Combinational Controllability Controllability Formulas (Cont.)
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1 Outline Digital Testing: Testability Measures The case for DFT Testability Measures Controllability and observability SCOA measures Combinational circuits Sequential circuits Adhoc techniques Easily testable structures C-testability 1/29/2008 Based on text by S. Mourad "riciples of Electronic Systems" Fab. 2, 2001 Copyrights(c) 2001, Samiha Mourad 2 hat is Design for Test? Also called design for testability That is design to facilitate testing No formal definition for testability ossible definition, testability increases as the cost and time of testing decreases The Case for DFT High device density Large number of gates per pin see next chart High cost of ATG particularly for sequential circuits Need for a shorter design & test cycle shorter-time-to-market Complexity: Gates per in 800 Testing complexity index, in thousands of transitors per pin Feature size, µm 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) 1
2 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 hat 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. SCOA Measures SCOA Sandia Controllability and Observability Analysis rogram 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 , Sep Range of SCOA 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. Combinational Controllability Controllability Formulas (Cont.) 2
3 Combinational Observability Observability Formulas (Cont.) To observe a gate input: Observe output and make other input values non-controlling. Fanout stem: Observe through branch with best observability. An Example A B C G1 G2 G3 H F G G4 G5 Y Z An Example Assume that controllability of all inputs and observability of all outputs is 1 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 A B C G1 G2 G3 H F G G4 G5 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. Y Z Comb. Controllability Controllability Through Level 2 Circled numbers give level number. (CC0, CC1) 3
4 Final Combinational Controllability Combinational Observability for Level 1 Number in square box is level from primary outputs (Os). (CC0, CC1) CO Combinational Observability for Level 2 Final Combinational Observability Sequential Measures D Flip-Flop Equations 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. 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 4
5 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 Testability Computation 1. For all Is, CC0 = CC1 = 1 and SC0 = SC1 = 0 2. For all other nodes, CC0 = CC1 = SC0 = SC1 = 3. Go from Is to Os, using CC and SC equations to get controllabilities -- Iterate on loops until SC stabilizes -- convergence is guaranteed. 4. Set CO = SO = 0 for Os, for all other lines. 5. ork from Os to Is, se 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). Sequential Example Initialization After 1 Iteration After 2 Iterations After 3 Iterations 5
6 Stable Sequential Measures Final Sequential Observabilities Testability Measures are Not Exact Exact computation of measures is N-Complete and impractical Blue (Italicized) measures show correct (exact) values SCOA measures are in orange -- CC0,CC1 (CO) 1,1(6) 1,1(5, ) (6) 1,1(5) (5) 1,1(4,6) (6) (4,6) 1,1(6) 1,1(5, ) 2,3(4) 2,3(4, ) 2,3(4) 2,3(4, ) 6,2(0) 4,2(0) 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 Exercise Compute (CC0, CC1) CO for all lines in the following circuit. Test oints Test points insertion improves observability and controllability O Questions: 1. Is observability of primary input correct? 2. Are controllabilities of primary outputs correct? (a) (b) 3. hat do the observabilities of the input lines of the AND gate indicate? C C1 C2 (c) (d) 6
7 CAD Tools Observation oints G1 faults are masked due to circuit redundancy but they are testable if O observation point is added A B C G1 F G2 H G3 (b) O G4 G5 G Y Z 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, lace and route, DRC, LVS, arameter extraction Most these problems are N-complete There is a need for algorithms that utilize some heuristic and a cost function to stop the computation. Logic and hysical Design Specs Behavioral HDL Simulation Synthesis Logic Simulation Electrical Rule Checker Static Timing Analysis Models Netlist ATG &R Models Fault Grading Back-annotation Mask Models 7
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