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CMP238: Projeto e Teste de Sistemas VLSI Marcelo Lubaszewski Aula 4 - Teste PPGC - UFRGS 2005/I

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Lecture 4 – Testability Measures and Test Pattern Generation Testability Purpose, origins Analysis, measures and computation Summary Automatic test pattern generation Structural vs. functional test Definitions Types of Algorithms Summary

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Purpose Need approximate measure of: –Difficulty of setting internal circuit lines to 0 or 1 by setting primary circuit inputs –Difficulty of observing internal circuit lines by observing primary outputs Uses: –Analysis of difficulty of testing internal circuit parts – redesign or add special test hardware –Guidance for algorithms computing test patterns – avoid using hard-to-control lines –Estimation of fault coverage –Estimation of test vector length

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Control theory Rutman 1972 -- First definition of controllability Goldstein 1979 -- SCOAP –First definition of observability –First elegant formulation –First efficient algorithm to compute controllability and observability Parker & McCluskey 1975 –Definition of Probabilistic Controllability Brglez 1984 -- COP –1 st probabilistic measures Seth, Pan & Agrawal 1985 – PREDICT –1 st exact probabilistic measures Origins

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Testability Analysis Involves Circuit Topological analysis, but no test vectors and no search algorithm Static analysis Linear computational complexity Otherwise, is pointless – might as well use automatic test-pattern generation and calculate: Exact fault coverage Exact test vectors

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Types of Measures SCOAP – Sandia Controllability and Observability Analysis Program Combinational measures: CC0 – Difficulty of setting circuit line to logic 0 CC1 – Difficulty of setting circuit line to logic 1 CO – Difficulty of observing a circuit line Sequential measures – analogous: SC0 SC1 SO

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Range of SCOAP Measures Controllabilities – 1 (easiest) to infinity (hardest) Observabilities – 0 (easiest) to infinity (hardest) Combinational measures: –Roughly proportional to # circuit lines that must be set to control or observe given line Sequential measures: –Roughly proportional to # times a flip-flop must be clocked to control or observe given line

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AND gate O/P 0 controllability: output_controllability = min (input_controllabilities) + 1 AND gate O/P 1 controllability: output_controllability = S (input_controllabilities) + 1 XOR gate O/P controllability output_controllability = min (controllabilities of each input set) + 1 Fanout Stem observability: S or min (some or all fanout branch observabilities) Goldsteins SCOAP Measures

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Controllability Examples

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More Controllability Examples

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Controllability Through Level 0 Circled numbers give level number. (CC0, CC1)

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Controllability Through Level 2

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Final Combinational Controllability

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To observe a gate input: Observe output and make other input values non-controlling Observability Examples

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To observe a fanout stem: Observe it through branch with best observability More Observability Examples

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Combinational Observability for Level 1 Number in square box is level from primary outputs (POs). (CC0, CC1) CO

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Combinational Observabilities for Level 2

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Final Combinational Observabilities

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Testability Computation 1. For all PIs, CC0 = CC1 = 1 and SC0 = SC1 = 0 2. For all other nodes, CC0 = CC1 = SC0 = SC1 = 3. Go from PIs to POS, using CC and SC equations to get controllabilities -- Iterate on loops until SC stabilizes -- convergence guaranteed 4. For all POs, set CO = SO = 0 5. Work from POs to PIs, Use CO, SO, and controllabilities to get observabilities 6. Fanout stem (CO, SO) = min branch (CO, SO) 7. If a CC or SC (CO or SO) is, that node is uncontrollable (unobservable) 8 8

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Testability approximately measures: –Difficulty of setting circuit lines to 0 or 1 –Difficulty of observing internal circuit lines Uses: –Analysis of difficulty of testing internal circuit parts –Redesign circuit hardware or add special test hardware where measures show bad controllability or observability –Guidance for algorithms computing test patterns – avoid using hard-to-control lines –Estimation of fault coverage – 3-5 % error –Estimation of test vector length Summary

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Functional vs. Structural ATPG Functional ATPG generate complete set of tests for circuit input-output combinations 129 inputs, 65 outputs: 2 129 = 680,564,733,841,876,926,926,749, 214,863,536,422,912 patterns Using 1 GHz ATE, would take 2.15 x 10 22 years

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Sum and Carry Circuits

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Structural test: –No redundant adder hardware, 64 bit slices –Each with 27 faults (using fault equivalence) –At most 64 x 27 = 1728 faults (tests) –Takes 0.000001728 s on 1 GHz ATE Designer gives small set of functional tests – augment with structural tests to boost coverage to 98 + % Functional vs. Structural (Contd)

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Definition of Automatic Test-Pattern Generator Operations on digital hardware: –Inject fault into circuit modeled in computer –Use various ways to activate and propagate fault effect through hardware to circuit output –Output flips from expected to faulty signal Test generation cost –fault-dependent or not Quality of generated test –fault coverage (fault simulation) Test application cost –test time, memory requirements

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TG Types Exhaustive –cheap generation, high FC, expensive application Fault-Oriented (deterministic) –expensive generation, possibly high FC, cheaper application –reduction of generation costs Random (pseudo-random) –cheap generation, low FC, + - expensive application

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Exhaustive Algorithm For n-input circuit, generate all 2 n input patterns Infeasible, unless circuit is partitioned into cones of logic, with 15 inputs –Perform exhaustive ATPG for each cone –Misses faults that require specific activation patterns for multiple cones to be tested

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Random-Pattern Generation Flow chart for method Use to get tests for 60- 80% of faults, then switch to D-algorithm or other ATPG for rest

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Path Sensitization Method 1Fault Sensitization (activation) 2Fault Propagation 3Line Justification

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Path Sensitization Method Fault l s-a-v Activation –set l to v Propagation –find a path from l to a primary output that keeps faulty value Justification –set the primary inputs to activate the fault

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Composite Logic Values consider line value for original AND faulty circuit v/v f = original/faulty Symbols D and D (Roth, 1966) D = 1/0 D = 0/1 0 = 0/0 1 = 1/1

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Operations on Composite Values D + 0 = 0/1 + 0/0 = 0/1 = D

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Path Sensitization Method 1 Propagation D

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Path Sensitization Method Propagation: try path f – h – k – L 1 D D D D 0 1 1

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Path Sensitization Method Propagation: try path f – h – k – L 1 D D D D 0 1 1

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Path Sensitization Method Justification: Try path f – h – k – L blocked at j, since there is no way to justify the 1 on i 1 0 D D 1 1 1 D D D

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Path Sensitization Method Justification: Try path f – h – k – L blocked at j, since there is no way to justify the 1 on i 1 D D D 1 1 D D 1 1 1

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Path Sensitization Method Backtracking! 1 D D D 1 1 D D 1 1 1 X X X X X X X X

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Try other propagation: path g – i – j – k – L 0 D D D 1 D D 1 1 Path Sensitization Method D

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Try other propagation: path g – i – j – k – L 0 D D D 1 D D 1 1 Path Sensitization Method D

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Try other propagation: path g – i – j – k – L 0 D D D 1 D D 1 0 1 Path Sensitization Method D

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Major Combinational Automatic Test- Pattern Generation Algorithms D-Algorithm (Roth) -- 1966 PODEM (Goel) -- 1981 FAN (Fujiwara and Shimono) --1983

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Sequential Circuit ATPG Time-Frame Expansion Problem of sequential circuit ATPG Time-frame expansion

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Example of Sequential Circuit

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Sequential Circuits A sequential circuit has memory in addition to combinational logic. Test for a fault in a sequential circuit is a sequence of vectors, which Initializes the circuit to a known state Activates the fault, and Propagates the fault effect to a primary output Methods of sequential circuit ATPG Time-frame expansion methods Simulation-based methods

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Extended D-Algorithm 1. Pick up a target fault f. 2. Create a copy of a combinational logic, set it time-frame 0. 3. Generate a test for f using D-algorithm for time- frame 0. 4. When the fault effect is propagate to the DFFs, continue fault propagation in the next time-frame. 5. When there are values required in the DFFs, continue the justification in the previous time-frame.

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Example for Extended D- Algorithm

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Example: Step 1

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Example: Step 2

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Example: Step 3

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Summary Hierarchical ATPG -- 9 Times speedup (Min) –Handles adders, comparators, MUXes Advances over D-algorithm Results of 40 years research – mature – methods: –Path sensitization –Simulation-based –Boolean satisfiability and neural networks –Genetic algorithms

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Appendix: Other ATPG algorithms 1. TOPS – Dominators Kirkland and Mercer (1987) n Dominator of g – all paths from g to PO must pass through the dominator.

Appendix: Other ATPG algorithms 1. TOPS – Dominators Kirkland and Mercer (1987) n Dominator of g – all paths from g to PO must pass through the dominator.

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