1993
"... this paper. Given the MOS circuit topology, the delay can be controlled byvarying the sizes of transistors in the circuit. Here, the size of a transistor is measured in terms of its channel width, since the channel lengths in a digital circuit are generally uniform. Roughly speaking, the sizes of ..."
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Cited by 117 (20 self)
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this paper. Given the MOS circuit topology, the delay can be controlled byvarying the sizes of transistors in the circuit. Here, the size of a transistor is measured in terms of its channel width, since the channel lengths in a digital circuit are generally uniform. Roughly speaking, the sizes of certain transistors can be increased to reduce the circuit delay at the expense of additional chip area
Gate Sizing for Constrained delay/power/area optimization
 in IEEE Transcation on VLSI Design
, 1997
"... Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to mini ..."
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Cited by 43 (1 self)
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Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to minimize the power consumption and/or the area of a circuit under some userdefined delay constraints, or to obtain the fastest circuit within a given power budget. Although this technologydependent optimization has been investigated for years, the proposed approaches sometimes rely on assumptions, cost models, or algorithms that make them unrealistic or impossible to apply on reallife large circuits. We discusse here a gate sizing algorithm (GS), and show how it is used to achieve constrained optimization. It can be applied on large circuits within a reasonable CPU time, e.g., minimizing the power of a 10000 nodes circuit under some delay constraint in 2 hours. Keywords—Gate sizing, discrete constrained optimization, delay/power/area tradeoff I.
New Algorithms for Gate Sizing: A Comparative Study
 IN DAC
, 1996
"... Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing alg ..."
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Cited by 40 (1 self)
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Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing algorithms targeting discrete, nonlinear, nonunimodal, constrained optimization. The goal is to overcome the nonlinearity and nonunimodality of the delay and the power to achieve good quality results within a reasonable CPU time, e.g., handling a 10000 node network in 2 hours. We compare the five algorithms on constraint free delay optimization and delay constrained power optimization, and show that one method is superior to the others.
Gate Sizing Using Lagrangian Relaxation Combined with a Fast GradientBased PreProcessing Step
 Proc. ICCAD, 2002
"... Abstract ─ In this paper, we present Forge, an optimal algorithm for gate sizing using the Elmore delay model. The algorithm utilizes Lagrangian relaxation with a fast gradientbased preprocessing step that provides an effective set of initial Lagrange multipliers. Compared to the previous Lagrang ..."
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Cited by 28 (1 self)
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Abstract ─ In this paper, we present Forge, an optimal algorithm for gate sizing using the Elmore delay model. The algorithm utilizes Lagrangian relaxation with a fast gradientbased preprocessing step that provides an effective set of initial Lagrange multipliers. Compared to the previous Lagrangianbased approach, Forge is considerably faster and does not have the inefficiencies due to difficulttodetermine initial conditions and constant factors. We compared the two algorithms on 30 benchmark designs, on a Sun UltraSparc60 workstation. On average Forge is 200 times faster than the previously published algorithm. We then improved Forge by incorporating a slewratebased convex delay model, which handles distinct rise and fall gate delays. We show that Forge is 15 times faster, on average, than the AMPS transistorsizing tool from Synopsys, while achieving the same delay targets and using similar total transistor area. 1
Transistor Sizing for Minimizing Power Consumption of CMOS Circuits under Delay Constraint
 Proc. of Int'l Symp. on Low Power Design, Monterey CA
, 1995
"... We consider the problem of transistor sizing in a static CMOS layout to minimize the power consumption of the circuit subject to a given delay constraint. Based on our characterization of the short circuit power dissipation of a CMOS circuit we show that the transistors of a gate with high fanout l ..."
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Cited by 21 (0 self)
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We consider the problem of transistor sizing in a static CMOS layout to minimize the power consumption of the circuit subject to a given delay constraint. Based on our characterization of the short circuit power dissipation of a CMOS circuit we show that the transistors of a gate with high fanout load should be enlarged to minimize the power consumption of the circuit. We derive analytical formulation for computing the power optimal size of a transistor and isolate the factor a ecting the power optimal size. We extend our model to analyze powerdelay characteristic of a CMOS circuit and derive the powerdelay optimal size of a transistor. Based on our model we develop heuristics to perform transistor sizing in CMOS layouts for minimizing power consumption while meeting given delay constraints. Experimental results (SPICE simulations) are presented to con rm the correctness of our analytical model. 1
Gate Sizing: a General Purpose Optimization Approach
, 1996
"... Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. The methods previously proposed to address this problem suffer from problems that makes them difficult to apply on reallife large c ..."
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Cited by 20 (2 self)
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Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. The methods previously proposed to address this problem suffer from problems that makes them difficult to apply on reallife large circuits. This paper presents the gate sizing algorithm GS, which has the following characteristics. It is a general purpose optimizer, e.g., it can optimize the power or/and area under some delay constraints, or the delay under some power or/and area constraints. It is oriented to a pure combinatorial optimization, and addresses nonlinear, nonunimodal, constrained optimization, which enables it to handle complex cost models. It can take into account user defined or library dependent design rules. It can be applied on large circuits within a reasonable CPU time, e.g., 10000 nodes in 2 hours.
Timing and Area Optimization for StandardCell VLSI Circuit Design
, 1995
"... A standard cell library typically contains several versions of any given gate type, each of which has a different gate size. We consider the problem of choosing optimal gate sizes from the library to minimize a cost function (such as total circuit area) while meeting the timing constraints imposed o ..."
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Cited by 16 (1 self)
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A standard cell library typically contains several versions of any given gate type, each of which has a different gate size. We consider the problem of choosing optimal gate sizes from the library to minimize a cost function (such as total circuit area) while meeting the timing constraints imposed on the circuit. After
Simultaneous Gate and Interconnect Sizing for CircuitLevel Delay Optimization
 Proceedings of the 32nd Design Automation Conference
, 1995
"... Abstract—With delays due to the physical interconnect dominating the overall logic path delays, circuitlevel delay optimization must take interconnect effects into account. Instead of sizing only the gates along the critical paths for delay reduction, the tradeoff possible by simultaneously sizi ..."
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Cited by 16 (1 self)
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Abstract—With delays due to the physical interconnect dominating the overall logic path delays, circuitlevel delay optimization must take interconnect effects into account. Instead of sizing only the gates along the critical paths for delay reduction, the tradeoff possible by simultaneously sizing gate and interconnect must also be considered. We show that for optimal gate and interconnect sizing, it is imperative that the interaction between the driver and the RC interconnect load be taken into account. We present an iterative sensitivitybased approach to simultaneous gate and interconnect sizing in terms of a gate delay model which captures this interaction. During each iteration, the path delay sensitivities are efficiently calculated and used to size the components along a path. I.
Optimization of Custom MOS Circuits by Transistor Sizing
 IEEE INTERNATIONAL CONFERENCE ON COMPUTERAIDED DESIGN
, 1996
"... Optimization of a circuit by transistor sizing is often a slow, tedious and iterative manual process which relies on designer intuition. Circuit simulation is carried out in the inner loop of this tuning procedure. Automating the transistor sizing process is an important step towards being able to r ..."
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Cited by 13 (5 self)
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Optimization of a circuit by transistor sizing is often a slow, tedious and iterative manual process which relies on designer intuition. Circuit simulation is carried out in the inner loop of this tuning procedure. Automating the transistor sizing process is an important step towards being able to rapidly design highperformance, custom circuits. JiffyTune is a new circuit optimization tool that automates the tuning task. Delay, rise/fall time, area and power targets are accommodated. Each (weighted) target can be either a constraint or an objective function. Minimax optimization is supported. Transistors can be ratioed and similar structures grouped to ensure regular layouts. Bounds on transistor widths are supported. JiffyTune uses