1. VLSI/CAD Laboratory Department of Computer Science National Tsing Hua University TH EDA Estimation of Maximum Instantaneous Current for Sequential Circuits Cheng-Tao Hsieh and Shih-Chieh Chang National Tsing Hua University Hsinchu, Taiwan

2. 2 Maximum Instantaneous Current (MIC) To calculate the MIC, must decide which input vectors and at which time. 0 0 MIC=3 at time t=3 MIC=4 at time t=1. t=1t=2t=3

3. 3 Two Types of Methods Vector dependent  Deriving the worst case vectors  Lower bound estimation Vectorless  No vector search  Upper bound estimation

4. 4 Two Types of Methods Vector dependent  Deriving the worst case vectors  Lower bound estimation Vectorless  No vector search  Upper bound estimation

5. 5 Vectorless Methods Definition: Two gates are Mutually Exclusive Switching (MES) at time t 1 if they cannot switch simultaneously at t 1.  [C.T. Hsieh, J.C. Lin, and S.C. Chang, accepted by TCAD] The two transitions cannot occur simultaneously

6. 6 Combinational Correlation Signal correlation in a combinational circuit. The two transitions cannot occur simultaneously

7. 7 Sequential Correlation Correlation across sequential elements. (f 1, f 2 )= (0, 0) (0, 1) (1, 0) (1, 1) f2f2 f1f1 t=0 t=1

8. 8 Impact from Sequential Correlations Accuracy loss if ignore sequential correlations.

9. 9 The Use of Real Delay Model Do not impact on accuracy but impact on efficiency.  The number of transitions on a gate may be exponential to the circuit size. [H. Kriplani, et al., TCAD’95]  Large memory and run time to detect MES among many transitions.

10. 10 Solution for Efficiency Problem Detect MES in a time interval instead of at an exact time instant. time t1t1 t2t2 t3t3 Time interval t 1 to t 3

11. 11 Trade-off Between Accuracy and Efficiency Larger time interval  more efficient but less accurate. Circuit C7552

12. Accuracy of MIC Estimation circuitDelayiMax Our approach 0.50.20.10.050.01 C4324.9280206201161141117107 C4993.1495640472302280224220 C8803.6301471467383294265244 C13553.1706686546316278272236 C19084.6940793751531451424401 C26705.6569963897630476427 401 C35406.991413481291979829763 716 C53156.024027962738191516311496 1378 C628815.104637463723313028202701 2680 C75525.533534903415260222772149 1982 Avg.10.930.680.580.53 0.50

13. 13 Two Types of Methods Vector dependent  Deriving the worst case vectors  Lower bound estimation Vectorless  No vector search  Upper bound estimation

14. 14 Vector Dependent Methods GA-based, probability-based, ILP-based, and modified timed ATPG algorithm.  [Y.M. Jiang, A. Krstic, and K.-T. Cheng, TVLSI, ’00]. Modified timed ATPG algorithm can derive better results than other methods. Timed ATPG is not scalable.

15. 15 A Timed ATPG Problem A transition:  A logic change v  v ’ at a certain time t 1. Find a vector pair satisfying both functional and temporal conditions. Temporal condition Functional condition

16. 16 An Example of Timed ATPG (a 1,b 1,c 1 ), (a 2,b 2,c 2 ) = (0,0,1), (1,1,0) a b c g g=0  1 at t=2 a b c g 1 1 t=2

17. 17 Transition Characteristic Function Definition: A transition characteristic function (TCF),  g=01, t=t1 (v 1, v 2 ), characterizes all vector pairs v 1 and v 2 which causes gate g to have a rising transition at time t=t 1.

18. 18 An Example of TCF (a 1,b 1,c 1 ), (a 2,b 2,c 2 ) = (0,0,1), (1,1,0) (0,0,1), (1,1,1) (1,0,1), (1,1,0) (1,0,1), (1,1,1) (0,1,0), (1,1,0) (0,1,0), (1,1,1) (0,1,1), (1,1,0) (0,1,1), (1,1,1)  g=01, t=2 = a 1 ’b 1 ’c 1 a 2 b 2 c 2 ’ + a 1 ’b 1 ’c 1 a 2 b 2 c 2 + a 1 b 1 ’c 1 a 2 b 2 c 2 ’ + a 1 b 1 ’c 1 a 2 b 2 c 2 + a 1 ’b 1 c 1 ’a 2 b 2 c 2 ’ + a 1 ’b 1 c 1 ’a 2 b 2 c 2 + a 1 ’b 1 c 1 a 2 b 2 c 2 ’ + a 1 ’b 1 c 1 a 2 b 2 c 2 + a b c g g=0  1 at t=2

19. 19 Construction of TCF Construct a TCF by extracting information from circuit structure. A TCF is represented in the multi-level form, more compact than the two-level form.

20. 20 An Example  g=01, t=2 = (a 1 b 1 +b 1 ’c 1 ’)’(a 2 b 2 +b 1 ’c 1 ’) a b c g a1a1 b1b1 c1c1 a2a2 b2b2  g=01, t=2 g=0  1 at t=2

21. 21 Sequential Correlation a b c Flip-flop b1b1 c1c1 b2b2  g=01, t=2 a1a1 b1b1 c1c1 a2a2 The second vector on input b depends on the first vector.

22. Initial Experimental Results circuit#PIs#gates RandomOursMES MIC time (s)MIC s444323414171.428 s5101926216201.523 s526331316212.334 s6413523428312.042 s7133525226312.445 s8201852428342.339 s11961457439416.549 s12381466821267.252 s14231771453751481 s537835188880176174252 s923436169260151112176 Avg. 11.43 1.96

23. 23 Conclusion Propose vectorless and vector dependent estimation for the MIC. Consider sequential correlations, which can significantly impact the MIC estimation.

24. 24 Acknowledge Prof. Shih-Chieh Chang Jian-Cheng Lin Yu-Min Kuo Yue-Lung Chang Download: http://nthucad.cs.nthu.edu.tw/~sclab/