number of trials extraction delay calculation and timing flow to produce full

Number of trials extraction delay calculation and

This preview shows page 57 - 62 out of 75 pages.

number of trials (extraction, delay calculation, and timing flow) to produce full circuit delay distribution Attractive properties: Considered very accurate and represent reality Conceptually easy to implement Well understood by the designers Disadvantages: High computational cost Number of trials is typically in the order of 5000-10000 Using Monte-Carlo techniques in circuit optimization loop is difficult and has limitation Chapter 5: Timing Analysis and Optimization 5-57
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Statistical Static Timing Analysis (SSTA) SSTA = STA + Statistical distributions of: Gate delays : Delay behavior of the gate at different values of the parameters influenced by process and operating conditions Interconnect parasitics Operating conditions : Uncertainty in environmental conditions during the operation of a chip (power supply, temperature, etc.) The distribution of gate delays ( pdf or CDF) can be in any form: normal, uniform, etc... SSTA computes node and path delay distributions and estimate the circuit delay as the joint distributions The distribution of circuit delays can be represented by continuous or discrete functions (either pdf or CDF) Key difference between STA and SSTA : Single values versus distribution functions Chapter 5: Timing Analysis and Optimization 5-58
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Some Fundamentals Chapter 5: Timing Analysis and Optimization   1 2 2 2 1 2 2 2 ; for ; 1 1 Shift: Sca e: l 1 X x X X X X n X i X i n X i X i X X i X X Y X Y X CDF F x P X x x d pdf f x F x F x f t dt dx m E X x xf x dx n VAR X x m x m f x dx n E X E X STD X Y X a f y f y a y Y aX f y f a a         5-59
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Chapter 5: Timing Analysis and Optimization 2 2 Joint Joint If and are independent the , , , ; , , : , , n XY y x XY XY XY XY XY X Y XY XY XY XY XY X F x y P X x Y y f x y F x y F x y f d d x y F x y P X x Y y P X x P Y y F x F y d d f x y F x F y F x F y f x x y dx d CDF pd y f X Y             Y f y 2 2 2 2 2 1 : ( ) ; ; 2 12 1 : ; ( , Uniform distrib ) ution Gaussian (Normal) 2 X X X X X x m X X f x a x b b a a b b a m E X VAR X f x e x    5-60
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