756
IEEE
TRANSACTIONS
ON
CIRCUITS
AND
SYSTEMS,
VOL.
36,
NO.
5,
MAY
1989
A
P og ammable Neu al Oscilla o Cell
BERNABE
LINARES-BARRANCO,
EDGAR
SANCHEZ-SINENCIO,
SENIOR
MEMBER,
IEEE,
ANGEL
RODR~GUEZ-VAZQUEZ,
MEMBER,
IEEE,
AND
JOSE
L.
HUERTAS,
MEMBER, IEEE
Abs uc
-A
p og ammable
analog
neu al oscilla o cell a chi ec u e
is
p esen ed. The p oposed neu on ci cui is
o
hys e e ic neu al na u e wi h
i s implemen a ion based on ope a ional ansconduc ance ampli ie s
(OTA’s).
The
hys e esis
loop
as
well
as
he equency o oscilla ion a e
ol age
(o
cu en ) dependen . The a chi ec u e, which in ol es
wo
OTA’s,
a cu en + o , a capaci o , a diode, and a esis o
is
e y sui able o
monoli hic in eg a ed ci cui s. Expe imen al esul s con i m he expec ed
lexibili y
o
he syn he ic neu on.
I. INTRODUCTION
HE
MOST
e icien compu a ional sys em is he hu-
T
man b ain. Biological sys ems o dina ily pe o m ea-
soning and logcal manipula ions beyond he capabili ies
o ou mos mode n sophis ica ed compu e sys ems. Many
esea che s mo i a ed by ha e iciency y o mimic he
human ne ous sys em o sol e a a ie y o complex engi-
nee ing p oblems, among hem: con ol sys ems, knowl-
edge p ocessing and signal/image (senso ) p ocessing. A
neu al sys em consis s o many highly in e connec ed neu-
ons. Since in gene al neu al ne wo ks in ol e a e y la ge
numbe
o
pa allel a ays o basic cells (neu ons), hey a e
e y app op ia e o VLSI echnology. Besides, he e a e
some in e es ing applica ions whe e only a limi ed numbe
o
neu ons a e used, e.g., low-o de op imiza ion p oblems
[l],
[2], c ude espi a o con ol sys ems simula ion
[l],
[3].
A biological neu on has bo h exci a o y and inhibi o y
connec ions. Each neu on has inpu s which a e he ou pu s
o o he neu ons as well as ex e nal (s imuli) signals, and i
he sum o he inpu s is g ea e han a ce ain h eshold
le el, a i ing sequence o pulses is gene a ed, o he wise
below hs le el he neu on will no i e. The numbe o
pulses i ed ou depends on he in ensi y and du a ion o
he inpu pulse, as well as on he inhe en cha ac e is ics o
he neu on.
Manusc ip ecei ed June 24, 1988; e ised Decembe 20, 1988.
This
pape was ecommended by Gues Edi o s R.
W.
Newcomb and
N.
El-Lei hy.
B. Lina es-Ba anco was wi h he Uni e si y
o
Se ille, 41012 Se ille,
Spain.
He is now wi h he Depa men
o
Elec ical Enginee ing, Texas
A&M
Uni e si y, College S a ion, TX 77843.
E. Sanchez-Sinencio is wi h he Depa men
o
Elec ical Enginee ing,
Texas
A
&
M
Uni e si y, College S a ion, TX 77843-3128.
A.
B.
Rod iguez-Vasqua and
J.
L. Hue as a e wi h he Depa men
o
Elec onics and Elec omagne ics, Facul y
o
Physics, Uni e si y
o
Se ille, 41012 Se ille, Spain.
IEEE Log Numbe 8826710.
Syn he ic neu ons beha e in a c ude simila way o he
ac ual neu ons. In hs pape , a p og ammable neu on
ci cui a chi ec u e is p esen ed. The implemen a ion is
based on he ope a ional ansconduc ance ampli ie
(OTA), his ol age (o cu en ) p og ammable de ice is
e y sui able o syn he ic neu ons. The p oposed neu on
ci cui is o he hys e e ic neu al- ype pulse oscilla o [4]
wi h he inhibi o y and exci a o y p ope ies as unc ion o
he inpu sum exceeding (o no ) a i ing h eshold le el.
11. MATHEMATICAL DESCRIPTION
OF
A
HYSTERETIC NEURON
A basic i s -o de s a e- a iable ype equa ion
[
11, [4]
simula ing (in a p imi i e way) a neu on is gi en by
dx
d
C-
=
-
G,x
-
G,H(x)
-
GJJ
y=x
(W
whe e
U
=
inpu ,
y
=
ou pu ,
x
=
in e nal s a e a iable;
C,
G,, G,,
and
G,
a e non-nega i e cons an s, and
H(x)
desc ibes he hys e esis na u e o he neu on model
i
x>x,
-
H-,
H,
I,
i x=-x-
o x=x+
(2)
Obse e ha he e a e o he neu on models wi h simila
ma hema ical cha ac e iza ion. Fo ins ance, he e m
-
G,H(x)
in o he cha ac e iza ions
[2],
[5] is ela ed o
-C,”=,DJ,h(x)
whe e
DJ,
is a weigh ing unc ion, and
,(
.)
a e nonlinea unc ions imposing cons ain s and can
be conside ed as h eshold-ac i a ion unc ions.
In wha ollows, we ew i e
(1)
in a o m mos use ul o
ou ci cui implemen a ion, i.e.,
dx
C-=-GG,(~)~+Z,(x) d
y=x
(3b)
whe e
I,(x)
is
-
G,H(x),
and he inpu a iable
U
con-
0098-4094/89/0500-0756$01
.OO
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e
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:
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OSCILLATOR
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Fig.
1.
Equilib ium
poin
cha ac e is ics
ols he alue o
GJu),
and he
-
G,u
e m has been
dele ed. The equilib ium poin s a e ob ained when
dx/d
=
0,
his yields
Z,(X)
=G,(u)x.
(4)
The in e sec ions o he hys e esis unc ion
Zo(x)
wi h
esis i e (load-line)
G,(
u)x
p o ide he equilib ium poin s,
as shown in Fig.
1.
I can be obse ed om Fig.
1
ha
poin
A
is a s able poin , and poin
B
is an uns able poin .
The asymme y o he hys e esis loop is needed o gua an-
ee only one s able poin . Fo ou ci cui implemen a ion
we need a mechanism o change he slope
G,(u)
such ha
he s aigh line mo es om poin
A
o poin
A'
and
becomes uns able when
U
becomes exci a o y. Hence, he
ci cui oscilla es and i es nega i e pulses when he inpu
signal
U
exceeds a ce ain h eshold le el; hs package o
pulses is e mina ed when
U
alls below h eshold. Thus,
he e is a c i ical alue
G,
which sepa a es poin s like
A
and
A',
e.g.,
G,(
U)
>
G,
s able poin
A
(5)
Gx(
U)
<
G,
uns able poin
A'.
Fig. 2 illus a es he ime esponse o his neu on o a
cu en pulse
u( )
ha makes
G,( )
o jump be ween
G,
and
G,
so
ha
G,
<
G,
<
G,.
This inpu pulse makes he
s able equilib ium poin
A
o change o poin
A'
which is
uns able. A he ini ial ime o change o
U
he ou pu o
he hys e e ic elemen s a s a
I+,
and, since
x
canno
change ins an aneously, he di e en ial equa ion cha ac-
e izing he neu on yields
dx
I+
C-
=
-
G,x
+
I
wi h
x(0)
=
-.
d
Gl
(6a)
Hence, he ime solu ion ini ially is gi en by
This equa ion holds un il
x( )
becomes
x,
=
Z+/G,,
a
which ime he ou pu o he hys e e ic elemen changes o
-
I-
(we assume he ideal case whe e no ime is aken in
going om
I,
o
-
I-
on he hys e isis cu e) and le
o
be his ime, wi h
x( ,)
=
I+/G,.
The e o e sol ing o
o
II
I
o'
l'
2
Fig.
2.
Cha ac e is ic ime esponse
o
neu on cell
we ob ain
o=-ln(
C
1-G2/Gl
1
G2
1
-
G2/Gc
Now he cha ac e izing di e en ial equa ion becomes
(7)
which solu ion is gi en by
This si ua ion is main ained un il
x( )
becomes
-
x-,
and
Io(x)
hen changes back o
+
I+
o e u n o poin
A
and,
hence o comple e he cycle ha will gene a e a neu al- ype
pulse ou pu . Thus
x( ,)
=
-
x-.
(10)
Sol ing o
,
yields
C
,
=
-
In
G,
I'G,
1+-
I-
G,
G2
.
1--x-
I-
Now he di e en ial equa ion becomes (6a) again
dx
d
C-
=
-
G,x
+
I+
bu wi h
x(0)
=
-
x-
(12a)
and he solu ion is gi en by
The ime a which
Io(x)
changes om
I+
o
-
I-
occu s
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758
IEEE
TRANSACTIONS
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CIRCUITS
AND
SYSTEMS,
VOL.
36,
NO.
5,
MAY
1989
-
Fig.
3.
Block
diag am
o
neu al-pulse simula o .
when in (12b)
I+
x( ,)
=
-
GC
hus
,
esul s
I
T
is he du a ion o he inpu pulse
U
and
np
is he
numbe o pulses gene a ed by he neu on, he nex in-
equali ies hold:
o
+
(np -l)( ,+ ,)
<
T<
o+ n,( ,
+
,).
(15)
Hence,
i
one we e o hold
G,
cons an a
G,<Gc
hen
he numbe o pulses ha would occu while
G,
emains
cons an is
n,,
=
In
(:;;:)+1
-
whe e In (.) p oduces he in ege pa o he unc ion
((T-
o)/( ,+ 2)).
111.
A
PROPOSED NEURAL
PULSE
SIMULATOR
A block diag am o he p oposed neu al- ype ci cui
which implemen s (3a) and (3b) is shown in Fig. 3. In ou
ci cui , he ou pu s o he hys e e ic elemen
Io(x)
and o
he ex e nally con ollable linea ampli ie
G,(u)
a e cu -
en s, while hei inpu s a e ol ages. Acco dingly, he
in eg a o is buil wi h a simple capaci o and he cu en
summe elemen simply implemen s
KCL
and, hence needs
no addi ional ci cui y.
In o de o implemen he ansconduc ance hys e e ic
elemen o yield
Zo(x),
we used a di e en ial inpu
ansconduc ance compa a o wi h mul iple ou pu s all
aking alues
as shown in Fig.
4.
An an ime ic
ansconduc ance-hys e -
e ic elemen can be implemen ed as shown in Fig.
5
whe e
R
=l/Gc,
and
G,
is as de ined be o e. Fu he mo e,
i
I-
Fig.
4.
A
ansconduc ance compa a o wi h mul iple ou pu s.
(b)
Fig.
5.
An ime ic
ansconduc ance-hys e e ic
elemen . (a) Ci cui im-
plemen a ion.
(b)
Cha ac e is ics
o
load.
'h
-E
-*x
2
-I
-
Fig.
6.
Hys e esis cha ac e is ics
o
ci cui
o
Fig.
5.
obse e ha since
ui
=
V,
-
x
1)
i
x
<
V,
hen
ui
>
0
and
I,,
=
I+
which back biases
2)
i
x
>
V,
hen
ui
<
0
and
I,,
=
-
I-
and
i
u he we
he diode, gi ing
V,
=
I'R
and
x
<
Z'R;
choose
E,
<
I-R
hen
V,
=
-
E,
and
x
>
-
E,;
whe e
I+
=
I-
=
Ibis
[8].
Ibis
is he con olling cu en o
he OTA. These obse a ions a e summa ized in Fig.
6.
The o he elemen needed o build up he block diag am o
Fig. 3 is an ex e nally cu en con olled linea anscon-
duc ance ampli ie . A con en ional OTA is employed
[SI,
[9].
The ansconduc ance gain
G,
is con olled by he bias
cu en
U.
This
is shown
in
Fig.
7.
Now we can pu oge he he basic elemen s o o m he
p og ammable neu al oscilla o cell
as shown in Fig.
8.
The
equa ion desc ibing he beha io o he ci cui o Fig.
8
is
gi en by (3) o which
x
is chosen as he capaci o ol age,
ZJx)
has
Z+=Z-=
Ibis,
and
G,=hu
wi h
U
he bias
cu en in he bo om OTA in Fig.
8,
and
h
[9]
is a
p opo ional cons an which depends upon empe a u e,
de ice geome y, and he p ocess.
Neu ons a e in e connec ed h ough synapses. A synapse
can be conside ed as a weigh ed ela ion be ween he
ou pu o a neu on and he inpu ecei ed by ano he one.
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OSCILLATOR
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Fig.
9.
Hys e esis
loop
measu emen .
/
I
Fig.
7.
A
linea
ansconduc ance ampli ie .
&A
--
Fig.
8.
A
hys e e ic neu al cell implemen a ion.
This ela ion can be inhibi o y o exci a o y. In he p o-
posed neu on ci cui , he nega i e cu en pulses can be
a bi a ily conside ed o be exci a o y signals, while o he
posi i e cu en pulses could be conside ed he inhibi o y
signals. This exci a o y and inhibi o y p ope y o he
neu on ci cui can be implemen ed as an in eg a ed ci cui
e sion by means
o
complemen a y cu en mi o s o
aking ou pu o one neu on o eed o he neu ons.
IV.
EXPERIMENTAL
RESULTS
The ci cui o Fig.
8
was buil as a es p o oboa d. The
comme cial ansconduc ance de ices used we e he
VA703
OTA's. Fo he linea ized OTA implemen ing
G,(
U),
he
linea izing diodes
[8]
p o ided wi hin he chip we e used as
well as an addi ional esis i e a enua o o inc ease he
inpu ol age swing. The inpu linea ange ob ained was
abou
+3
V
o a
k5-V
powe supply.
759
Fo
he ansconduc ance compa a o wi h mul iple ou -
pu s, h ee OTA's
(VA703)
we e used. These h ee OTA's
had hei inpu s and bias connec ed oge he
so
ha hey
would wo k like an
OTA
wi h h ee equal ou pu s. The
inpu impedances o bo h ansconduc ance de ices ( he
compa a o and he linea ized one,
G,)
a e no e y high,
so
a ol age bu e had o be added. The alues (a bi a ily
chosen) o he passi e elemen s we e
R
=1.8
k!d and
C
=
33
nF.
The measu ed hys e esis loop o
Io,'
e sus
x
is de-
pic ed in Fig.
9.
The bias cu en o he compa a o was
adjus ed o
Ibis
=
0.8
mA,
and he ol age
E,
=
0.5
V.
The uppe ace o Fig. 10(a) shows he ou pu cu en
o
he neu on
(Io2
=
I,,,
=
Ih)
o Fig.
8
when he inpu
U
is
a squa e wa e (shown in he lowe ace)
o
4.4
mA.
This
squa e wa e makes he ansconduc ance o
G,(
U)
o jump
om
G,
=
7.7
X
mho,
(uns able poin ) being he wid h o he pulse (exci a-
ion ime)
T
=
900
ps.
The c i ical poin o
G,(
U)
is
gi en
by
G,
=
1/R
=
5.6
x
mho.
I
T,
C,
G,,
G,,
G,,
I+,
and
E,
a e known, we can
calcula e he alues o
o,
,,
,,
( ia
(7),
(11)
and
(14))
as
well as he numbe o pulses
np
i ed du ing he exci a ion
ime
T
(eq.
(16)).
mho
(s able poin ) o
G,
=
1.6
X
The calcula ed alues a e
o
=
22
ps
,
=
75
ps
2
=
89
ps
np
=
6.
I can be seen om he uppe ace o Fig. 10(b), whe e he
ol age ac oss capaci o
C
is shown o he same inpu
signal
U
as in Fig. lO(a) ha he expe imen al alues o he
p e ious calcula ed imes a e app oxima ely:
o
=
24
ps
,
=
80
p~
,
=
94
ps
np
=
6.
'Iol
was measu ed ac oss a esis o
o
1.0
kQ.
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TRANSACTIONS
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36, NO. 5, MAY 1989
(b)
cu en
U.
Time esponse
Vc
o a squa e wa e inpu
U.
Fig.
10.
(a) Cu en ime esponse
V,/R
o a squa e wa e inpu
Fig.
11.
Same as Fig.
10(a)
wi h smalle ampli ude and du a ion o
U.
The di e ence be ween measu ed and calcula ed alues is
less han
10
pe cen , which can be due o componen
ole ances and pa asi ic elemen s.
Fig.
11
shows he ou pu esponse
V,
o ci cui o Fig.
8
when he inpu signal becomes a pulse o smalle mag-
ni ude and du a ion,
(T-300
ps
and
np
=1
since
(T-
4J/(4
+
12)
<I.
.
CONCLUSIONS
AND
FUTURE
WORK
An analog syn he ic neu on a chi ec u e wi h ol age (o
cu en ) p og ammable p ope ies has been p esen ed. In
ac , e e ing o Fig.
8,
he p oposed a chi ec u e has wo
deg ees o eedom
(Ibia
and
U)
o modi y he neu on
ou pu ; hey a e unc ions o he wo OTA’s which can be
ol age (o cu en ) dependen . This cu en dependence
modi ies
H(I+)
and
G,
in
(1).
I needed, he weigh o he
in e connec ions be ween neu ons (synapses) could be de-
e mined by means o cu en mi o s. The addi ion o
cu en signals om o he ou pu neu ons o ex e nal
s imulus a each neu on ci cui is accomplished h ough
he con olling e minal o he OTA’s (i.e., see signal
U).
Con a y o some o he analog neu al ci cui s whe e i is
di icul o change hei pa ame e s
[6],
his neu on a chi-
ec u e has addi ional lexibili y o modi y i s pa ame e s
acco ding o a ce ain p ede e mined algo i hm. We a e
cu en ly wo king on he
MOS
in eg a ed e sion o he
p oposed neu on a chi ec u e aking in o accoun a ea
[7],
lexibili y, and powe consump ion.
ACKNOWLEDGMENT
The au ho s wish o hank P o esso
R.
W.
Newcomb
o his aluable commen s, sugges ions, and encou age-
men in he p epa a ion o his pape .
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[31
[41
[51
F.
C. Hoppens ead ,
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F.
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V.
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B.
Lina es-Ba anco
e
al.,
“A no el CMOS analog neu al oscilla o
cell,” o be p esen ed a he ISCAS, May 1989.
Be naM Lina es-Ba anco
ecei ed he
B.Sc.
de-
g ee in elec onic physics in 1986, and he M.S.
deg ee in mic oelec onics in 1987, om he Uni-
e si y
o
Se ille, Spain. Cu en ly, he
is
wi h he
Depa men o Elec ical Enginee ing, Texas
A&M Uni e si y, Texas, whe e he is wo king
owa ds he Ph.D. deg ee.
His
esea ch in e es is in he a ea
o
nonlinea
analog mic oelec onic design and neu al ne -
wo ks.
Edga
Shchez-Sinencio
(S’72-M74-SM83) ecei ed he M.S.E.E. de-
g ee om S an o d Uni e si y, CA, in 1970, and he Ph.D. deg ee om
he Uni e si y
o
Illinois, Champaign-U bana, in 1973.
Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 01,2020 a 16:04:47 UTC om IEEE Xplo e. Res ic ions apply.

LINARES-BARRANCO
e al.
:
PROGRAMMABLE
OSCILLATOR
CELL
761
In
1974,
he held an indus ial Pos -Doc o al Since Oc obe
1978,
he has been wi h he
posi ion wi h he Cen al Resea ch Labo a o ies, Depa amen o de Elec icidad y Elec 6nica a
Nippon Elec ic Company L d., Kawasaki, he Uni e si y o Se ille, whe e he is cu en ly
Japan. F om
1976
o
1983
he was he Head o employed
as
an Associa e P o esso .
His
esea ch
Ins i u o Nacional de As o isica, Op ica y Elec- in e es lies in he ields o analog/digi al in e-
bnica, Puebla, Mexico. He was a isi ing p o- g a ed ci cui design, neu al ne wo ks and non-
esso
in
he Depa men o Elec ical Enginee - linea ne wo ks analysis and syn hesis.
ing a Texas A&M Uni e si y du ing he aca-
demic yea s
o
1979-1980
and
1983-1984,
whe e
he
is
cu en ly a P o esso .
He
was he Gene al
Chai man o he
1983
16 h Midwes S$nposium
on
Ci cui s and Sys ems.
He was an Associa e Edi o o
ZEEE
Ci cui s and Sys ems Magazine
(1983-1985),
IEEE
Ci cui s and De ices Magazine
(1985-1988)
and
o
he IEEE
TRANSACTIONS
ON CIRCUITS
AND
SYSTEMS
(1985-1987).
He is
he co-au ho
o
he book,
Swi ched-Capaci o Ci cui s
(Van Nos and-
Reinhold,
1984).
His
cu en esea ch in e es include ope a ional
ansconduc ance ampli ie s and applica ions, compu e -aided design o
solid-s a e ci cui s and neu al ne wo k ci cui implemen a ions.
c
J&
L.
Hw as
(M’74)
ecei ed he Licenciado
en Fisica and he Doc o en Ciencias Fisicas
deg ees om he Uni e si y
o
Se ille, Spain, in
1969
and
1973,
espec i ely.
F om Oc obe
1970
o Sep embe
1971,
he was
wi h he Philips In e na ional Ins i u e, Eind-
ho en, The Ne he lands,
as
a Pos -G adua e S u-
den . Since Oc obe
1971,
he
has
been wi h he
Depa amen o de Elec icidad y Elec 6nica a
he Uni e si y
o
Se ille, whe e he became Assis-
an P o esso in
1973
and a P o esso in Elec-
onics in
1981.
His
esea ch in e es lies in he ield o mul i alued logic,
sequen ial machines, analog ci cui design, and nonlinea ne wo k analy-
sis and syn hesis.
Angel
Rod iguez-Vbquez
(M80)
ecei ed he Licenciado en Fisica and
he Doc o en Ciencias Fisicas deg ees om he Uni e si y o Se ille,
Spain, in
1977
and
1983,
espec i ely.
Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ap il 01,2020 a 16:04:47 UTC om IEEE Xplo e. Res ic ions apply.