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This paper delves into a detailed comparison between Linear Feedback Shift Registers (LFSR) and Cellular Automata (CA) for Built-In Self-Test (BIST) applications in VLSI testing. It discusses the implementation of BIST, the characteristics of LFSRs and CAs, their functionalities, and performance in generating test patterns and detecting faults. The study highlights the advantages and disadvantages of both LFSRs and CAs in terms of design complexity, fault coverage, randomness in test patterns, and area overhead. Moreover, it provides insights into the practical applications and considerations for choosing between LFSRs and CAs in different scenarios. References to essential literature that support the analysis are also included.
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Comparison of LFSR and CA for BIST Sachin Dhingra ELEC 7250: VLSI Testing Dhingra: ELEC7250
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 Dhingra: ELEC7250
Built-In Self Test Test Mode Normal Operation System Inputs System Circuit Input Outputs Under Isolation Test Circuitry Test Output Pattern Response Generator Analyzer • 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) Test Controller Dhingra: ELEC7250
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 Dhingra: ELEC7250
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 Dhingra: ELEC7250
Comparison Dhingra: ELEC7250
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 Dhingra: ELEC7250
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 842 - 859, 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. 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,” 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. 767-778, 1990 Dhingra: ELEC7250