Statistical timing research is a space of turning out to be value in nanometer te- nologies‚ because the uncertainties linked to method and environmental var- tions raise‚ and this bankruptcy has captured the various significant efforts during this region. This is still a truly energetic box of analysis‚ and there's prone to be loads of new examine to be present in meetings and journals after this e-book is released. as well as the statistical research of combinational circuits‚ a great deal of paintings has been performed in reading the influence of diversifications on clock skew. even if we can't deal with this topic during this e-book‚ the reader is spoke of [LNPS00‚ HN01‚ JH01‚ ABZ03a] for info. 7 TIMING research FOR SEQUENTIAL CIRCUITS 7.1 advent A normal sequential circuit is a community of computational nodes (gates) and reminiscence parts (registers). The computational nodes might be conceptualized as being clustered jointly in an acyclic community of gates that varieties a c- binational good judgment circuit. A cyclic direction towards sign propagation 1 is authorized within the sequential circuit provided that it includes not less than one sign up . as a rule, it truly is attainable to symbolize any sequential circuit when it comes to the schematic proven in determine 7.1, which has I inputs, O outputs and M registers. The registers outputs feed into the combinational good judgment which, in flip, feeds the sign in inputs. therefore, the combinational common sense has I + M inputs and O + M outputs.
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TRANSISTOR-LEVEL COMBINATIONAL TIMING OPTIMIZATION eight. 1 advent eight. 2 Transistor sizing eight. three The TILOS set of rules eight. four Transistor sizing utilizing convex programming eight. five Lagrangian multiplier methods eight. 6 Timing funds dependent optimization eight. 7 Generalized posynomial hold up types for transistor sizing eight. eight twin optimization eight. nine Resolving brief course violations eight. 10 precis 151 151 152 157 161 162 166 167 one hundred seventy five 177 178 nine. CLOCKING AND CLOCK SKEW OPTIMIZATION nine. 1 unintentional and planned clock skew nine. 2 Clock community development nine. three Clock skew optimization nine. four Clock skew optimization with transistor sizing nine. five Timing research of sequential circuits for skew scheduling nine. 6 Wave pipelining matters nine. 7 planned skews for top present aid nine. eight precis 181 181 183 one hundred ninety 196 201 203 204 205 123 126 132 Contents ix 10. RETIMING 10. 1 advent to retiming 10. 2 A wide evaluation of study on retiming 10. three Modeling and assumptions for retiming 10. four minimal interval optimization of edge-triggered circuits 10. five minimal sector retiming of edge-triggered circuits 10. 6 minimal interval retiming of level-clocked circuits 10. 7 minimal sector retiming of level-clocked circuits 10. eight precis 207 207 211 214 216 227 240 247 247 eleven. end 249 Appendices 251 A–Closed-form formulæ for the roots of cubic and quartic equations A. 1 Cubic equations A. 2 Quartic equations 251 251 252 B–A Gaussian approximation of the PDF of the utmost of 2 Gaussians C–On the convexity of the generalized posynomial formula for transistor sizing C. 1 facts of convexity C. 2 Relation of a generalized posynomial software to a posynomial application 253 255 255 257 References 259 Index 291 This web page deliberately left clean Acknowledgements i want to recognize the assistance and aid of numerous those who have supported this attempt. particular and worthy suggestions that has helped to orient this e-book at a number of degrees has come from Haihua Su, David Blaauw, and Chandramouli Kashyap. numerous of my scholars have helped boost parts of this booklet in the course of their stories, together with Hongliang Chang, Rahul Deokar, Jiang Hu, Yanbin Jiang, Kishore Kasamsetty, Mahesh Ketkar, Daksh Lehther, Naresh Maheshwari, Harsha Sathyamurthy, Vijay Sundararajan, and Min Zhao. Collaborations and different interactions through the years with Chuck Alpert, Weitong Chuang, Madhav Desai, Jack Fishburn, Noel Menezes, Sani Nassif, Rajendran Panda, Darshan Patra, and Chandu Visweswariah have helped so as to add fabric to this publication. Haihua Su and Shrirang Karandikar have significantly helped in proofreading elements of the ebook, as has my EE 5302 type within the Spring of 2004. My graduate scholars were very forgiving of my tardiness in responding to them during the last 12 months, and i'm obliged to them for his or her persistence. i need to express my appreciation to Vasant Rao, Steve Kang, Ibrahim Hajj and Res Saleh at Illinois, Vijay Pitchumani at Syracuse and H. Narayanan at IIT Bombay, for introducing me to this sector. This e-book is encouraged through their sessions, and by way of different conversations with them.