Comparison of LFSR and CA for BIST

1
Comparison of LFSR and CA for BIST

• Sachin Dhingra
• ELEC 7250 VLSI Testing

2
Introduction

• Built-In Self Test
• Circuit capable of testing itself
• Two major components
• Test Pattern Generator
• Output Response Analyzer
• Implementation of BIST
• Linear Feedback Shift Register (LFSR)
• Shift Register with feedback path linearly
  related to the nodes using XOR gates
• Cellular Automata (CA)
• A collection of nodes logically related to their
  neighbors using XOR gates

3
Built-In Self Test
Normal Operation
Test Mode
System
Inputs
System
Circuit
Input
Outputs
Under
Isolation
Test
Circuitry
Test
Output
Pattern
Response
Generator
Analyzer
Test
Controller

• TPG generates pseudo random test vectors
• Input Isolation Circuitry isolates the normal
  system inputs from the CUT
• Output Response Analyzer performs polynomial
  division for test data compaction (signature
  analysis)

4
Linear Feedback Shift Register (LFSR)

• Two Types
• External Feedback
• Internal Feedback
• Characteristic Polynomial
• All zero state is invalid
• Max. Sequence Length 2n 1
• Primitive and Non-primitive
• Reciprocal of primitive polynomial is also
  primitive
• P(x) xnP(1/x)
• Compact Design
• Less than one gate per node
• Parallel Pattern generation
• Signature Analysis
• Signature Analysis Register (SAR)
• Multiple Input Signature Register (MISR)

P (x) x0 x1 x3 x4
5
Cellular Automata (CA)
Rule 150
Rule 90
Rule 90
Rule 90
Null boundary condition

• One-Dimensional Linear CA
• Linear Hybrid Cellular Automata (LHCA)
• Linear Cellular Automata Register (LCAR)
• Rules define the logical relationship of a node
  with its neighbors
• Rule 90 xi(t1) xi-1(t) ? xi1(t)
• Rule 150 xi(t1) xi-1(t) ? xi(t) ? xi1(t)
• Combination of Rules Characteristic Polynomial
  of LFSRs
• Boundary Condition
• Null Boundary Condition No Feedback ? Faster
• Cyclic Boundary Condition Feedback ? Slower
• Highly Random Vectors

6
Comparison
7
Summary and Conclusion

• LFSRs are more popular because of their compact
  and simple design
• CAs are more complex to design but provide
  patterns with higher randomness
• CAs perform better in detection of faults such as
  stuck-open or delay faults, which need
  two-pattern testing
• In applications where area overhead is a big
  concern, LFSRs prove to be a better choice
• CAs provide a good alternative for LFSRs when
  high fault coverage is needed

8
References

• M.L. Bushnell, V.D. Agrawal, Essentials of
  Electronics Testing for Digital, Memory Mixed
  Signal VLSI Circuits, Kluwer Academic Publishers,
  Boston MA, 2000
• C. Stroud, A Designers Guide to Built-In
  Self-Test, Kluwer Academic Publishers, Boston MA,
  2002
• S. Zhang et. al, Why cellular automata are
  better than LFSRs as built-in self-test
  generators for sequential-type faults, IEEE
  International Symposium on Circuits and Systems,
  Vol. 1, pp 69-72, 1994
• P.D. Hortensius et. al, Cellular automata-based
  pseudorandom number generators for built-in
  self-test, IEEE Transactions on Computer-Aided
  Design of Integrated Circuits and Systems, Vol.
  8, pp 842 - 859, 1989
• K. Furuya, E.J. McCluskey, Two-Pattern test
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  1991.
• L.T. Wang, E.J. McCluskey, Circuits for
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  7, pp. 1068 1080, 1988
• P.D. Hortensius et. al, Cellular automata-based
  signature analysis for built-in self-test, IEEE
  Transactions on Computers, Vol. 39, pp. 1273
  1283, 1990
• K. Furuya et. al, Evaluations of various TPG
  circuits for use in two-pattern testing,
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• M. Serra, et. al, The Analysis of One
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