VLSI/CAD LaboratoryVLSI/CAD LaboratoryDepartment of Computer ScienceDepartment of Computer ScienceNational Tsing Hua UniversityNational Tsing Hua University

TH EDATH EDA

Estimation of Estimation of Maximum Instantaneous Current for Maximum Instantaneous Current for

Sequential CircuitsSequential Circuits

Cheng-Tao Hsieh and Shih-Chieh Chang

National Tsing Hua University

Hsinchu, Taiwan

2

Maximum Instantaneous Current (MIC)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

Two Types of MethodsTwo Types of Methods

Vector dependent Deriving the worst case vectorsLower bound estimation

Vectorless No vector searchUpper bound estimation

4

Two Types of MethodsTwo Types of Methods

Vector dependent Deriving the worst case vectorsLower bound estimation

Vectorless No vector searchUpper bound estimation

5

Vectorless MethodsVectorless 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]

The two transitions cannot occur simultaneously

6

Combinational CorrelationCombinational Correlation

Signal correlation in a combinational circuit.

The two transitions cannot occur simultaneously

7

Sequential CorrelationSequential Correlation

Correlation across sequential elements.

(f1, f2)= (0, 0)

(0, 1)

(1, 0)

(1, 1)f2

f1

t=0t=1

8

Impact from Sequential CorrelationsImpact from Sequential Correlations

Accuracy loss if ignore sequential correlations.

0%

20%

40%

60%

80%

S38

2

S40

0

S44

4

S52

6

S83

8

S14

23

S53

78

S92

34

S15

850

S13

207

S38

584

S38

417

S35

932

Avg

.

9

The Use of Real Delay ModelThe 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 ProblemSolution for Efficiency Problem

Detect MES in a time interval instead of at an exact time instant.

timet1 t2 t3

Time interval t1 to t3

11

Trade-off Between Accuracy and EfficiencyTrade-off Between Accuracy and Efficiency

Larger time interval more efficient but less accurate.

0

1000

2000

3000

4000

iMax 0.5 0.2 0.1 0.05M

IC

0

500

1000

1500

iMax 0.5 0.2 0.1 0.05

Run

tim

e (s

)

Circuit C7552

Accuracy of MIC EstimationAccuracy of MIC Estimation

circuit Delay iMaxOur approach

0.5 0.2 0.1 0.05 0.01

C432 4.9280 206 201 161 141 117 107

C499 3.1495 640 472 302 280 224 220

C880 3.6301 471 467 383 294 265 244

C1355 3.1706 686 546 316 278 272 236

C1908 4.6940 793 751 531 451 424 401

C2670 5.6569 963 897 630 476 427 401

C3540 6.9914 1348 1291 979 829 763 716

C5315 6.0240 2796 2738 1915 1631 1496 1378

C6288 15.1046 3746 3723 3130 2820 2701 2680

C7552 5.5335 3490 3415 2602 2277 2149 1982

Avg. 1 0.93 0.68 0.58 0.53 0.50

13

Two Types of MethodsTwo Types of Methods

Vector dependent Deriving the worst case vectorsLower bound estimation

Vectorless No vector searchUpper bound estimation

14

Vector Dependent MethodsVector 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

A Timed ATPG ProblemA Timed ATPG Problem

A transition:

A logic change v v’ at a certain time t1.

Find a vector pair satisfying both functional and temporal conditions.

Temporal condition

Functional condition

16

An Example of Timed ATPGAn Example of Timed ATPG

(a1,b1,c1), (a2,b2,c2) =(0,0,1), (1,1,0)

ab

c

gg=01 at t=2

ab

c

g

1

1 t=2

17

Transition Characteristic FunctionTransition Characteristic Function

Definition:

A transition 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

An Example of TCFAn Example of TCF

(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)

g=01, t=2 = a1’b1’c

1a2b2c2’ + a1’b1’c1a2b2c2 +a1b1’c1a2b2c2’ + a1b1’c1a2b2c2 +

a1’b1c1’a2b2c2’ + a1’b1c1’a2b2c2 +a1’b1c1a2b2c2’ + a1’b1c1a2b2c2 +

ab

c

gg=01 at t=2

19

Construction of TCFConstruction 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

An ExampleAn Example

g=01, t=2 = (a1b1+b1’c1’)’(a2b2+b1’c1’)

ab

c

g

a1

b1

c1

a2b2

g=01, t=2

g=01 at t=2

21

Sequential CorrelationSequential Correlation

a

bc

Flip-flop

b1

c1

b2g=01, t=2

a1

b1

c1

a2

The second vector on input b depends on the first vector.

Initial Experimental ResultsInitial Experimental Resultscircuit #PIs #gates

Random Ours MES

MIC MIC time (s) MIC

s444 3 234 14 17 1.4 28

s510 19 262 16 20 1.5 23

s526 3 313 16 21 2.3 34

s641 35 234 28 31 2.0 42

s713 35 252 26 31 2.4 45

s820 18 524 28 34 2.3 39

s1196 14 574 39 41 6.5 49

s1238 14 668 21 26 7.2 52

s1423 17 714 53 75 14 81

s5378 35 1888 80 176 174 252

s9234 36 1692 60 151 112 176

Avg. 　 1 1.43 　 1.96

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ConclusionConclusion

Propose vectorless and vector dependent estimation for the MIC.

Consider sequential correlations, which can significantly impact the MIC estimation.

24

AcknowledgeAcknowledge

Prof. Shih-Chieh Chang Jian-Cheng Lin Yu-Min Kuo Yue-Lung Chang

Download: http://nthucad.cs.nthu.edu.tw/~sclab/