An Analog CMOS Uni e sal Membe ship Func ion
Ci cui Wi h Fully Independen , Adjus able Pa ame e s
R. G. Ca ajal, A. To alba, F. Colod o and L. G. F anquelo
Dp o. de Ingenie ´ıaElec ´
onica
EscuelaSupe io de Ingenie os,
A da. ReinaMe cedes s/n, Se illa–41012(SPAIN)
e–mail: [email p o ec ed]
Abs ac — A no el CMOS membe ship unc ionci cui (MBC) is p e-
sen ed. I is based on a linea unable ansconduc o p oposed in
[1] and implemen s apezoidal/ iangula unc ions wi hall pa ame-
e s(slope,posi ion,wid h,heigh andampli ude)independen lyand
con inuouslyadjus able. I is sui able o be usedin analog uzzy ci -
cui swo king in cu en mode. The compu e simula ions ha e i y
hecha ac e is icsandpe o manceso hisci cui a e shown.
I. INTRODUCTION
In he las ew yea s se e al implemen a ions o
analog uzzy con olle s ha e been p oposed us-
ing ei he , a ol age-mode [2], [3] and a cu en -
mode app oach [3], [4], [5]. The ad an ages o
he cu en -mode app oach a e a g ea e and lexi-
ble ange o alues and highe speed ( he ol age-
mode basic building block is he Ope a ionalAm-
pli ie which is inhe en ly slowe han he OTA).
Mos o heCMOScu en -modeci cui sp oposed
o build a MBC a e based on he di e en ial pai .
This ci cui p oduces sigmoidal ype shapes and
has good p og amming p ope ies. Bu iangu-
la / apezoidal a e he mos used shape in uzzy
li e a u e.
In his pape a no el CMOS MBC is p esen ed. I
is based on a linea unable ansconduc o p o-
posed in [1]. This OTA has excellen p ope ies in
e mso linea i y and unabili y, and wi h he help
o cu en mi o s i is possible o build iangu-
la and apezoidal shapes. Fu he mo e, wi h he
help o MAX-MIN ci cui s, i is possible o gen-
e a e any ype o piecewise linea (PWL) unc ion
[6]. Besides, he MBCs ob ained wi h his me hod
a e ully and con inuously p og ammable.
This pape is o ganized as ollows. Sec ion II de-
sc ibes he a chi ec u e o he MBC. The way o
gene a e iangula , apezoidal and PWL ci cui s
is de ailed in Sec ion III. Sec ion IV p esen s some
esul s and ad ances u u e esea ch.
II. ARCHITECTURE OF TH MBC
Figu e 1 shows he OTA ci cui used o build he
MBC. A linea ela ion be ween he di e en ial
ou pu cu en and he di e en ial inpu ol age
can be seen in he equa ion shown in his igu e.
This ela ion depends on he con ol ol age
V
c
and i is possible o modi y he gain by changing
i s alue.
V
1
V
2
1
I
2
I
bias
V
1
I
2
I
2
IKn
1
IV
cV
ss
Tn
V
Teq
V
V
1V
2
=
(
-2-- -
)
*
(
-
)
Vc
Vss
Vdd
-
Figu e 1: OTAci cui
I
V
I
V
I
V
I
V
MIN
MAX
a) b)
Figu e 2: Kind o MBF shapes
The unc ionsshownin igu e 2a(Z- unc ions)can
be gene a ed wi h his ci cui . As he in e ence
p ocess in he main uzzy ha dwa e applica ions
is ca ied ou by means o MAX/MIN ope a o s,
V
1
V
2
1
I2
I
bias
V
bias
V
Vdd
bias
V
Vdd
amp
I
1
I
2
I
-
IZ- unc
I
V
Vc
Vss
Vdd
Vss
I
V
V
I
Figu e 3: Z- unc ions ci cui y
i is easy o see ha i he posi ion and slope o
he Z- unc ions a e con olled, any ype o ian-
gula / apezoidal shapes can be cons uc ed wi h
he help o MAX/MIN ope a o s ( igu e 2b).
MAX/MIN ope a o s a e needed o pe o m he
in e ence p ocess and his ype o MBC only du-
plica es henumbe o inpu so heMAX/MINci -
cui s. Thecomplexi yo hein e encep ocessdoes
no g owexcessi elybecause henumbe o inpu s
o MAX/MIN ope a o s is equal o he numbe o
inpu s o he con olle and his numbe is usually
small.
To build a Z- unc ion is necessa y o unca e he
le and igh side o he OTA esponse. This op-
e a ion is ca ied ou by means o cu en mi o s
as can be seen in igu e 3. A uzzy con olle in-
pu di ec ly d i es one OTA inpu , while he o he
de ines he posi ion o he Z- unc ion on he X-
axis. The ampli ude o he Z- unc ion can be p o-
g ammedby hecu en sou ce
I
amp
and he slope
wi h he alue o he ol age
V
c
.
III. USE OF THE Z-FUNCTION
Wi h he Z- unc ioni ispossible ogene a e ian-
gula and apezoidal shapes. We only need wo
Z- unc ions o build one MBC as can be seen in
igu e 4. In his igu e a MIN ci cui is equi ed,
bu in usual applica ions his ci cui is pa o he
MIN ci cui who pe o ms he in e ence p ocess.
The MAX ci cui p oposed in [7] and la e im-
I
MBF2
I
MBFK
I
MBFmax
I
MBF1
V
Vdd
bias
Figu e 5: Max Ci cui y
p o ed in [8] o uzzy ha dwa e applica ions, is
shown in igu e 5. The way obuild a MIN ci cui
(wi h MAX ci cui s) wi h he echnique p oposed
in [9] is also shown is igu e 6. This ci cui has
O(n)complexi yand is e y sui able o hisappli-
ca ion.
Changing he MIN ci cui o igu e 4 by a MAX
I
MBF1
I
amp
I
MBF1
I
amp
MBFmin
I
Vbias
I
MBF1
I
MBF
MAX
CIRCUIT
I
MBFmax
Figu e 6: Min Ci cui y
I
MBF
Vpos1
Vpos2
I
MBF
Vslop2
Vslop1
Vpos2
Vpos1
IN
V
I
amp
I
amp
Vslop1
Vslop2
I
amp
I
MBF1
I
VIN
I1
V
slop2
I2
Vpos2
I= 1
-I
2
MIN
Ci cui
MBF2
IMBF2
Figu e 4: Membe ship Func ion Gene a o
MIN
V
I
V
I
Figu e 7: An example o PWL unc ion gene a ion
ci cui hecomplemen a yshapecan bep oduced.
Fu he mo e i is easy o see ha we can con-
s uc any PWL unc ion by combining se e al Z-
unc ions wi h MAX/MIN ci cui s ( igu e 7). In
he nex sec ion he esul s ob ained wi h his ci -
cui and he unabili y o all he pa ame e s is
shown.
IV. SIMULATION RESULTS
HSPICE simula ions using a s anda d 0.7
m
CMOS echnology ha e been pe o med. In ig-
u e 8 he unabili yo he posi iono he shapesis
shown. In igu e 9 he gain unabili y o he OTA
ci cui can be seen. This igu e has been ob ained
changing he
V
c
o one OTA.
As said be o e, he posi ion o he Z- unc ion is
con olled by he alue o one o he wo OTA in-
pu ol ages. Changing he same inpu o he sec-
ond OTA he membe ship unc ion ape u e can
be modi ied ( igu e 10).
Finally in igu e 11 he ansien analysis o he
MIN ci cui is shown. This simula ion also shows
how o gene a e PWL unc ions by means o se -
e al OTAs and MAX/MIN ci cui s (MIN ci cui s
in his case).
P esen ly, membe ship unc ion ci cui is being
sen o ab ica ion in o de o expe imen ally es
he ci cui beha io . Besides new OTA opologies
a e being explo ed o elimina e he gain depen-
dence on he ansis o s h eshold ol ages.
V. ACKNOWLEDGMENTS
The au ho s would like o acknowledge inancial
suppo byCICYT h ough heTIC86-0860p ojec .
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