1. Comparison of LFSR and CA for BIST
Sachin Dhingra
ELEC 7250: VLSI Testing
4/26/05
Dhingra: ELEC7250

2. Introduction Built-In Self Test Implementation of BIST
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
4/26/05
Dhingra: ELEC7250

3. Built-In Self Test Test Mode Normal Operation
System
Inputs
System
Input
Circuit
Outputs
Isolation
Under
Circuitry
Test
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)
4/26/05
Dhingra: ELEC7250

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
4/26/05
Dhingra: ELEC7250

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(t+1) = xi-1(t)  xi+1(t)
Rule 150 xi(t+1) = xi-1(t)  xi(t)  xi+1(t)
Combination of Rules ≡ Characteristic Polynomial of LFSRs
Boundary Condition
Null Boundary Condition – No Feedback ⇒ Faster
Cyclic Boundary Condition – Feedback ⇒ Slower
Highly Random Vectors
4/26/05
Dhingra: ELEC7250

6. Comparison Characteristic LFSR CA Area Overhead Max. Length Sequence
Least
Less than one Gate/node
Higher than LFSR
One Gate/node
Max. Length Sequence
Easy to implement
Well defined P(x)
Harder to implement
Combination of rules not well defined
Performance
Lower – External Feedback
XOR gates in Feedback
Higher – Internal Feedback
Max. one gate/path
High
No gates in feedback
Parallel Pattern Randomness
Low
Shifting of Data
Logical relation with neighbors
Stuck-at-fault detection
Stuck-open and Delay fault Detection
Less number of transitions
Higher number of transitions due to higher randomness
CAD friendliness No
Nodes cannot be cascaded
Yes
Nodes can be easily cascaded
Signature Aliasing
Higher Probability
Lower Probability
4/26/05
Dhingra: ELEC7250

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
4/26/05
Dhingra: ELEC7250

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 Designer’s 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 , 1989
K. Furuya, E.J. McCluskey, “Two-Pattern test capabilities of autonomous TPG circuits,” Proc. of International Test Conference, pp 704 – 711, 1991.
L.T. Wang, E.J. McCluskey, “Circuits for Pseudoexhaustive Test Pattern Generation,” Proc. IEEE International Conference on Computer-Aided Design of Integrated Circuits and Systems, Vol. 7, pp – 1080, 1988
P.D. Hortensius et. al, “Cellular automata-based signature analysis for built-in self-test,” IEEE Transactions on Computers, Vol. 39, pp – 1283, 1990
K. Furuya et. al, “Evaluations of various TPG circuits for use in two-pattern testing,” Proceedings of the Third Asian Test Symposium, pp. 242 – 247, 1994
M. Serra, et. al, “The Analysis of One Dimensional Linear Cellular Automata and Their Aliasing Properties,” IEEE Trans. on CAD, pp , 1990
4/26/05
Dhingra: ELEC7250