Dynamic Power Estimation for Deep Submicron Circuits with Process Variation

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1 Dynamic Power Estimation for Deep Submicron Circuits with Process Variation Quang Dinh, Deming Chen, Martin D. F. Wong Department of Electrical and Computer Engineering University of Illinois, Urbana-Champaign This work is partially supported by two NSF grants and Altera Corp.

2 Outline Introduction and motivation Related work Algorithm Description Definitions Gate characterization under process variation Power estimation for a switch segment Power estimation for a transition waveform Power estimation for the circuit Experimental Results Conclusions 2

3 Glitches Signal transitions consists of: Functional transitions Spurious transitions (Glitches) A A B A and B B A and B Glitch Glitch transitions can be 4-5X of functional transitions in some dataflow intensive designs [Raghunathan, TCAD 99] They can be 20% of total power in FPGAs [Li, TCAD 05] 3

4 Dynamic power under process variation Mean of the dynamic power of a logic gate vs. input glitch width Standard deviation of the dynamic power of a logic gate vs. input glitch width 5X difference (e.g., between width 50ps and 100ps)

5 Related work Circuit power under process variation mainly focused on leakage power [Mukhopadhyay, ISLPED 03], [Rao, TVLSI 04], [Chang, DAC 05], etc. Two previous works on dynamic power modeling with process variation [Pilli & Sapatnekar, ISCAS 97]: Pioneer work; didn t estimate variation of dynamic power [Alexander & Agrawal, ISVLSI 09]: only minimum and maximum bounds for delays are considered; no consideration of partial swing transitions

6 Definition: Transition Event A transition event at a particular node n in the circuit describes a possible transition at that node. No distinguishing between 0 1 and 1 0 transitions. Represented by three values (p, t, σ t ) as follows: p is the probability for the transition to occur. t is the mean of the time of the transition. σ t is the standard deviation of the transition time. For a transition event (0.2, 0.42 ns, 0.21 ns) there is a likelihood of 20% that a transition occurs at a time around 0.42 ns, with a standard deviation of 0.21 ns.

7 Transition Waveforms The set of all transition events for a node are collectively represented by a transition waveform {(p 1, t 1, σ t1 ), (p 2, t 2, σ t2 ),, (p N, t N, σ tn )}. N transition events: E 1, E 2,, E N The events E i of (p i, t i, σ ti ) are sorted according to the increasing order of t i E 1 E 2 E 3 E k E N 1 E N time In this example, events E 2, E 3 and E N correspond to actual transitions, while events E 1 and E N 1 do not.

8 Switching Segments A switching segment is the duration from the beginning of a transition to just before the beginning of the next transition. A switching segment corresponds to exactly one transition. Switching segment for partial-swing transition (E 1,E 2 ) and full-swing transition (E 6, E 7 ).

9 Algorithm: propagation through a wire segment or a gate Source: E S (p S, t S, σ ts ) Target: E T (p T, t T, σ tt ) p = p T S t = t + d T S 2 2 = + tt ts d s s s Wire segment Input: E I (p I, t I, σ ti ) Output: E O (p O, t O, σ to ) t = t + d O I 2 2 = + to ti d s s s 踐カ f p = p エP O I カ顏 x Gate i

10 Dynamic power for an input glitch width A w i Input glitch width B A and B Glitch at the output DPower(w i ) is a random variable due to variation in the load capacitance variation in the gate delay from different inputs to the output

11 Gate power characterization Gate Characterization under different input glitch widths (20 different widths, from 0ps to 190ps) different load capacitances Build look-up tables Look up and interpolate the mean μ C (w i ) and standard deviation σ C (w i ) of dynamic power for a given w i and a given load capacitance.

12 Compute probability for w i Discretize the width into w 0, w 1,, w L. The probability that w = w i is: Pr 踐 1 = = exp i - s 2p { w w } w ( w m ) 2 - 顏 i 2s Normalize this probability as follows: 2 w w PN i = j Pr { w = w } Pr i { w = w } j

13 Compute the mean of the dynamic power for a switch segment For each w i, we can look-up and interpolate the corresponding mean power μ C (w i ) and standard deviation σ C (w i ) m s ( ) E 鴿 ( ) w = DPower w w = w C i i 鴿 w = ( DPower w - w ) 2 w = w ( ) E ( ) m ( ) C i C i i The overall (unconditional) mean dynamic power μ DP m = E 鴿 DPower w = PN エ w () m ( ) DP i C i i

14 Compute the standard deviation for a switch segment The overall (unconditional) standard deviation σ DP is s DP 鴿 = E - ( DPower () w m ) 2 DP 鴿 ( ( ) ) ( ) ( ) ( ) E DPower w - m = m w - m + s w i DP C i DP C i PN 鴿 s = エ mc w - m + s DP w ( ( ) ) ( ) 2 2 DP i i C i i

15 Compute dynamic power for a gate For a gate with the transition waveform {(p 1, t 1, σ t1 ), (p 2, t 2, σ t2 ),, (p N, t N, σ tn )}. m DP gate N- 1 裹 N = Pr i j エ i= 1 j= i+ 1 (, ) m (, i j) DP s DPgate N- 1 裹 N = Pr i j エ i= 1 j= i+ 1 (, ) s (, i j) j - 1 DP (, ) = エエ ( 1 i j ユ - k) Pr i j p p p k= i+ 1 2

16 Dynamic power for the circuit Assume that the power for the gates are independent random variables of normal distribution, the total dynamic power is: m DP circuit = all gates m DP gate s DPcircuit = all gates s 2 DPgate

17 Experiment Settings We used a 45nm Nangate FreePDK45 Generic Open Cell Library We introduced 20% random variation of normal distribution to four process parameters W g, L eff, T OX and na Similar variation is added to the unit R and C for wires Monte Carlo samples, each with 1000 clock cycles

18 Dynamic power estimation vs. HSPICE-based Monte Carlo simulation Dynamic Power (μw) HSPICE Our Model Differences (%) mean σ mean σ mean σ Circuit Circuit Circuit Circuit Circuit Average of Absolute Differences

19 Runtime comparison HSPICE (hours) Our Model (seconds) Speed-up ( 10 6 ) Circuit Circuit Circuit Circuit Circuit Average 8.5

20 Results for ISCAS89 circuits Dynamic Power Runtime (sec) Mean (mw) σ (%) C C C C C C C C C C

21 Conclusions We presented a novel dynamic power estimation method for circuits with process variation Our estimation takes into account the difference between partial-swing and full-swing glitches We obtained high accuracy estimates, with average errors of 3% for the means and 5% for the standard deviations Our estimation is also very fast, more than six orders of magnitude comparing to SPICE-Monte Carlo Future work includes consideration of the correlation among the process parameters 21

22 Thank You 22

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