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Lecture 13 Sequential Circuit ATPG Time-Frame Expansion (Lecture 12alt in the Alternative Sequence)

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Lecture 13Sequential Circuit ATPGTime-Frame Expansion(Lecture 12alt in the Alternative Sequence)

- Problem of sequential circuit ATPG
- Time-frame expansion
- Nine-valued logic
- ATPG implementation and drivability
- Complexity of ATPG
- Cycle-free and cyclic circuits
- Asynchronous circuits
- Summary and Exercise

VLSI Test: Lecture 13/12alt

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

VLSI Test: Lecture 13/12alt

Time-Frame Expansion

Bn-1

An-1

Bn

An

Time-frame -1

Time-frame 0

1

1

1

1

s-a-0

s-a-0

D

X

D

D

1

1

D

1

Cn-1

X

D

1

Cn

1

Cn+1

X

1

Combinational logic

Combinational logic

1

Sn-1

Sn

X

D

FF

VLSI Test: Lecture 13/12alt

Concept of Time-Frames

- If the test sequence for a single stuck-at fault contains n vectors,
- Replicate combinational logic block n times
- Place fault in each block
- Generate a test for the multiple stuck-at fault using combinational ATPG with 9-valued logic

Vector – n +1

Vector – 1

Vector 0

Fault

Unknown

or given

Init. state

Time-

Frame

- n+1

Time-

frame

0

Time-

frame

-1

Next

state

State

variables

Comb.

block

PO – 1

PO 0

PO – n +1

VLSI Test: Lecture 13/12alt

Five-Valued Logic (Roth)0,1, D, D, X

A

0

A

0

s-a-1

s-a-1

D

D

X

X

X

FF1

FF1

X

D

D

FF2

FF2

B

B

X

X

Time-frame 0

Time-frame -1

VLSI Test: Lecture 13/12alt

Nine-Valued Logic (Muth)0,1, 1/0, 0/1,1/X, 0/X, X/0, X/1, X

A

0

A

X

s-a-1

s-a-1

X/1

0/1

0/X

0/X

X

FF1

FF1

0/1

X

X/1

FF2

FF2

B

B

X

0/1

Time-frame 0

Time-frame -1

VLSI Test: Lecture 13/12alt

Implementation of ATPG

- Select a PO for fault detection based on drivability analysis.
- Place a logic value, 1/0 or 0/1, depending on fault type and number of inversions.
- Justify the output value from PIs, considering all necessary paths and adding backward time-frames.
- If justification is impossible, then use drivability to select another PO and repeat justification.
- If the procedure fails for all reachable POs, then the fault is untestable.
- If 1/0 or 0/1 cannot be justified at any PO, but 1/X or 0/X can be justified, the the fault is potentially detectable.

VLSI Test: Lecture 13/12alt

Drivability Example

(11, 16)

(22, 17)

(10, 15)

(10, 16)

d(0/1) =

d(1/0) = 32

8

s-a-1

d(0/1) = 4

d(1/0) =

d(0/1) =

d(1/0) = 20

8

8

(5, 9)

(4, 4)

(17, 11)

d(0/1) = 9

d(1/0) =

(6, 10)

(CC0, CC1)

= (6, 4)

d(0/1) = 120

d(1/0) = 27

FF

8

d(0/1) = 109

d(1/0) =

8

CC0 and CC1 are SCOAP combinational controllabilities

d(0/1) and d(1/0) of a line are effort measures for driving

a specific fault effect to that line

VLSI Test: Lecture 13/12alt

Complexity of ATPG

- Synchronous circuit -- All flip-flops controlled by clocks; PI and PO synchronized with clock:
- Cycle-free circuit – No feedback among flip-flops: Test generation for a fault needs no more than dseq + 1 time-frames, where dseq is the sequential depth.
- Cyclic circuit – Contains feedback among flip-flops: May need 9Nff time-frames, where Nff is the number of flip-flops.
- Asynchronous circuit – Higher complexity!

Time-

Frame

max-1

Time-

Frame

max-2

Time-

Frame

-2

Time-

Frame

-1

Time-

Frame

0

Smax

S2

S1

S0

S3

max = Number of distinct vectors with 9-valued elements= 9Nff

VLSI Test: Lecture 13/12alt

Cycle-Free Circuits

- Characterized by absence of cycles among flip-flops and a sequential depth, dseq.
- dseq is the maximum number of flip-flops on any path between PI and PO.
- Both good and faulty circuits are initializable.
- Test sequence length for a fault is bounded by dseq + 1.

VLSI Test: Lecture 13/12alt

2

F3

F1

Level = 1

3

Cycle-Free ExampleCircuit

F2

2

All faults are

testable in

this circuit.

F3

F1

3

Level = 1

s - graph

dseq = 3

VLSI Test: Lecture 13/12alt

Modulo-3 Counter

- Cyclic structure – Sequential depth is undefined.
- Circuit is not initializable. No tests can be generated for any stuck-at fault.
- After expanding the circuit to 9Nff = 81, or fewer, time-frames ATPG program calls any given target fault untestable.
- Circuit can only be functionally tested by multiple observations.
- Functional tests, when simulated, give no fault coverage.

VLSI Test: Lecture 13/12alt

F2

F1

Adding Initializing HardwareInitializable modulo-3 counter

Z

CNT

F2

F1

s-a-0

s-a-1

CLR

s-a-1

s-a-1

Untestable fault

Potentially detectable faults

VLSI Test: Lecture 13/12alt

Benchmark Circuits

Circuit

PI

PO

FF

Gates

Structure

Seq. depth

Total faults

Detected faults

Potentially detected faults

Untestable faults

Abandoned faults

Fault coverage (%)

Fault efficiency (%)

Max. sequence length

Total test vectors

Gentest CPU s (Sparc 2)

s1494

8

19

6

647

Cyclic

--

1506

1379

2

30

97

91.6

93.4

28

559

19183

s1238

14

14

18

508

Cycle-free

4

1355

1283

0

72

0

94.7

100.0

3

308

15

s1196

14

14

18

529

Cycle-free

4

1242

1239

0

3

0

99.8

100.0

3

313

10

s1488

8

19

6

653

Cyclic

--

1486

1384

2

26

76

93.1

94.8

24

525

19941

VLSI Test: Lecture 13/12alt

Asynchronous Circuit

- An asynchronous circuit contains unclocked memory often realized by combinational feedback.
- Almost impossible to build, let alone test, a large asynchronous circuit.
- Clock generators, signal synchronizers, flip-flops are typical asynchronous circuits.
- Many large synchronous systems contain small portions of localized asynchronous circuitry.
- Sequential circuit ATPG should be able to generate tests for circuits with limited asynchronous parts, even if it does not detect faults in those parts.

VLSI Test: Lecture 13/12alt

Asynchronous Model

Synchronous PIs

CK

Combinational

Feedback Paths:

Feedback set

Feedback-free

Combinational

Logic

C

PPI

PPO

Synchronous POs

CK

Clocked

Flip-flops

System

Clock, CK

Feedback

delays

Fast model

Clock, FMCK

Modeling circuit is

Shown in orange.

VLSI Test: Lecture 13/12alt

Time-Frame Expansion

Vector k

PI

Feedback

set

Feedback

set

C

CK

C

FMCK

C

FMCK

C

FMCK

PPO

PPI

Asynchronous feedback

stabilization

PO

Time-frame

-k-1

Time-frame

-k+1

Time-frame k

VLSI Test: Lecture 13/12alt

Asynchronous Example

s-a-0

0

0

1

0

1

1

0

1

s-a-0

s-a-0

1

0

1

1

0

1

X

X

0

1

0

1

s-a-0

s-a-0

s-a-0

s-a-1

s-a-0

Vectors

1 2 3 4

Outputs

1 2 3 4

Gentest results:

Faults: total 23, detected 15, untestable 8 (shown in red),

potentially detectable none

Vectors: 4

Sparc 2 CPU time: test generation 33ms, fault simulation 16ms

VLSI Test: Lecture 13/12alt

Summary

- Combinational ATPG algorithms are extended:
- Time-frame expansion unrolls time as combinational array
- Nine-valued logic system
- Justification via backward time
- Cycle-free circuits:
- Require at most dseq+ 1 time-frames
- Always initializable
- Cyclic circuits:
- May need 9Nff time-frames
- Circuit must be initializable
- Partial scan can make circuit cycle-free (Chapter 14)
- Asynchronous circuits:
- High complexity
- Low coverage and unreliable tests
- Simulation-based methods are more useful (Section 8.3)

VLSI Test: Lecture 13/12alt

Exercise

- Which type of circuit is easier to test? Circle one in each:
- Combinational or sequential
- Cyclic or cycle-free
- Synchronous or asynchronous
- What is the maximum number of input vectors that may be needed to initialize a cycle-free circuit with k flip-flops?

VLSI Test: Lecture 13/12alt

Answers to Exercise

- Which type of circuit is easier to test? Circle one in each:
- Combinational or sequential
- Cyclic or cycle-free
- Synchronous or asynchronous
- What is the maximum number of input vectors that may be needed to initialize a cycle-free circuit with k flip-flops?

k vectors. Because that is the maximum sequential depth possible. An example is a k bit shift register.

VLSI Test: Lecture 13/12alt

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