Transcript slides

Analyzing Reconvergent
Fanouts in Gate Delay Fault
Simulation
Hillary Grimes & Vishwani D. Agrawal
Dept. of ECE, Auburn University
Auburn, AL 36849
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Outline
• Problem Statement
• Reconvergent Fanout Analysis
Ambiguity Lists
• Fault Detection
Detection Threshold
Detection Gap
• Results
• Conclusion
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Definitions
• Gate Delay Fault Model
Assume that a delay fault is lumped at a single
faulty gate
• Detection Threshold
Minimum size delay fault that is guaranteed to
be detected by the test
• Detection Gap
Relates the detection threshold to the slack at
the fault site
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Problem Statement
• When signals produced by a common
fanout point reconverge, the inputs to the
reconvergent gate are correlated
• Conventional simulation ignores this
correlation when bounded gate delays are
used
Produces pessimistic results in both bounded
delay simulation and gate delay fault simulation
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Bounded Delay Simulation
0
1
3
3
1,3
5
1,2
4
1,2
1,2
2
1
11
5
1
1,3
3,4
5
9
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Reconvergent Fanout Analysis
Fall occurs at time ‘x’
0
Hazard cannot occur
1x 3
3
1,3
5
1,2
4
1,2
6
11
1,2
x+1 5
1
1
3,4
1,3
Output rises at least 1
unit after ‘x’
5
9
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Ambiguity Lists
• Ambiguity Lists generated at fanout points
contain
originating fanout name
ambiguity interval – min and max delays from
fanout to gate
• Ambiguity list propagation is similar to fault
list propagation in concurrent fault
simulation
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Ambiguity List Propagation
• Ambiguity lists at the inputs of a
reconvergent gate help determine its
output
If signal correlations are such that no hazard
can occur, the hazard is suppressed
Otherwise, the ambiguity lists are propagated
to the gate’s output, and ambiguity intervals are
updated
10/25/2007
ITC-07 Paper 26.3
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Ambiguity List Propagation
• Bounded Delay Simulation
Ambiguity lists propagated through every gate
• Detection Threshold Evaluation
Ambiguity Lists propagated through downcone
of the fault site
10/25/2007
ITC-07 Paper 26.3
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Detection Threshold
Ts = 12
Det. Threshold = 8
0
1,3
1
3
3
5
1,2
4
1,2
1
1
1,3
2
5
6
11
1,2
Corrected
Det. Threshold = 6
3,4
5
9
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Detection Gap for a Gate
PI
p1 - longest delay
path through gate
Ts
PO
p1
delay
t
gap
Gate
p2
slack
p2
delay
DT(p2)
• Ideal gate delay test should activate longest path p1,
detection threshold = slack, gap = 0
• A test that activates path p2, p2 < p1, gap =
detection threshold – slack
• Smaller the gap, better is the test
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Results
• ISCAS85 benchmark circuits simulated
with 10,000 random vectors
• Simple wireload model
Bounded delays set to (3.5n ± 14%), where n is
the number of fanouts
 Program can accept any available gate delay
data, which may be normally available from
process technology characterization
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Results: Fault-Free Simulation
Circuit
Without Reconvergent
Fanout Analysis
With Reconvergent
Fanout Analysis
Largest EA
Largest LS
Largest EA
Largest LS
c3540
96.0
204.0
121.6
196.8
C5315
76.8
204.0
91.2
194.4
C6288
158.4
576.0
236.8
504.0
C7552
91.2
204.0
104.0
201.6
• Using reconvergent fanout analysis generally
results in larger EA and smaller LS values at
outputs
• More apparent for circuits that contain a large
number of reconvergent fanouts, such as in
multiplier circuit c6288
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Results: Fault Simulation
• Average detection gap and fault coverage
of faults detected with gap ≤ 3.5 recorded
• For fault coverage, faults are counted as
detected if they are detected:
Through the longest path through the gate
Through a path which is shorter than longest
path by only one gate delay
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Results: Fault Simulation
Without Reconvergent
Fanout Analysis
Circuit
c432
c499
c880
c1355
c1908
c2670
c3540
c5315
c7552
Average
Detection
Gap
110.4
51.7
16.4
50.8
55.2
41.8
50.4
21.7
39.4
Faults
Detected with
Gap ≤ 3.5
7.35%
4.91%
48.41%
4.80%
21.70%
31.25%
32.60%
55.72%
13.43%
With Reconvergent
Fanout Analysis
Average
Detection
Gap
108.9
44.0
12.9
42.2
47.1
36.0
44.0
6.1
22.5
Faults
Detected with
Gap ≤ 3.5
7.08%
12.85%
48.86%
13.62%
25.10%
36.54%
33.19%
57.31%
22.83%
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Conclusion
• When reconvergent fanout analysis is used,
gate delay fault simulation results are less
pessimistic
• During simulation, ambiguity lists can grow
quite large
Efficiency in list propagation needs to be improved
• This min-max delay simulator has found
application in hazard-free delay test generation
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