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ELEC Digital Logic Circuits Fall 2015 Logic Testing (Chapter 12)

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Presentation on theme: "ELEC Digital Logic Circuits Fall 2015 Logic Testing (Chapter 12)"— Presentation transcript:

1 ELEC 2200-002 Digital Logic Circuits Fall 2015 Logic Testing (Chapter 12)
Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering Auburn University, Auburn, AL 36849 Fall 2015, Dec 2 ELEC Lecture 9

2 How to Test? Fall 2015, Dec 2 ELEC Lecture 9

3 ADVANTEST Model T200GS Automatic Test Equipment (ATE), Broun 318
Fall 2015, Dec 2 ELEC Lecture 9

4 Why Compromise on Testing?
Complexity and cost. Example: A digital circuit with 64 inputs (such as a 32-bit adder). There are 264 = possible input patterns or vectors. If we can apply one pattern in 1ns, then time to test the circuit with all patterns is 264 x 10-9 /3600 = hours Or days Or 585 years Fall 2015, Dec 2 ELEC Lecture 9

5 So, We Model Faults A fault model is not necessarily a real defect; model is an abstraction. Modeled faults should be countable; preferably, number of faults should be linear in circuit size. A modeled fault should be theoretically analyzable. Most popular model is the single stuck-at fault. Fall 2015, Dec 2 ELEC Lecture 9

6 Single Stuck-at Fault Three properties define a single stuck-at fault
Only one line is faulty The faulty line is permanently set to 0 or 1 The fault can be at an input or output of a gate Example: XOR circuit has 12 fault sites (●) and 24 single stuck-at faults Faulty circuit value Good circuit value c j 0(1) s-a-0 a d 1(0) g 1 h z i 1 b e 1 k f Test vector for h s-a-0 fault Fall 2015, Dec 2 ELEC Lecture 9

7 Fault Equivalence Total number of single stuck-at fault in a Boolean gate circuit = [ #PI + #gates + # (fanout branches) ] × 2 Fault equivalence: Two faults f1 and f2 are equivalent if the corresponding faulty functions are identical. If faults f1 and f2 are equivalent then any test that detects f1, will also detect f2, and vice-versa. Fault equivalence checking rule: Faults f1 and f2 are equivalent iff the corresponding faulty functions are identical. Fault collapsing: All single faults of a logic circuit can be divided into disjoint equivalence subsets, where all faults in a subset are mutually equivalent. A collapsed fault set contains one fault from each equivalence subset. Fall 2015, Dec 2 ELEC Lecture 9

8 Fault Equivalences Around Gates
sa0 sa1 sa0 sa1 WIRE sa0 sa1 sa0 sa1 AND OR sa0 sa1 sa0 sa1 sa0 sa1 NOT sa1 sa0 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 NAND NOR sa1 sa0 sa0 sa1 sa0 sa1 sa1 sa0 sa1 FANOUT Fall 2015, Dec 2 ELEC Lecture 9

9 Equivalence Collapsing Example
Faults in orange removed by equivalence collapsing sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 20 Collapse ratio = ── = 0.625 32 Fall 2015, Dec 2 ELEC Lecture 9

10 Exercise 1 What is the total number of single stuck-at faults, counting both stuck-at-0 and stuck-at-1, in the following circuit? Counting two faults on each line, Total number of faults = 2 × (#PI + #gates + #fanout branches) = 2 × ( ) = 12 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 Fall 2015, Dec 2 ELEC Lecture 9

11 Exercise 2 How many faults are left after equivalence fault collapsing? s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-0 s-a-1 s-a-1 s-a-0 s-a-0 s-a-1 s-a-1 s-a-0 s-a-1 s-a-0 Collapse ratio = 8/12 = 0.67 Fall 2015, Dec 2 ELEC Lecture 9

12 ■ Find a test for the stuck-at-1 fault shown in the circuit.
Exercise 3 ■ Find a test for the stuck-at-1 fault shown in the circuit. Step 1: Fault activation – Place a value different from faulty value at the fault site 0/1 0/1 s-a-1 Step 2: Path sensitization – activate a path from fault site to an observable output Step 3: Line justification – justify internal lines by setting primary inputs Fall 2015, Dec 2 ELEC Lecture 9

13 Redundant Fault Definition: Faulty function is identical to the fault-free function. No test can be found for a redundant fault. When a redundant fault is present in a circuit, the function is not changed. A circuit with a redundant fault can be simplified. Fall 2015, Dec 2 ELEC Lecture 9

14 Finding a Redundant Fault
Method 1: Compare the faulty function to the fault-free function. Method 2: Try to generate a test and find that no test is possible. Example: Fault A Sa1 This path cannot be sensitized 0/1 Sa1 A B 1 Z Conflicting requirements Fall 2015, Dec 2 ELEC Lecture 9

15 Removing Redundancy Fix line to faulty value and
determine all implications Redundant Sa1 fault 1 A B B B Z B Simplified Circuit B Z Fall 2015, Dec 2 ELEC Lecture 9

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