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Lec-08_ED-Optimization-a

# Lec-08_ED-Optimization-a - EE M216A Fall 2010 Lecture 8...

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EE M216A .:. Fall 2010 Lecture 8 Energy Delay Optimization Prof. Dejan Markovi ć [email protected] Some Common Questions Is sizing better than V DD for energy reduction? What are the optimal values of gate size and V DD ? What is the optimal ratio of leakage / switching for min E ? Shall we increase or decrease V DD for energy reduction? What is the optimal circuit topology? D. Markovic / Slide 2 How many levels of parallelism is good? Etc. EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 2

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Energy Minimization Problem Goal: achieve the lowest energy under the delay constraint Unoptimized Energy Unoptimized design W V DD W & V DD E max E D. Markovic / Slide 3 Delay W & V DD & V TH D max D min min (f clk max ) (f clk min ) EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 3 Energy Delay Sensitivity Slope of E D curve around a design point (e.g. ( A 0 , B 0 )) E / A S = D / A A = A 0 A S B S A f ( A , B 0 ) Energy ( A 0 , B 0 ) D. Markovic / Slide 4 [D. Markovic, V. Stojanovic, B. Nikolic, M.A. Horowitz, R.W. Brodersen, JSSC, Aug’04] f ( A 0 , B ) Delay D 0 EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 4
Solution: Equal Sensitivities A fixed point is reached when all sensitivities are equal E = S A ·( −∆ D )+ S B · D f ( A B ) f ( A , B 0 ) Energy ( A 0 , B 0 ) D 1 , D. Markovic / Slide 5 f ( A 0 , B ) Delay D 0 EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 5 Circuit Optimization topology A topology B Energy/op Constraints D. Markovic / Slide 6 Reference design D min sizing @ V DD max , V TH ref Delay Goal: find optimal E D tradeoff for a logic function EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 6

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Alpha power based Delay Model Combined with Logical Effort Formulation (*) 1.5 2 2.5 3 3.5 4 4 delay (norm.) V on = 0.37 V α d = 1.53 simulation model Fitting parameters V on , α d , K d Effective fanout D. Markovic / Slide 7 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 V dd / V dd ref FO4 (*) [Sutherland et al., Logical Effort, 1999] V DD ref = 1.2V, FO4 ( V DD ref ) = 25ps . EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 7 Energy Model Switching energy Leakage energy D. Markovic / Slide 8 with: D : the cycle time I 0 ( S in ) : normalized leakage current with inputs in state S in EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 8
Adjusting Switching Energy of a Gate , dd i V , 1 dd i V + i i +1 W wire p nom,i W i W i W i+1 W i W par,i W out Sizing Supply D. Markovic / Slide 9 = energy stored on the logic gate i EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 9 Optimization Setup Reference/nominal circuit Sized for D min @ V DD nom D fi d l t i t nergy reference Define delay constraint D con = D min (1 + d inc /100) Minimize energy under delay constraint V DD scaling (global, discrete, per stage) Gate sizing ( W ) D min Delay En D. Markovic / Slide 10 Threshold adjustment ( V TH ) Optional buffering EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 10

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Profitability of Optimization ( E / D ) Gate sizing ( W ) for equal h eff ( D min ) Supply voltage ( V DD ) V TH V DD V DD ref S ( V DD ) D. Markovic / Slide 11 Threshold voltage ( V TH ) 0 V TH V TH ref S ( V TH ) EEM216A .:. Fall 2010 Lecture 8: Energy Delay Optimization | 11
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