{"title":"栅极尺寸变化感知功率最小化的新方法","authors":"V. Mahalingam, N. Ranganathan, J. Harlow","doi":"10.1145/1165573.1165614","DOIUrl":null,"url":null,"abstract":"Increasing dominance of process variations in the nanometer designs is posing significant challenges for circuit design and optimization. The variations in parameters such as channel length and the gate oxide thickness impacts circuit delay and power. In this paper, we propose a new gate sizing algorithm using fuzzy mathematical programming (FMP) in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay, which is a function of gate sizes and the fan-outs of the gate, are represented using triangular fuzzy numbers with linear membership functions. The variation aware gate sizing problem is formulated as a fuzzy mathematical program to perform a delay constrained power minimization in the presence of variations. Initially, a deterministic optimization is performed by fixing the fuzzy parameters to the worst and the average case values and the results are used to convert the fuzzy optimization problem into a crisp non-linear problem which is then solved using a non-linear optimization solver. The above model with delay and power as constraints, maximizes the robustness, i.e., the variation resistance of the circuit and thus the yield. The proposed approach was tested on ISCAS'85 benchmarks and the results were validated for timing yield using Monte-Carlo simulations. The fuzzy approach yields significantly better results compared to stochastic programming based gate sizing approach with a comparable runtime","PeriodicalId":119229,"journal":{"name":"ISLPED'06 Proceedings of the 2006 International Symposium on Low Power Electronics and Design","volume":"1997 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"A Novel Approach for Variation Aware Power Minimization during Gate Sizing\",\"authors\":\"V. Mahalingam, N. Ranganathan, J. Harlow\",\"doi\":\"10.1145/1165573.1165614\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Increasing dominance of process variations in the nanometer designs is posing significant challenges for circuit design and optimization. The variations in parameters such as channel length and the gate oxide thickness impacts circuit delay and power. In this paper, we propose a new gate sizing algorithm using fuzzy mathematical programming (FMP) in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay, which is a function of gate sizes and the fan-outs of the gate, are represented using triangular fuzzy numbers with linear membership functions. The variation aware gate sizing problem is formulated as a fuzzy mathematical program to perform a delay constrained power minimization in the presence of variations. Initially, a deterministic optimization is performed by fixing the fuzzy parameters to the worst and the average case values and the results are used to convert the fuzzy optimization problem into a crisp non-linear problem which is then solved using a non-linear optimization solver. The above model with delay and power as constraints, maximizes the robustness, i.e., the variation resistance of the circuit and thus the yield. The proposed approach was tested on ISCAS'85 benchmarks and the results were validated for timing yield using Monte-Carlo simulations. The fuzzy approach yields significantly better results compared to stochastic programming based gate sizing approach with a comparable runtime\",\"PeriodicalId\":119229,\"journal\":{\"name\":\"ISLPED'06 Proceedings of the 2006 International Symposium on Low Power Electronics and Design\",\"volume\":\"1997 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ISLPED'06 Proceedings of the 2006 International Symposium on Low Power Electronics and Design\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1165573.1165614\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ISLPED'06 Proceedings of the 2006 International Symposium on Low Power Electronics and Design","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1165573.1165614","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Novel Approach for Variation Aware Power Minimization during Gate Sizing
Increasing dominance of process variations in the nanometer designs is posing significant challenges for circuit design and optimization. The variations in parameters such as channel length and the gate oxide thickness impacts circuit delay and power. In this paper, we propose a new gate sizing algorithm using fuzzy mathematical programming (FMP) in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay, which is a function of gate sizes and the fan-outs of the gate, are represented using triangular fuzzy numbers with linear membership functions. The variation aware gate sizing problem is formulated as a fuzzy mathematical program to perform a delay constrained power minimization in the presence of variations. Initially, a deterministic optimization is performed by fixing the fuzzy parameters to the worst and the average case values and the results are used to convert the fuzzy optimization problem into a crisp non-linear problem which is then solved using a non-linear optimization solver. The above model with delay and power as constraints, maximizes the robustness, i.e., the variation resistance of the circuit and thus the yield. The proposed approach was tested on ISCAS'85 benchmarks and the results were validated for timing yield using Monte-Carlo simulations. The fuzzy approach yields significantly better results compared to stochastic programming based gate sizing approach with a comparable runtime