Download E-books Statistical Analysis and Optimization for VLSI: Timing and Power (Integrated Circuits and Systems) PDF

By Ashish Srivastava

Covers the statistical research and optimization matters coming up because of elevated strategy diversifications in present applied sciences.

Comprises a worthy reference for statistical research and optimization thoughts in present and destiny VLSI layout for CAD-Tool builders and for researchers drawn to beginning paintings during this very energetic sector of study.

Written by author who lead a lot study during this region who offer novel rules and techniques to address the addressed issues

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This is often completed through matching the 1st moments of dk acquired utilizing expression for the max of 2 Gaussian RV and matching the correlation of di with all the important parts. those expressions, that have been constructed in [35], are mentioned in Chap. three. utilizing those expressions, the set of n + 2 equations might be written as ai^o = E[ma,x{dm,dn)] ai^i = Cov{di, Zi) = Cov{ma,x{dm, dn), zi) Vi == 1,2,... , n / n ttn+i,/ == I Far(max(dm, dn)) - ^ (5. forty six) \ half a\i \ to judge the phrases within the set of equations above, we have to use expressions for the suggest and variance of the canonical hold up expression. We additionally have to estimate the covariance of 2 hold up expressions which might be expressed as n Cov{dm,dn) = ^ (5. forty seven) i=l through modeling the random part, the timing research steps may be able to shield the suggest, variance and correlations, fending off the necessity to scale the coefficients of the critical parts to check variance, as we did in 5. 2 Gate-Level Yield Estimation 185 Chap. three, which leads to the hold up expressions wasting their specified correlation with the important parts. For gates with greater than inputs, the procedure defined above is utilized iteratively. utilizing the procedure defined above, we will enhance an expression for the hold up of a circuit by way of the RVs linked to method parameter adaptations. We now speak about the stairs to accomplish leakage research, the place the target is to maintain the correlation among hold up and tool, that's completed by way of appearing the same vital component-based research technique utilizing an analogous underlying RVs. five. 2. 2 Leakage energy research As in (5. 38), leakage energy is expressed as an exponential of a Gaussian RV, that is identified to have a lognormal distribution. The leakage energy for an entire circuit block will be expressed as a sum of correlated lognormal RVs. The authors in [1] exhibit that this sum may be adequately approximated as one other lognormal RV. it's also proven that the approximation played utilizing an extension of Wilkinson's approach [127], that is in accordance with matching the 1st moments, presents sturdy accuracy. utilizing the important elements of timing research, we will be able to write the canonical shape for leakage energy as Ij = exp I bo J + ^ bijZi + bn-{-i,jR j (5. forty eight) the place the Zi^s are imperative elements of the RVs (used for timing research besides) and the coefficients 6j's should be computed utilizing (5. 36) and (5. 38). utilizing expressions for suggest and variance of lognormal RVs, the suggest and variance of leakage energy of gate j should be expressed as / 1 ^+^ \ E[lj] = exp\boj + -Y. blA ( n+l (5. forty nine) \ 1 '^•^^ / \ 2boj + J2 ^h j - exp f 2boj + -Y^ 4j j • The correlation of the leakage of a specific gate with the lognormal RV linked to one of many critical elements is expressed as: / E[lj,Zi]=exp\boj ^ +- n+i Y. \ 4,i + okay j + l)' Vi = l , 2 , . . . , n . (5. 50) equally, the correlation among the leakage currents of 2 gates should be expressed as: 186 five Yield research E[lmJn\ = exp I 6o,m^O,n ^ + 6i,n)' j + 6^+1,^ + 6^+1,^ j J.

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