SYNTHESIS
OF
IDDQ-TESTABLE CIRCUITS:
INTEGRATING BUILT-IN CURRENT SENSORS
H.-J. Wunde lichl,
M.
He zogl
J. Figue as2, J.A. Ca asco2, and A. Calde 6n2
(1)Ins i u e
o
Compu e S uc u es, Uni e si y
o
Siegen,
Hoelde lins .
3,57068
Siegen, Ge many
(2)Depa men
o
Elec onics Enginee ing, Uni e si a Poli ecnica de Ca alunya,
Diagonal
647,
pl a.
9,08028
Ba celona, Spain
Abs ac
"On-Chip"
IDDQ
es ing by he inco po a ion
o
Buil -
In Cu en (BIC) senso s has some ad an ages o e
"o -
chip" echniques. Howe e , he in eg a ion o senso s
poses analog design p oblems which a e ha d o be sol-
ed by a digi al designe . The au oma ic inco po a ion
o
he senso s using pa ame e ized BIC cells could be a p o-
mising al e na i e. The wo k epo ed he e iden i ies
pa i ioning c i e ia o guide he syn hesis o
IDDQ-
es able ci cui s. The ci cui mus be pa i ioned, such
ha he de ec i e
IDDQ
is obse able, and he powe
supply ol age pe u ba ion is wi hin speci ied limi s. In
addi ion o hese cons ain s, also cos c i e ia a e consi-
de ed: ci cui ex a delay, a ea o e head
o
he
BIC
sen-
so s, connec i i y cos s
o
he es ci cui y, and he es
applica ion ime. The pa ame e s a e es ima ed based on
logical as well as elec ical le el in o ma ion
o
he a -
ge cell lib a y o be used in he echnology mapping
phase
o
he syn hesis p ocess. The esul ing cos unc-
ion is op imized by an e olu ion-based algo i hm. When
un o e la ge benchma k ci cui s ou me hod gi es
signi ican ly supe io esul s o hose ob ained using
simple and less comp ehensi e pa i ioning me hods.
1
In oduc ion
The es me hodology based on he obse a ion o
he quiescen cu en (IDDQ) complemen s logic ( ol-
age) es ing
in
CMOS echnologies. The quiescen
cu en consumed by he IC is a good indica o o he
p esence o a la ge class o de ec s escaping logic es
[l-61. On-chip Buil -In Cu en (BIC) senso s ha e been
p oposed o o e come some o he p oblems encoun-
e ed in o -chip IDDQ es ing: long es ing imes and
low disc imina ion
o
small de ec i e cu en s. These
This wo k has been pe o med
wi hin
he amewo k o he
ESPRIT P ojec
7107
A chimedes
p oblems can be sol ed by pa i ioning he Ci cui
Unde Tes (CUT) in subci cui s, each p o ided wi h a
BIC senso . In ecen yea s, di e en BIC senso s ha e
been p oposed [7-111. Some BIC senso s (i.e. pn junc i-
ons
o
bipola de ices) in oduce a ol age d op du ing
ansien swi ching which can be unaccep able in some
applica ions due o i s e ec s in delay and noise ma -
gin educ ion.
Fo
hese applica ions he BIC senso s
ha e o inco po a e a bypass elemen
so
ha he pe -
u ba ion
in
he i ual g ound is below a ce ain maxi-
mum.
The class o BIC senso s conside ed in his pape is
illus a ed
in
igu e
1.
The BIC senso includes a sen-
sing de ice, a bypass
MOS
swi ch and a de ec ion ci -
cui y. A con ol signal
C
is applied o he ga e o he
bypass
MOS
de ice. Du ing no mal ope a ion,
C
=
1,
u ns he MOS on. Du ing es ing, i s
C
is se o
1
and
a es pa e n is applied o he CUT. When he ansien
iDD
cu en has decayed,
C
is se o
0,
u ning he
MOS
o , and he sensing de ice p oduces a ol age
signal which is p ocessed by he de ec ion ci cui y o
p oduce a PASSFAIL signal, depending on whe he
he sensed IDDQ alls below/abo e a gi en h eshold
alue
IDDQ,~~.
Se e al sensing de ices can be used
[7-
121,
each wi h i s ad an ages and disad an ages. This
kind o es abili y enhancemen may cause ex a delay
and a ea o e heads as well as a educ ion o he noise
immuni y ma gins
[8,9,12,13,15],
and he objec i e o a
sophis ica ed BIC senso placemen should be minimi-
zing hese d awbacks.
Im- es o la ge CUTS canno be done e ec i ely
using a single BIC senso . One ob ious eason is he
need
o
an app op ia e disc iminabili y. E ec i e es
o de ec s in CMOS ypically equi es
IDDQ, h
=
IPA
and non de ec i e IDDQ cu en s
o
la ge ci cui s can be
la ge han
1
PA. Also, he la ge pa asi ic capaci ance
in oduced a he sensing node by he CUT and he sen-
sing de ice ad e sely impac s es imes. These p o-
blems can be alle ia ed by pa i ioning he CUT in o
573
1066-1409/95 $4.00
0
1995
IEEE
g oups o ga es and in oducing a BIC senso o each
L
de ec ion
i ual
GND
-
ci cui y
-
g oup [12,13].
+
PASS
/
FAIL
pe io i y o his app oach o e a s aigh o wa d manual
BIC senso placemen .
"DD
4
Figu e
1:
A chi ec u e
o
a
BIC
senso
wi h
a
bypass de ice.
Fine-g ain pa i ions yield high disc iminabili y and
low es imes bu incu in high a ea o e head due o
he ( eplica ed) de ec ion ci cui y, ex a ou ing
caused by he in oduc ion o he i ual ail and ou ing
among BIC senso s. Coa se-g ain pa i ions ha e
smalle a ea o e heads bu gi e smalle disc imina-
bili ies and longe es imes. In addi ion, he ,,shape"
o he g oups can ha e a g ea in luence on he equi ed
BIC senso a ea. This is illus a ed
in
igu e 2, which
shows wo di e en pa i ions o a CUT wi h a wo-di-
mensional a ay s uc u e in ol ing h ee cell ypes.
Pa i ion
1
has an a e age maximum
iDD
in
each g oup
smalle han pa i ion
2
as he h ee cells C1, C2, C3
will no swi ch
in
pa allel; hus, using pa i ion 2, he
swi ching de ices ha e o be g ea e o gua an ee he
same limi s o he i ual ail pe u ba ion, and pa i ion
1
should be p e e ed.
Finding good pa i ions o
IDDQ
es abili y is a
complex p oblem whe e disc iminabili y be ween aul y
and aul ee cu en , a ea o e head, delay deg ada ion
and es applica ion ime ha e o be conside ed. In his
pape we p opose an e olu i e op imiza ion me hod o
minimizing a cos unc ion subjec o es ic ions. The
cons ain s a e disc iminabili y and i ual ail pe u ba-
ion. The cos unc ion is ob ained by weigh ing es ima-
o s o he di e en cos s in ol ed
in
he ade-o .
These es ima o s make an app op ia e ade-o be -
ween accu acy and compu a ion complexi y and a e
e alua ed using pa ame e ized elec ical le el in o ma-
ion o he a ge echnology. The es o he pape is
o ganized as ollows. Sec ion
2
s a es o mally he pa -
i ioning p oblem and i s cons ain s. Sec ion
3
de-
sc ibes he es ima o s used in he cos unc ion. Sec ion
4 su eys he e olu ion op imiza ion algo i hm. The ex-
pe imen al esul s discussed
in
sec ion
5
show he
su-
Pa i ion
1
;
BIC-Senso
a
BIC-Senso
I
BIC-Senso
I
Pa i ion
2
Figu e
2:
Two pa i ions
illus a ing
he impac
o
he g oup
shape
in
BIC
senso a ea.
2.
P oblem s a emen and cons ain s.
To se -up o mally he pa i ioning p oblem, he
CUT is modelled by a di ec ed g aph
C
=
(G,
T),
whe e
G
is he se o ga es and
T
includes he connec ions
among he ga es.
.4
pa i ion
Il
o
G
is a collec ion
{MI,
...,
Mk}
o disjoin g oups o ga es (modules) co-
e ing
G
(U;"=,
M,
=
G).
Each ga e is comple ely
included
in
one g oup, hence no ansis o g oup is spli
among g oups, a oiding po en ial la chup p oblems
[11,14]. Le
IDDQ,~~
be he minimum de ec i e IDDQ
cu en which has o be de ec ed and le
IDDQ,~,,
be
he maximum non-de ec i e cu en o module
M,
The
disc iminabili y o
M,
is de ined as
'DDQ. h
2d.
IDDQ.nd.1
4
(4
1
=
Fo he easibili y o an
IDDQ
es ,
d
>
1
is equi ed,
574
and a ypical alue is 10. This es ic ion can be ex-
p essed by a cons ain e alua ion unc ion de ined on
he se o all possible pa i ions
P
as :
P
-+
(0,l) wi h
K
V
d(Mi)
2
d
i=l
(n)
=
1
The o he a ge s conce ning speed and a ea can be
desc ibed by a global cos unc ion
C
on each pa i-
ion. I is de ined as
C:
P
-+
R
in
e ms o he ela i e
weigh s
ai
o he me ics
ci:
n
i=l
The pa ame e s de ined abo e allow es ablishing
he global cos unc ion o op imiza ion in he design
space Speed-A ea-Tes abili y acco ding o di e en
p io i ies e lec ed on he alues o he weigh ac o s
ai.
Cons ain s and cos s lead o a pa i ioning p oblem
as ollows:
Pa i ioning P oblem PART-IDDQ
:
Find a pa i-
ion
ll*
sa is ying he cons ain s
(Il*)
and a he
same ime minimizing he global cos unc ion
c(n*).
In gene al, his p oblem is NP-ha d, and heu is ics
o ind accep able solu ions a e p oposed. In addi ion,
he p ecise e alua ion o he cons ain s and he cos
unc ions a e elec ical le el p oblems which a e no
sol able
in
accep able ime excep o e y small ci -
cui s. In he nex sec ion, app oxima e es ima ing p o-
cedu es a e p esen ed using he ga e le el desc ip ion
o he CUT and he a ge cell lib a y.
3
Maximum cu en and cos es ima o s
In his sec ion a se o es ima o s o he a iables
necessa y o e alua e he cons ain s and cos s a logic
le el a e p oposed. A a ge cell lib a y ully cha ac e-
ized a elec ical le el is assumed a ailable.
3.1
A pe u ba ion o he Vi ual G ound (Vi ual VDD)
is
caused by he inco po a ion o he I~SQ
(IDDQ)
BIC
senso s. This a ia ion o he powe supply ol age cau-
ses a educ ion o he noise immuni y ma gins. In addi-
ion, ci cui s wi h memo y elemen s may loose he
memo ized in o ma ion. The wo s pe u ba ion occu s
du ing swi ching when he cu en is maximal. A con-
s ain pu on his ol age d opping is usual o choosing
he size o he BIC senso s. The ol age d opping de-
pends on he maximum ansien cu en
D,,,,,j
h ough module
Mi
and on he senso a ea.
Fo each module
Mi
he maximum ansien cu en
A ea o e head due o
BIC
sensing.
is es ima ed by he maximum numbe o
ga es o modules swi ching simul aneously. In o de o
es ima e a alue a logic le el we assume ha all
ga es loca ed a he same dep h on di e en pa hs,
swi ch in a way ha hei maximum cu en s add. This
is a pessimis ic assump ion as we do no conside pa hs
possibly blocked. This simpli ies he p oblem, and only
he possible pa hs o all ansi ions and he maximum
simul anei y o ansi ions a e iden i ied. Fo each ga e
gi
all possible
Li
ansi ion pa hs and he imes o
ansi ion
..
a i al a e de e mined. In his way a se o in-
ege s i, i,.
.
.,
&
,
...,
'pL, is compu ed indica ing he
possible imes o ansi ions a he ga e
gi
o each
pa h
Pk,
whe e
k:=
1
,...,
Li.
An uppe limi o
max(iDD} o a g oup
Mi
o ga es is compu ed by
1
The es ima e o
DD,mm,,
is app oxima e and
pessimis ic, bu is compu a ionally e icien enough o
allow explo a ion o a la ge numbe o pa i ions
in
easonable amoun s o CPU ime.
Le
Rs,~
be he ON esis ance o he BIC senso o
Mi,
he maximum i ual ail pe u ba ion can be ap-
p oxima ed by
Rs,i
*
DD,m,,i.
The maximum i ual
ail pe u ba ion
o
each module is limi ed o a gi en
p ede ined alue
,
yielding
*
Since he equi emen s o
a e ypically e y
s ingen (be ween
l00mV
and
300mV)
he impac o
he easible
Rs,~
on he delay o he CUT ends o be
small. Then, o simpli y he op imiza ion p oblem we
ake:
*
..
I
Rs,i
=
,
l4iIK.
The senso a ea cos es ima o is compu ed using an
a ea model o he o m
4
+A,
I
Rs
o each BIC
senso , whe e he e m
4
accoun s o he de ec ion
ci cui y and he e m
AI
I
Rs
accoun s o he sensing
elemen and he bypass de ice. This gi es
DD,
max,i
As
all componen s o he objec i e unc ion should
ha e simila ange and a ia ion o op imiza ion
easons
we
ac ually compu e
CI
(II):=
log(A)
515
3.2
Delay o e head due o BIC senso s.
The delay o e head cos is compu ed as:
whe e
D
is he delay o he ci cui wi hou BIC senso s
and
DBIC
is he delay o he ci cui wi h BIC senso s.
Bo h delays a e compu ed using a longes pa h algo-
i hm. The ga e delays
DBIc(g, )
( hese delays a e
ime g id unc ions) used o
DBIC
a e ob ained om
he nominal ga e delays (wi hou BIC senso )
D(g)
and deg ada ion ac o s
6(g, )
as
The ga e delay deg ada ion ac o
6(g, )
is ob-
ained using a second o de elec ical ne wo k model
ha ing as pa ame e s
Rs
( he BIC senso
ON
esi-
s ance),
Cs
( he pa asi ic capaci ance a he i ual
ail node),
Cg
( he equi alen capaci ance a he ou -
pu o
g),
Rg
(an a e age equi alen ON esis ance o
he discha ging ne wo k o a ga e o he CUT), and
n( )
( he ac i i y-numbe o simul aneously swi ching
ga es a ime
).
Wi h hese assump ions he exp es-
sion o he ga e delay deg ada ion becomes
The in e connec ion cos s a e di ided in o cos s o
linking he BIC senso s o he ga es wi hin each mo-
dule, and he cos s o connec ing he BIC senso s o
all modules by he es clock and es ou pu . The mo-
dule in e connec ion cos s ake in o accoun he di i-
cul y
in
sensing ga es placed in emo e loca ions. The
sepa a ion pa ame e
S(gj,gj)
o wo ga es
gj
and
gj
is he minimum numbe o nodes a e sed when going
om
gj
o
gj in
he
undi ec ed
g aph
o he logic ci -
cui .
I
S(gj,gj)
exceeds a ce ain pa ame e say
p,
o
i
no pa h exis s be ween
gj
and
gj,
we se
The sepa a ion pa ame e
S(M)
o a module
M
is
de ined as he sum o he sepa a ion pa ame e s o all
ga e pai s:
S(gi,gj):=
P.
R;
.Rj EM
In ui i ely, he pa ame e dec eases
i
many nodes o
S(M)
a e connec ed, and i is minimum i
M
is a
clique o he undi ec ed ci cui g aph.
The o e all in e connec ion cos o a pa i ion
El
o
K
g oups o ga es
Mk
whe e
k
=
1,.
.
.,
K
can be es i-
ma ed by:
K
S(n)
=
S(Mk
>.
k=l
As
a cos unc ion we use
c3
(El):
=
log(
S(
n)).
The calcula ion ime o his me ic g ows quad a-
ically wi h he numbe o ga es o each pa i ion g oup
Mk.
Since,
in
p ac ice, he numbe o ga es o a pa -
i ion g oup is ela i ely small he p oblem is no oo
se e e.
As
also he senso s mus be in e connec ed by he
es clock line and he es signal line we use
~,(n):=
K.
3.4
Tes applica ion cos s.
The es applica ion ime o a p ecompu ed es ec-
o se o he global CUT is es ima ed. Since he p opo-
sed pa i ioning app oach does no modi y he logic
s uc u e, he es ec o se needed o achie e a ce -
ain quali y goal, does no change. Howe e , he ime
equi ed o each ec o may be signi ican ly di e en
due o di e en IDDQ
se ling
imes
o di e en pa i-
ions.
Fo he es applica ion ime we use
we e
DiIc
is he sum o
DBIc
and a e m
A(zi)
ac-
coun ing o he
iDD
decay ime and he sensing ime,
es ima ed om SPICE le el simula ions as a unc ion
o he BIC senso ime cons an
ZS,~
=
Rs,iCs,i
((2s.;
is
he pa asi ic capaci ance a he i ual ail o g oup
Mi
).
4
Pa i ioning Algo i hm
Looking o a pa i ion ha sa is ies condi ion
(n)
and minimizes he cos unc ion is a e y complex, NP-
ha d op imizing p oblem, and i is impossible o
e alua e he cos unc ion
C(n)
o all he pa i ions.
Also
e alua ing
C(n)
o a single pa i ion is a he
complex as
i
a ies be ween
O(n)
and
O(m;)
whe e
mi
is he size o a module.
Hence a heu is ic algo i hm is needed which
e alua es jus a mode a e numbe o pa i ions bu is
no caugh
in
a local minimum.
A
a ie y o algo i hms
has been p oposed o such kind o p oblems ( o ce-d i-
en, simula ed annealing, Mon e Ca lo, gene ic, e. g.),
in
his pape an e olu ion-based algo i hm is applied.
576
4.1
Sol ing
combina o ial p oblems by
e olu ion based algo i hms
Fo
con olling he op imiza ion s eps an e olu ion-
based algo i hm is adap ed [17,18,19]. A single cycle o
such an algo i hm consis s o h ee s eps epea ed su i-
cien ly o en: ecombina ion, mu a ion, and selec ion.
Recombina ion:
A
popula ion consis s o a numbe
o indi iduals called pa en s which co espond o pa i-
ions in ou case. These pa en s p oduce descendan s by
ecombining hei a ibu es. In ou case
i
u ned ou
ha his s ep should be simpli ied such ha jus one pa-
en is su icien o a child, and ecombina ion is jus
duplica ion.
Mu a ion: The child pa i ions a e modi ied an-
domly co esponding o ce ain ules. These ules en-
su e ha he modi ied pa i ion is s ill
in
he neighbou -
hood o he o iginal one.
Selec ion: The indi iduals p oduced
so
a a e
e alua ed. The bes o hem a e he pa en s in he nex
cycle.
The con e gence o his p ocedu e depends on he
s a popula ion, and on he se o con ol pa ame e s
used.
4.2
Adap a ion o PART-IDDQ
The s a pa i ions a e de e mined by simpli ying
he cos unc ion such ha jus
cl(l7)
(a ea o e head)
and
cz(Il)
(delay o e head) a e conside ed. Fi s he
app op ia e module size is es ima ed. This can be done
by e alua ing
cl(Il)
and c,(Il) by a e age numbe s
o he equi ed pa ame e s and by abs ac ion om
s uc u al in o ma ion. Then ga es a e clus e ed o mo-
dules as ollows: s a ing om a ga e close o a p ima y
inpu ga e, chains a e o med owa ds a p ima y ou pu .
The p ocess s ops i his pa h eaches a p ima y ou pu ,
o i he e is no ee ga e anymo e,
o
i he maximum
module size is eached. Modules a e o med as long as
he e a e ee ga es. Using di e en chains he equi ed
numbe o s a pa i ions is cons uc ed.
The e olu ion cycle is con olled by a se o pa a-
me e s as p oposed in
[
18,193
:
CL:
Numbe o pa en s
h:
Numbe o child en pe pa en
x:
Numbe o Mon e Ca lo descendan s
0:
Maximum li e ime
m:
Maximum numbe o ga es o be
mo ed
E:
Va ia ion o m
The e olu ion cycle s a s wi h
p
di e en s a pa -
i ions
Ill,.
. .
,
Ilp
.
Child en a e gene a ed by copying
each o he pa en indi iduals
A
imes, and by mu a-
ion a e wa ds.
The mu a ion scheme o each o he
(p*A)
de-
scendan s is as ollows: A module
Mi a
om he pa -
i ion
I?:=
{M:,
...,Mii}
is selec ed, and he numbe
mbpu,& y
o i s bounda y ga es is de e mined. A ga e o
Mi a
is a bounda y ga e i i is di ec ly connec ed o a
ga e ou side
Mi a .
As a uni o mly dis ibu ed andom
a iable we selec he ac ual numbe
mmo e
E
{I
,...,
min{m,m~ounda y)) o ga es o be mo ed.
The
m,,,,
ga es a e chosen andomly, and pu in o he
a ge module hey a e connec ed wi h. I hey a e
connec ed wi h se e al a ge modules a andom one is
chosen.
In addi ion o hese
(p*A)
mu a ed child en,
(p
*x)
Mon e-Ca lo
child en a e gene a ed. Again,
each pa en indi idual is copied
x
imes. A andom
numbe o ga es o a andom module
AIs a
is mo ed
in o a andom module
M a ee .
The andom a ia ion o
hese descendan s is highe compa ed wi h mu a ions,
and hey educe he p obabili y o being caugh in a lo-
cal minimum. I all ga es o
M,,,
a e mo ed, his
module is dele ed. A e ga e mo ing, cos s a e ecom-
pu ed jus o he modi ied modules, and he global
cos s
o
he pa i ion a e upda ed. As no he en i e cos
unc ion has o be ecompu ed, he pa i ions gene a ed
his way can be e alua ed e y e icien ly.
A e exchanging ga es, he s ep wid h o mu a ion
m
is ecompu ed o each descendan . The new
m
is
subjec o no mal dis ibu ion wi h a iance
E
a ound
he
m
o s ep be o e. This scheme esul s in
(1
+
A
+
x)
*
p
pa i ions. Du ing selec ion, all pa en
indi iduals olde han
o
gene a ions a e dele ed. Ou
o he emaining ones, he
p
pa i ions wi h bes cos
unc ions a e selec ed as pa en s o he nex cycle.
i
4.3
Example
The pa i ioning s eps a e illus a ed using he
ISCAS85 benchma k ci cui C17 as an example [16].
Fi s s a pa i ions
Ill,.
.
.
,
lIp
ha e o be cons uc ed
as desc ibed abo e, igu e
4
shows pa i ion
Ill.
The
ecombina ion s ep c ea es pa i ion
Il:
by duplica ing
Ill.
Du ing mu a ion
Ms a
:=
(4,6) is selec ed an-
domly, and he bounda y ga es
Sboud:=
{g4,&} a e
de e mined. Randomly
m,,,,
=
1 and g4 as ga es o be
mo ed a e chosen. Wi h
M a ge
=
(2,3) he descendan
is shown in igu e 4. Du ing he nex gene a ion he al-
go i hm c ea es pa i ion
Il:,
M,,,:
=
(2,3,4) is selec-
ed and he bounda y se becomes
Sbound
=
{g2, g3, g4
1
.
Then ga e
g3
mo es o module (6) ( igu e
5).
Fo he
las s ep he algo i hm selec s module (3,6) o
n:.
Now bo h ga es g3, g4 mo e o hei speci ic des ina-
ion-modules and module
(3,6)
becomes emp y. A e
hese 3 gene a ions he pa i ion
Il
consis s o wo
modules (1,3,5), (2,4,6) and is he op imum pa i ion
o C17.
511

I5 I4 I3 I2 I1
02
03
I5 I4 I3 I2 I1
02
03
I5
I4 I3 I2 I1
02
03
Figu e
5:
IIi
=
{(1,5)(2,4)(3,6)],
II
=
{(1,3,5)(2,4,6)}
5
Expe imen al Resul s
In his sec ion we p esen a s aigh o wa d me hod
o s anda d pa i ioning, and we compa e he esul s
o
he me hods discussed
so
a .
The p ocess o s anda d pa i ioning s a s wi h a
ga e as nea o a p ima y inpu as possible. New ga es
a e added un il a speci ied size o he module is gene-
a ed, he module size can be de e mined elec ically
as desc ibed in sec ion 3, in
ou
case
we
ake he num-
be s ob ained by he e olu ion based algo i hm. The
new ga e added is ha ga e whose pa h leng h o all
he ga es al eady clus e ed gi es a minimum sum. I
he e a e mul iple choices, a ga e o his se is selec ed
such ha he pa h leng hs o all he ga es no ye
clus e ed gi e a maximum sum.
A
pa i ion gene a ed
his way con ains modules such ha hei ga es a e
connec ed mos closely.
5.1
Pa i ioning he
ISCASS5
Ci cui s
As
all componen s o
he
cos unc ion should ha e
simila ange and a ia ion o op imiza ion easons and
in
o de o ob ain IDDQ- es able ci cui s wi h minimal
a ea-o e head which s ill sa is y pe o mance equi e-
men s, he ollowing weigh ac o s we e chosen:
C(n)
=
9
*
c1
(n)
+
IO5
*
c2
(n)
+
c,(n)
+
c4
(n)
+
10
*
c5
(n)
The e olu ion-based algo i hm was applied o he
ISCAS85
ci cui s using his cos unc ion un il he e-
sul s con e ged o a s able alue. compu ing ime de-
pends on he s a popula ion, and is no de e minis ic.
Bu e en
o
he la ges ci cui con e gence was ob-
ained wi hin a ew hou s on a Sun Spa c wo ks a ion.
The esul s a e lis ed in able 1.
A
s anda d pa i ioning needs om 14.5% o 30.6%
mo e ha dwa e o BIC senso s han he op imal pa i-
ioning o he e olu ion based algo i hm, bu does no
show any imp o emen
in
sys em pe o mance and es
ci cui
11
C1908
1
C2670
I
C3540
I
C5315
I
C6288
I
C7522
#modules
II
2
I
3
I
4
I
6
I
5
I
6
a ea o BIC senso s
senso a ea o e head
s anda d 1.08E+6 5.67E+5 2.79E+6 2.87E+6 9.19E+5 5.65E+6
8.27E+5 4.95E+5 2.27E+6 2.29E+6 7.30E+5 4.72E+6
o s an- 30.6% 14.5% 22.9% 25.3% 25.9% 19.7%
e olu ion
5.95E-2
e olu ion 5.94E-2
Table
1
:
Resul s
o
s anda d
pa i ioning
and
e olu ion-based pa i ioning.
578
pe o mance. Delays and applica ion imes a e gi en as
pe cen age how he inco po a ion o BIC senso s slows
down pe o mance. The a ea o he BIC senso s is gi en
in
uni s whose ac ual size depends on echnology.
As
echnology mapping is no ca ied ou
so
a wi ing is
no conside ed. Since bo h in case o he s anda d and
he e olu ion-based app oach he numbe o modules is
he same, he ac ual ou ing cos s a e no expec ed o
di e signi ican ly.
6.
Conclusions
Pa i ioning c i e ia a e es ablished o guiding he
au oma ed design o IDDQ- es able ci cui s. They a e
exp essed by a mul i- a ge objec i e unc ion o be op-
imized by an e olu ion-based algo i hm. Ci cui ex a
delay, a ea o e head o he BIC senso s, connec i i y
cos s o he es ci cui y, and he es applica ion ime
a e conside ed as cos c i e ia. The pa ame e s a e
es ima ed based on logical as well as elec ical le el
in o ma ion o he a ge cell lib a y o be used
in
he
echnology mapping phase o he syn hesis p ocess. Fo
he benchma k ci cui s in es iga ed, he inal design is
supe io o esul s o a s anda d pa i ioning.
So
a only
esyn hesis o including BIC senso s has been conside-
ed. Nex s ep is con olling he logic syn hesis p oce-
du e such ha he p esen ed cos unc ion is conside ed
a he ea ly beginning.
7.
Glossa y
BIC:
CUT,
C:
n:
gi:
M:
n:={Gi,
...,
GK}:
d:
:
P
-+
(0,l):
ai
:
CI
:
C:
:
Li
:
:
ASj
6SlC
:
buil -in cu en senso
ci cui unde es
numbe o ga es o CUT
ga e numbe
i
g oup o ga es (module)
pa i ion, disjoin g oup
o
ga es
disc iminabili y o aul y and
aul - ee case
cons ain s
weigh ac o
cos unc ion
global cos unc ion
maximum i ual g ound
pe u ba ion
ansi ion pa h
ansi ion ime o pa h j
a ea o BIC senso i
delay wi h connec ed BIC
senso
delay wi hou BIC senso
o ced sepa a ion pa ame e
numbe o pa en s
h:
x:
0:
m:
E:
Re e ences
numbe o child en pe pa en
numbe o Mon e Ca lo
descendan s
maximum li e ime
maximum numbe o ga es o
be mo ed
a ia ion o m
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580