Final Exam Review
Homework Notes
• Pay attention to significant digits
• Should not have more significant digits in answer than in problem
• Example: HW1 #1.1
• 90% yield (1 significant digit), 80% fault coverage (1 significant digit), DPM
= 20,000 or maybe 21,000, not 20,851.638!
• Provide answers, not data dumps
• Answers in HW3 problems 1 and 2 were far longer than necessary,
correct, but unnecessary
• Example:
• Question: Explain how SCOAP metrics are related to combinational and
sequential testability.
• Key part of answer: Combinational SCOAP is roughly related to the number
of necessary assignments for the test, and sequential scope is related to
the number of time frames to sensitize and propagate the fault. A data
dump on all SCOAP detail is not necessary.
Homework Notes
• Pay attention to what question is asked
• Example: HW3 #3
• Question: What is the drawback of time-domain expansion for
sequential ATPG of deeply sequential circuits?
• The question is not asking about the difficulty of testing deeply
sequential circuits (that is hard), or whether they are acyclic or
cyclic, or have a reset state, but of using time-frame expansion
for sequential test.
• Obvious issues: 1) large numbers of time frames and large
amounts of memory are required; 2) large state space to
search; 3) large number of inputs (inputs in each time frame);
4) need to avoid fault site when sensitizing and propagating.
• Many missed the issue of the size of the circuit representation.
Remember my example of a testing a SA0 on the MSB of a 32bit counter.
Homework Notes
• Problem 1.11: How many mandatory and optional
pins are required for IEEE 1500?
• 8 mandatory – WSI, WSO, WRCK, WRSTN, SelectWIR,
CaptureWR, ShiftWR
• Optional – TransferDR, AUXCKn, WPI, WPC, WPO
• It is IEEE 1149.1 that has 4 required pins – TCK, TMS,
TDI, TDO, and optional TRST*
Homework Notes
• Question 2.18(c): How many errors can be detected by
the X-compactor?
• Solution: Theorem 2.2
• Errors from 1, 2, or odd # of scan chains at the same scan-out
cycle are guaranteed to produce errors if every row of the
matrix is non-zero, distinct and contains an odd number of 1s.
• True for this matrix
• Total errors = C(8,1)+C(8,2)+C(8,3)+C(8,5)+C(8,7) = 156
• Looking at columns in matrix gets 8x3 = 24, but ignores
combinations
• At most 7 faulty scan chains can be detected in one cycle
• Over multiple cycles, an infinite number of faults can be
detected
Final Exam 2013
• More up-to-date on coverage than practice exams
Question 1
• In a regular SOC, a TAM is used to deliver test patterns and
collect test results from the cores. Suppose you have a TAM
that has 10 data lines, and all cores have MISRs so that test
results do not have to be read while the test patterns are
delivered. We will ignore the time to read back the MISRs.
Consider an SOC with 4 cores. Core 1 has test patterns that
can be delivered on 3 lines in 10000 cycles with 400 mW
power dissipation, 6 lines in 5000 cycles and 750 mW, or 10
lines in 3000 cycles and 1000 mW. Core 2 has test patterns
that can be delivered on 3 lines in 20000 cycles and 300
mW, 4 lines in 15000 cycles and 400 mW or 5 lines in 12000
cycles and 500 mW. Cores 3 and 4 each have test patterns
that can be delivered on 2 lines in 20000 cycles and 300 mW
or 4 lines in 10000 cycles and 600 mW.
Question 1(a)
• (10 pts) Draw the shortest test schedule you can find. What is the
maximum power dissipation during this schedule?
• Solution 1: Test core 1 with 6 lines in 5k cycles, then core 2 with 5 lines in
12k cycles, so 17k cycles total. At the same time test core 3 and core 4
with 2 lines in 20k cycles, so the total time is 20k cycles. So using initially
9 lines for 5k cycles, then 9 lines for 12k cycles, then 4 lines for 3k cycles.
This uses a peak power of 750mW + 300mW + 300mW = 1350mW,
which drops to 500mW + 300mW + 300mW = 1100mW.
• Solution 2: Test core 1 with 3 lines in 10k cycles, core 2 with 3 lines in 20k
cycles, core 3 and 4 with 2 lines each and 20k cycles. So total time is 20k
cycles, with peak power of 400mW+300mW+300mW+300mW =
1600mW.
• Note that we are assuming that you cannot vary the number of TAM
wires used by a core during the test, since not enough information has
been given to assume the transitions between the number of TAM wires
(e.g. is the total number of bits conserved).
Question 1(b)
• (10 pts) Draw the shortest test schedule you can find that
dissipates no more than 1000 mW.
• Solution 1: Test core 1 with 10 lines for 3k cycles @ 1000
mW, then core 2 with 3 lines and 20k cycles @ 300mW, and
cores 3 and 4 with 2 lines and 20k cycles @ 300 mW. So
total time is 23k cycles. Power is 1000 mW for the first 3k
cycles, then 300mW+300mW+300mW = 900mW for the
next 20k cycles.
• Solution 2: Test core 3 with 4 lines and 10k cycles @ 600mW
and then core 4 with 4 lines and 10k cycles @ 600mW, while
at the same time test core 2 with 3 lines and 20k cycles @
300mW. Then test core 1 with 10 lines and 3k cycles @
1000mW. So total time is 23k cycles. The power is 900mW
for the first 20k cycles, then 1000mW for the last 3k cycles.
• There are other 23k cycle schedules.
Question 2(a)
• (10 pts) In the figure below, show the test for a SA0 on the output of gate 11
that will be generated by the PODEM algorithm. Write on the figure and explain
the sequence of decisions.
• Combinational controllability values shown on relevant parts of the circuit. To set
1 on G11, set 1 on G9 since has lower CC1, then set 1 on inputs of G9, set 0 on
input of G8, which propagates a 1 on G7, which is consistent. Therefore C=0 and
the test is generated.
Question 2(b)
• (5 pts) List the stuck-at faults (e.g. gate 1 SA0, gate 2 SA1,…) that are fortuitously
detected by the resulting test. Assume an X value does not sensitize or
propagate a fault.
• The output of G6 is an X. Normally that means the output of G10 is an X, so SA1
on C, SA0 on G7, SA0 on G8, and SA0 on G9 cannot be detected, using the D
algebra. However, if there is a SA0 on G7, then both G9 and G10 will be 0, so
G11 will be 0, in contrast to the fault-free value of 1. So the SA0 on G7 will be
detected.
(4,2)
(1,1)
(5,5)
(5,5)
(2,3)
(1,1)
(6,8)
(7,2)
SA0
(7,2)
(1,1)
(1,1)
1
1
(4,2)
1
(1,1)
(2,2)
0
(1,1)
(3,5)
1
(10,6)
Question 3
• (15 pts) For the circuit below, FFs 7 and 8 are connected together in a scan chain (the
scan chain is from 7 to 8). Their D inputs can be directly observed as PPOs. FF outputs Q1
and Q2 are PPIs. You wish to generate a launch-on-capture test to detect a slow-to-rise
(STR) transition fault on Z. We assume Z can be directly observed by a tester. What scan
pattern (each bit is 0, 1, or X) and value on R (0, 1, X, the value is not allowed to change)
will detect the TF? Draw on the diagram as necessary to explain your answer. For
example, you can show 0 → 1 for a 0 to 1 transition on a line. If the STR fault on Z is
untestable, explain where the conflict is located. Extra copies of the circuit are attached
to work out your solution.
0
0
1→0
0→1
0→1
0→1
STR
0→1
0→1
1
1
0→1
0
0
1→0
1→0
0→1
1
Detecting a STR on Z
requires a 0 → 1 on G5.
Working backwards, this
requires R=0, Q1=0 and
Q2=1.
Question 4
• (5 pts) What is the basic idea of testing a source
synchronous high-speed I/O?
• In a source synchronous I/O, the signal and clock
both come from the output, and then drive a flipflop at the receiver. To test it, the clock can be
skewed early or late relative to the data, to verify
that the flip-flop setup and hold times will be met
given jitter between the clock and data.
Question 5
• (10 pts) In time frame expansion in sequential
testing, we “unroll” the circuit in time. Show this
for the circuit in Problem 3, for 2 time frames.
Assume there is a SA0 fault on the output of gate 1.
SA0
SA0
Question 6
• (10 pts) Consider an embedded core with 8 functional inputs a[0:7], 11 functional
outputs z[0:10], 9 internal scan chains of lengths 12, 12, 8, 8, 8, 6, 6, 6 and 6 scan cells
each, and a scan enable SE. The test wrapper for the core will be connected to two TAMs
– a 4-bit TAM and a 6-bit TAM. A signal c selects between them. Present a table for each
TAM. In each table, for each wrapper scan chain, list the scan chains (# scan cells),
wrapper input cells (# cells), wrapper output cells (# cells) that are included, along with
its scan-in length (excludes wrapper outputs), and scan-out length (excludes wrapper
inputs). What is the speedup in test time by using the 6-bit TAM instead of the 4-bit
TAM?
• Using TAM4, in the worst case we need 20+21 = 41 cycles to scan in the input and scan
out the results. Using TAM6, in the worst case we need 14+14 = 28 cycles to scan in the
input and scan out the results. The speedup by using TAM6 is 41/28 = 1.46x.
Scan chains
# input cells
1
12+8
=20
0
TAM4
2
3
12+8 8+6
=20
=14
0
6
4
6+6+6
=18
2
1
12
2
12
0
0
TAM6
3
4
8+6 8+6
=14 =14
0
0
5
8+6
=14
0
6
6
8
# output cells
0
1
7
3
2
1
0
0
0
8
Scan-in length
20
20
20
20
12
12
14
14
14
14
Scan-out length
20
21
21
21
14
13
14
14
14
14
Question 7
• (5 pts) How can one assign values to don’t care (X) bits in a scan
pattern to reduce power dissipation during scan testing?
• If we copy the previous bit in the chain, known as adjacent filling,
then the scan chain shift will only produce transitions where bits
are changing from 0 to 1 or 1 to 0. Since the typical pattern has
only about 1% care bits, then only about 1% of the scan cells will
generate an input transition on each shift.
• Example:
101XXXX0110XXX
10111110110000 – 5 transitions per shift
• For capture cycles, we can attempt to fill the X bits so that they
have the same value on launch and capture.
Question 8
• (5 pts) Why is it easier to detect bridging faults with
IDDQ test instead of detecting erroneous logic values?
• IDDQ provides 100% observability if the bridged fault
has a 0-1 or 1-0 across it. There is no need to propagate
the value to an output, so no need to set necessary
assignments for observability. It is only necessary to set
the 0-1 or 1-0 sensitization. This means that more faults
can be detected per pattern.
• Another interpretation is that it can detect bridges that
do not cause a logic fault. These might be delay faults
or IDDQ-only failures.
Question 9
• (5 pts) What is the key assumption we usually make
about failures when building fault-tolerant
systems?
• We assume a single fault in the system. For
example, triple modular redundancy will always
correct any single fault, but cannot handle more
than one.
• We also assume that the faults are independent.
Question 10
• (5 pts) How do X values on a circuit output cause
problems in logic BIST?
• If using a MISR on the output, each captured X
means the MISR could be in two possible states, so
for n X outputs, the MISR could be in 2n states, and
one of those states could alias to the fault-free
state.
Question 11
• (5 pts) What is the basic idea in using BIST to test
reconfigurable FPGAs?
• We can have the FPGA test itself. Some logic blocks
can be configured as LFSRs and others as MISRs, to
test the logic or the interconnect in between. The
configuration is changed to move the LFSRs and
MISRs around and their connectivity to test
everything.