Models for Power-Aware Testing - Models in Hardware Testing - page 194

2000000

1500000

1000000

500000

0

0 1 2 3 4 5 6 7

Primitive polynomial

Fig. 7.8 Impact of LFSR polynomial on energy

To analyze the impact of these parameters on the switching activity generated
in the CUT, a number of experiments were conducted on various types of circuit.
For each circuit, several characteristic polynomials were used for the LFSR, and for
each of these polynomials, several seeds were tried. Polynomials were taken from
the list of primitive polynomials of an n-stage LFSR (n being the number of primary
inputs of the CUT), and seeds were randomly chosen for each selected polynomial.
In each experiment, the length of the test sequence required to reach the target fault
coverage was determined through fault simulation. Results of these experiments are
reported in Fig. 7.8 for circuit c1908 of the ISCAS'89 benchmark suite. The stuck-at
fault coverage is equal to 99%. Each value on the X axis corresponds to a particular
primitive polynomial of the LFSR, and each dot corresponds to the internal WSA
resulting from a randomly selected seed for the particular polynomial. Note that the
internal WSA refers to the Weighted Switching Activity of the internal nodes of
the CUT.
As can be seen, the WSA obtained for a given primitive polynomial of the LFSR
strongly depends on the seed selected. Indeed, the deviation between best seeds and
worst seeds is very significant in terms of WSA. On the other hand, sensitivity of
the WSA to a given primitive polynomial is much lower; the value of the minimum
WSA is almost the same regardless of which primitive polynomial is used. There-
fore, selecting a primitive polynomial to minimize energy dissipation during BIST
is not as crucial as selecting a good seed for the LFSR.

7.4.2.2 LFSR Seed Selection for Energy Minimization During BIST

Finding the best seed of a given primitive polynomial LFSR to achieve the low-
est energy and a given fault coverage is a rather complex problem. Consequently,
a nearly optimal solution proposed in Girard et al. ( 1999 ) is based on a simu-
lated annealing algorithm that follows the basic strategy of Johnson et al. ( Johnson
et al. 1989 ) . This method is built on an analogy with thermodynamics, and allows
to converging to a final solution by only considering a limited number of partial
solutions that are selected partly based on randomness.
The algorithm is reported in Fig. 7.9 . The inputs to this algorithm are the number
of stages of the LFSR, which is given by the number of primary inputs of the circuit,