Efficient Estimation of Maximum Instantaneous Current in Sequential Circuits

1. Estimation of Maximum Instantaneous Current for Sequential Circuits Cheng-Tao Hsieh and Shih-Chieh Chang National Tsing Hua University Hsinchu, Taiwan

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

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

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

5. The two transitions cannot occur simultaneously Vectorless Methods • Definition: Two gates are Mutually Exclusive Switching (MES) at time t1 if they cannot switch simultaneously at t1. • [C.T. Hsieh, J.C. Lin, and S.C. Chang, accepted by TCAD]

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

7. t=0 t=1 Sequential Correlation • Correlation across sequential elements. (0, 1) (f1, f2)= (0, 0) (1, 0) (1, 1) f2 f1

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

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. Solution for Efficiency Problem • Detect MES in a time interval instead of at an exact time instant. t1 t2 t3 time Time interval t1to t3

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

12. Accuracy of MIC Estimation

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

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. Functional condition Temporal condition A Timed ATPG Problem • A transition: • A logic changev v’ at a certain time t1. • Find a vector pair satisfying both functional and temporal conditions.

16. a a g g b b c c 1 t=2 1 An Example of Timed ATPG g=01 at t=2 (a1,b1,c1), (a2,b2,c2) = (0,0,1), (1,1,0)

17. Transition Characteristic Function • Definition: Atransition characteristic function (TCF), g=01,t=t1(v1, v2), characterizes all vector pairs v1 and v2 which causes gate g to have a rising transition at time t=t1.

18. a g b c An Example of TCF g=01 at t=2 g=01, t=2 = a1’b1’c1a2b2c2’ + a1’b1’c1a2b2c2 + a1b1’c1a2b2c2’ + a1b1’c1a2b2c2 + a1’b1c1’a2b2c2’ + a1’b1c1’a2b2c2 + a1’b1c1a2b2c2’ + a1’b1c1a2b2c2 + (a1,b1,c1), (a2,b2,c2) = (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)

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

20. a1 b1 g=01, t=2 c1 a2 b2 An Example a g b g=01 at t=2 c g=01, t=2= (a1b1+b1’c1’)’(a2b2+b1’c1’)

21. a b c Flip-flop a1 b1 c1 b1 g=01, t=2 a2 c1 Sequential Correlation • The second vector on input b depends on the first vector. b2

22. Initial Experimental Results

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

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