1. 10/14/2015 Based on text by S. Mourad "Priciples of Electronic Systems" Digital Testing: Testability Measures

2. Fab. 2, 2001Copyrights(c) 2001, Samiha Mourad2 Outline The case for DFT Testability Measures Controllability and observability SCOAP measures Combinational circuits Sequential circuits Adhoc techniques Easily testable structures C-testability

3. What is Design for Test ? Also called design for testability That is design to facilitate testing No formal definition for testability Possible definition, testability increases as the cost and time of testing decreases

4. The Case for DFT High device density Large number of gates per pin see next chart High cost of ATPG particularly for sequential circuits Need for a shorter design & test cycle shorter-time-to-market

5. Complexity: Gates per Pin

6. Attempt to Assess Testability Test pattern generation requires: controlling a point in the circuit from the primary inputs observing the results at primary output Assessing the controllability of this point and its observability can be helpful in determining the ease or difficulty of its “testability” Hence the notion of Testability Measures (TM)

7. Testability Analysis  Determines testability measures   Involves Circuit Topological analysis, but no test vectors (static analysis) and no search algorithm.  Linear computational complexity  Otherwise, is pointless – might as well use automatic test-pattern generation and calculate:  Exact fault coverage  Exact test vectors

8. What are Testability Measures? Approximate measures of: Difficulty of setting internal circuit lines to 0 or 1 from primary inputs. Difficulty of observing internal circuit lines at primary outputs. Applications: 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.

9. SCOAP 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  Ref.: L. H. Goldstein, “Controllability/Observability Analysis of Digital Circuits,” IEEE Trans. CAS, vol. CAS-26, no. 9. pp. 685 – 693, Sep. 1979.

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

11. Combinational Controllability

12. Controllability Formulas (Cont.)

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

14. Observability Formulas (Cont.) Fanout stem: Observe through branch with best observability.

15. An Example

16. Controllabilities CC1(F)=CC1(A)+CC1(B)+CC1( C)+1=4 CC0(F)=min{CC0(A),CC0(B),CC0( C)}+1=2 CC1(H)=min{CC0(A),CC0(B)}+1=2 CC0(H)=CC1(A)+CC1(B)+1=3 CC1(G)=CC0( C)+1=2 CC0(G)=CC1( C)+1=2 CC1(Y)=min{CC1(F),CC1(H)}+1=3 CC0(Y)=CC0(F)+CC0(H)+1=6 CC1(Z)=min{CC0(H),CC0(G)}+1=3 CC0(Z)=CC1(H)+CC1(G)+1=5 Assume that controllability of all inputs and observability of all outputs is 1 Observabilities CO Y (F)=CO(Y)+CCO(H)+1=5 CO Z (G)=CO(Z)+CC1(H)+1=4 CO Y (H)=CO(Y)+CCO(F)+1=4 e.t.c.

17. Comb. Controllability Circled numbers give level number. (CC0, CC1)

18. Controllability Through Level 2

19. Final Combinational Controllability

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

21. Combinational Observability for Level 2

22. Final Combinational Observability

23. Sequential Measures  Combinational  Increment CC0, CC1, CO whenever you pass through a gate, either forward or backward.  Sequential  Increment SC0, SC1, SO only when you pass through a flip-flop, either forward or backward.  Both  Must iterate on feedback loops until controllabilities stabilize.

24. D Flip-Flop Equations  Assume a synchronous RESET line.  CC1 (Q) = CC1 (D) + CC1 (C) + CC0 (C) + CC0 (RESET)  SC1 (Q) = SC1 (D) + SC1 (C) + SC0 (C) + SC0 (RESET) + 1  CC0 (Q) = min [CC1 (RESET) + CC1 (C) + CC0 (C), CC0 (D) + CC1 (C) + CC0 (C)]  SC0 (Q) is analogous  CO (D) = CO (Q) + CC1 (C) + CC0 (C) + CC0 (RESET)  SO (D) is analogous

25. D Flip-Flop Clock and Reset  CO (RESET) = CO (Q) + CC1 (Q) + CC1 (RESET) + CC1 (C) + CC0 (C)  SO (RESET) is analogous  Three ways to observe the clock line: 1. Set Q to 1 and clock in a 0 from D 2. Set the flip-flop and then reset it 3. Reset the flip-flop and clock in a 1 from D  CO (C) = min [ CO (Q) + CC1 (Q) + CC0 (D) + CC1 (C) + CC0 (C), CO (Q) + CC1 (Q) + CC1 (RESET) + CC1 (C) + CC0 (C), CO (Q) + CC0 (Q) + CC0 (RESET) + CC1 (D) + CC1 (C) + CC0 (C)]  SO (C) is analogous

26. 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 is guaranteed. 4. Set CO = SO = 0 for POs, ∞ for all other lines. 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).

27. Sequential Example Initialization Circled numbers give level number. (CC0, CC1) Numbers in brackets represent (CC0, CC1) and [SS0, SS1]

28. After 1 Iteration

29. After 2 Iterations

30. After 3 Iterations

31. Stable Sequential Measures

32. Final Sequential Observabilities Boldface numbers represent CO and SO

33. Testability Measures are Not Exact Exact computation of measures is NP-Complete and impractical Blue (Italicized) measures show correct (exact) values – SCOAP measures are in orange -- CC0,CC1 (CO) 1,1(6) 1,1(5,∞) 1,1(5) 1,1(4,6) 1,1(6) 1,1(5,∞) 6,2(0) 4,2(0) 2,3(4) 2,3(4,∞) (5) (4,6) (6) 2,3(4) 2,3(4,∞)

34. Summary Testability measures are approximate measures of: Difficulty of setting circuit lines to 0 or 1 Difficulty of observing internal circuit lines Applications: Analysis of difficulty of testing internal circuit parts Redesign circuit hardware or add special test hardware where measures show poor controllability or observability. Guidance for algorithms computing test patterns – avoid using hard-to-control lines

35. Test Points Test points insertion improves observability and controllability

36. CAD Tools All aspect of ASIC design and test depends on CAD tools CAD programs perform different tasks: Design entry, Simulation, Synthesis, layout, Test pattern generation, Fault grading, Floor planning, Technology mapping, Place and route, DRC, LVS, Parameter extraction Most these problems are NP-complete There is a need for algorithms that utilize some heuristic and a cost function to stop the computation.

37. Logic and Physical Design