Testing of PLA and PAL.

1 1 1

+V

. . .. . .

0

.

.

.

y1 y2 y m

x 1 x 2 x n

+ V

Buffer

AND OR

. . .

.

.

.

. . .

x 1 x 2 x n

y1 y2 y m

PAL/PLA structure

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2

Example.

1. Permanent constant faults;2. Short-circuits;3. Crosspoint Faults ;

appearance of CP-s in the AND array;;

disappearance of CP-s from the AND array;

appearence of CP-s in the OR array;

disappearance of CP-s from the OR array.

Models of fault in PLA-s and PAL-s

fX fX

s-a-1s-a-0

f1X

f2X

Short

Classical model of fault: constant 1 and 0 (Stuck-at-0, Stuck-at-1, s-a-0, s-a-1)

f1X

X

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2

s-a-1

X3 s-a-1faulty1 = x1 x2 + x1 x2 x3 + x1 x2

y2 = x1 x2 + x1 x2

Permanent constant faults in PLA/PAL-s

Crosspoint Faults Appearance of CP-s to in the AND array

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2 Unnecessary CPy1 = x1 x2 x3 + x1 x2 x3 + x1 x2 x3

y2 = x1 x2 x3 + x1 x2 x3

UnnecessaryvariableShrinkage fault

Carnaugh Map

1 0

0

0

0

0

11

x10

1

00 01 11 10

x2x3y2

1 0

0

0

0

0

01x1

0

1

00 01 11 10

x2x3y2

Faultless Faulty

Disappearance of CP-s from the AND array

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2 CP does not exist y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1

Growth fault

Carnaugh Map

1 0

0

0

0

0

11

x10

1

00 01 11 10

x2x3y2

1 0

1

0

1

0

11x1

0

1

00 01 11 10

x2x3y2

Faultless Faulty

CP does not exist

Appearance of a new CP to the OR-array

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2 Unnecessary CPy1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2 + x1 x2 x3

Carnaugh Map

1 0

0

0

0

0

11

x10

1

00 01 11 10

x2x3y2

1 0

1

0

0

0

11x1

0

1

00 01 11 10

x2x3y2

Faultless Faulty

Appearance fault

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2 CP does not exist y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3

Carnaugh Map

1 0

0

0

0

0

11

x10

1

00 01 11 10

x2x3y2

1 0

0

0

0

0

00x1

0

1

00 01 11 10

x2x3y2

Faultless Faulty

Disappearance fault

Disapperance of the CP from the OR-array

CP does notexist

Missing CP-s are equivalent to some constant faults (Stuck-at-0/1) but additional CP-s do notcorrspond to that model.

n – number of inputsm – number of termsk – number of outputs

(2n + k) – different single and manifold CP faults

2 - 1 -different single and manifold CP faults(2n + k)m

CP faults may be untestifyiable in case of excessive functions

For example:

y1 = x1 + x2 + x1 x2 = x1 + x2

The missing of CP corresponding to whichever variable is not testifyiable in the AND array.

The missing of CP corresponding to this term is not testifyiable in theOR array.

1. Traditional methods for circuits equivalent to PAL/PLA-s;2. Random testing3. Exhaustive testing4. Semirandom methods 5. Deterministic Methods

Generation of tests for PLA-s and PAL-s

Traditional methods for equivalent circuits.

&

&

1

Cons:1.Ineffective due to convergent branching2. CP faults cannot be described as traditional s-a-0/1 faults.

Random testing

&0 0 1 1

0 1 1 0

0 0X

s-a-000

&0 0 1 1

0 1 1 0

0X

s-a-111 0

Discovery of the fault in AND array.

1

0

11

1

00/1 0/1 1

1 0

1/0 1/0

Bringing the impact of the fault to the outputthrough OR array

PAL/PLA...

ReactionsRandom combinations

Cons:1. A very large number of tests as in AND array combinations

where only one input is 1 and the rest are 0scan be used as tests.

2. A very large number of tests as the transport through the OR array requires that one input equals 1 and the rest are 0s.

Exhaustive testing and semirandom methods

PAL/PLA...

ReactionsAll possible combinations

Cons: A large number of tests when real arrays are considered (for example, 50 inputs, 67 outputs, 190 terms)

Exhaustive testing

Semirandom method

PAL/PLA...

ReactionsGenerator of

pseudorandom numbers

&0 1 1

1 0 1

1 1 0

Random numbers are not used. In stead, numbers with only one 0 are used.

Deterministic Test Generation

Special algorithms oriented at the structure of the array and testing of CP-s.

1 1 1+V

x 1 x 2 x 3

0

y 1 y 2

y1 = x1 x2 x3 + x1 x2 x3 + x1 x2

y2 = x1 x2 x3 + x1 x2

Example: let us test whether x1x2 has been Added in the function y2 with CP x3.

Let us define the operation: a # b = a b

Activating the impact of the fault: a = term that can be tested without faults b = term than can be tested with faults

Example. x1 x2 # x1 x2 x3 = x1 x2(x1 x2 x3) = x1 x2 x3

Transport of the impact of the fault to the output: a =result of the previous operation, b =functiwithout the tested term

Example. x1 x2 x3 # x1 x2 x3 = x1 x2 x3 (x1 x2 x3 ) = x1 x2 x3

Test : x1 = 1 x2 = 1

x3 = 0

1 1 0

1/0

0

1/0

0 0 1

Testable PLA Design

What is the objective?

Concurrent testing

Fault masking

Special Design

Self-testing

Test generation

YesNo

No

Yes

No

Yes

Yes No

Yes No

Must be taken into consideration:1. Indicators of testability;2. Impact on the original design;3. Requirements for the testing environment;4. Cost of design

Buffer

AND OR

. . .

.

.

.

. . .

x 1 x 2 x n

y1 y2 y m

Concurrent testing of PAL/PLA-s I

Examples of testable PLA/PAL-s

TSCTwo-rail Checker

f g

Ad

dit

ion

al li

ne TSC

1-out-of-mcode checker

Parity check

f g

faultless/faulty

Totaly Self Cheking (TSC) Two-rail Checker

x0 x1 y0 y1 x0 x1 y0 y1 f

TSCTwo-rail Checker

f g

g

0 1 0 1 0 1

1 0 1 0 0 1

1 0 0 1 1 0

0 1 1 0 1 0

If x0 = y0 and x1 = y1 then f = g

Concurrent testing of PAL/PLA-s I(using the Berger code)

Buffer

AND OR

. . .

.

.

.

. . .x 1 x 2 x n y1 y2 y m

Ad

dit

ion

alli

nes

TSCTwo-rail Checker

f g

Control codegenerator

Inverse value of thecontrol code

Control code

Berger code

0 1 1 0 1 0 1 1

Orders of infoOrder of control (number of 0s in the code)

011

Control ordergenerator

Orders of info

Orders of control

Comparison scheme True/false

Modifyied Berger code for a set of functions.

0 1

0

1

0

0

11x1 x2

00

00 01 11 10

x3x4y1

1 1

0

0

0

0

11

01

11

10

1 0

1

0

0

0

10x1 x2

00

00 01 11 10

x3x4y3

1 0

1

0

0

1

11

01

11

10

1 0

0

0

0

1

11x1 x2

00

00 01 11 10

x3x4y2

1 0

0

0

0

0

11

01

11

10

01 10

10

10

11

10

0001x1 x2

00

00 01 11 10

x3x4c1 c2

00

10

11

11

10

0000

01

11

10

10

PAL/PLA testable with universal tests

AND OR

. . .

.

.

.

. . .

x 1 x n

y1 y2 y k

c1

c2

s1

sm

. . .

sm+1

Par

ity

chec

k

z1

Additional line

Parity check

Additionalline

z2

Sel

ecti

on o

f te

rms

Decoder of the modified inputs

Decoder of the modifiedinputs

1

&

&

b2i-1

b2i

xi

c1 c2

It is possible to test an array without knowing how it has been programmed. The testing is not concurrent.

x1 … xi … xn c1 c2 s1 … sj … sm z1 z2 I1 - … - … - - - 0 … 0 … 0 0 0 For j=1, … , m

Ij0 0 … 000 … 0 1 0 0 … 010 … 0 1 1 Ij1 1 … 111 … 1 0 1 0 … 010 … 0 1 1 For I=1, … , n

Ji0 1 … 101 … 1 0 1 1 … 111 … 1 em - Ji1 0 … 010 … 0 1 0 1 … 111 … 1 em -

Universal tests

em =0, if m is odd1, if m is even

The length of the tests is 1+m+n, wherem is the number of terms and n is that of inputs.

A built-in Self-Testable PLA with Cumulative Parity Comparision

AND(the number of

used CP-s at each linemust be odd))

OR(the number of

used CP-smt each line must

be even)

. . .

.

.

.

. . .

x 1 x n

y1 y2 y k

c1

c2

s1

sm

. . .

sm+1

Additional line

Parity check

Ad

dit

ion

al li

ne

Sel

ecti

on o

f te

rms

Decoder of the modified inputsxor

T

Dz

While transmitting universal tests (n+m+1) the trigger takes at each test series the opposite value according to the previous series.

Methods using signature

LFSR - Linear Feedback Shift Register

T T + T T+

Signature Analyzer

T T + T T+++

Parallel.

Series

T T T T+

+

Signal from the checked object

Signals from the checked object

Buffer

AND OR

. . .

.

.

.

. . .

x 1 x 2 x n

y1 y2 y m

LFSR(Generator of

pseudorandomnumbers)

Signature analyzer I

Signature analyzer II

All possible input combinations may be usedinstead of the generator of pseudorandomnumbers

PLA/PAL with BILBO-s.

BILBO – Built-in Logic-Block Observer

LFSR that can be activated as the generator of pseudorandom numbers or as signature analyzer (depending on the conditions chosen)

Buffer

AND OR...

. . .y1 y2 y m

BILBO I BILBO II

BILBO III

. . .x 1 x 2 x n

More methods for improving the testability

1.    Counting of CP-s. Presupposes the conductivity of bit lines and term lines. Presupposes that the expected CP numbers are known (functioning array)2.    feedback from the signature analyzer to the inputs (to the LFSR generating pseudorandom values). Thus ate these blocks united into one. 3.    several signature analyzers are used for testing both the AND and OR part. For example, one is used for testing even bit lines and the other for odd. It results in the better use of the chip area as the analyzer behind the bit lines requires more space than the bit lines. 4.    AND and OR arrays are divided into parts that enables to test them simultaneously. Presupposes that additional requirements are set for thr programming of PAL/PLA-s.