L-3
A
LARGE
SIGNAL
NONLINEAR
MDDFET
DEL
mon
SMALL
SIGNAL
SPARMETERS*
J.
M.
O'Callaghan and
J.
B. Beye
Uni e si y o Wisconsin-Madison
1415 Johnson D i e, Madison,
WI
53706-1691
Depa men o Elec ical and Compu e Enginee ing
ABSTRACT
A
gene al echnique o p edic ing he FET
la ge signal pe o mance has been de eloped. The
echnique is based en i ely on expe imen al da a
(small signal S-pa ame e s a di e en bias
poin s) and he e o e is independen
o
he
s uc u e o he FET. La ge signal measu emen s
con i m he alidi y o he model.
I.
INTRODUCTION
Modula ion doped FETs (MODFETS) ha e al eady
been p o en o ha e good noise pe o mance o
mic owa e applica ions
(1).
MODFETs a e also well
sui ed o class B ampli ie s, since hei ans-
e cha ac e is ic can be app oxima ed by a
piecewise linea cu e and his leads o a la ge
signal ansconduc ance independen o he signal
le el. Howe e , he e a e ew la ge signal models
a ailable and he de e mina ion o he pa ame e s
o such models is di icul o equi es special
equipmen . Fu he mo e, he models canno be used
con enien ly in common CAD p og ams.
The model and measu emen echniques p e-
sen ed he e o e come hese p oblems. So wa e
equi emen s include: a p og am (1 ike TOUCHSTONE'")
o
i
an equi alen ci cui o
S
pa ame e da a;
a simple leas squa e polynomial app oxima ion
p og am; and he popula
SPICE
o nonlinea ime
domain simula ions. Ha dwa e equi emen s a e
basically limi ed o a ne wo k analyze o ca y
ou he small signal
S
pa ame e measu emen s.
11.
NONLINEAR MODFET CIRCUIT
MODEL
A.
Ci cui Elemen s
The nonlinea ci cui p oposed is an ex en-
sion o a widely used small signal equi alen
ci cui in which he nonlinea i y o Cgs( l) and
IdS(Vl,Vds)
is
aken in o accoun (see Fig.
1).
In his ci cui Ids( l, ds) models he nonlinea -
i ies o he ansconduc ance (gm) and he ou pu
conduc ance
(Go)
h ough Eqs.
1
and
2:
*This wo k is suppo ed by Honeywell Inc.,
ONR
and
Caja de Pensiones (Ba celona, Spain).
CH2725-0/89/0000-0347$01
.OO
0
1989
IEEE
-Q
Figu e
1
.A
:
MODFET
model
I
Figu e
1
.B
:
Small signal equi alen
o
Ids
B. De e mina ion
o
he Linea Elemen Values
The alues o cds and he ex insic elemen s
ha e been de e mined o a 300~m
SONY
MODFET by
measu ing i s
S
pa ame e s a
VDS,VGS
=
0
and
i ing i s equi alen ci cui a his bias poin
(Fig.
2)
(2),
(3) (See Table
1).
In ou model,
only
Cgs
and Ids a e allowed o be ol age-
dependen . To desc ibe his dependence we ha e o
adjus gm,
GO,
C
s,
Ri,
C
d and cdc in Fig.
1
o ma ch he
2
pa ameae s a se e al bias
poin s. Only he i s h ee pa ame e s a e
used o cha ac e ize he nonlinea beha io o
C
s( l) and Ids(Vl,Vds)(4). The linea ized equi -
agen s o
~i,
Cgd, and cdc a e ound by a e aging
hei alues a hese bias poin s. The ob ained
alues a e:
347
1989
IEEE
MTT-S
Diges
Ri
=
1.22
0;
C
=
0.0438
pF;
Cdc
=
0.0518
pF
gd
(.
.b.
70
KO
Ps
cF
I"
Ls
-
Figu e
2
Ze o-bias equi alen ci cui
Table
1:
Linea elemen s om ze o bias ci cui
Ld
=
0.0741
nH
Lg
=
0.0478
nH
L,
=
0.0588
nH
Rd
=
1.39
n
Rg
=
1.36
n
Rs
=
1.22
n
cds
=
0.0219 PF Cpg
=
0.0267
PF Cpd
=
0.0371 pF
C.
De e mina ion o Ids( l&d
Ids
*4.
)
"m
Figu e
3
Dis ibu ion
o
he
bias poin s
Figu e
3
shows he dis ibu ion o he bias poin s
o which a small signal equi alen ci cui has
been de e mined.
I
we assume ha Ids( l,yd,)
can be exp essed as a p oduc o wo one- a iable
unc ions; i.e.:
pq( l) can be ound om he ans e unc ion a
A
his poin we can se pd(VDS
)
1;
hen
pg( l) is o ced o ake he a8uei o he
ans e cha ac e is ic. F om Eq.
2
and knowing
ha
lds( TY DSQ)
=
(5)
(VT being he pinch-o ol age), we can w i e
Pg('1)
=
I
gm(uSVDSQ)dU
(6)
T
which allows
us
o e alua e he
VI
dependence o
Ids om he measu ed g, a se e al bias poin s.
Figu e
4
shows he alues o gm measu ed
o
VGS
anging om
-1.4V
o
0.4V
=
2V
and hei co esponding alues
o
and
pg
D
o
=
""?
Ids ~,VDSQ)) ound wi h Eq.
6.
Simila s eps a e aken o de e mine he
dependence o Ids wi h Vds: om Eqs.
1
and
3
we
know ha
GO( GSQY 'ds)
=
Pg( GCJ))Pi( ds)
(7)
50
40
30
20
10
0
-1.5
-1
-0.5 0
0.5
Vl
( ol s)
FIGURE
4:
TRANSCONWCI'AKE
AND
TRANSFER
CURVE
FUR
Vde=VLSQ=2V
This equa ion, wi h he condi ion pd( DSQ)
=
1
leads o pd o he nonze o alues o ds:
Also, since Ids(V1,O)
=
0,
Pd has o be ze o o
In Table
2,
he p ac ical applica ion
o
Eq.
9
is shown: S a ing om he alues o
G~(VG~Q,VDS! and pe o ming he nume ical in e-
g a ion indica ed in Eq.
9,
he alues o pd(VDS)
a e ound o
VDs
anging om
0.5
o
4V.
D.
Polynomial i ing o p,( l), P,+(V~~) and
Vds
=
0.
3
o class
B
applica ions
The app oach discussed
so
a has allowed us
o desc ibe he ol age dependencies wi h one-
a iable unc ions. Wha is needed now is o
exp ess hese unc ions in a o m ha can be
348
Table
2
-
De e mina ion
o
Pd(Vos)
om
O pu
Conduc ance
Da a
(VGs
=
VGso
-
-0.N)
VDS
0.5
1.0
2.0 3.0
4.0
GO
(ms)
18.9751
8.2583 5.2548
3.7447
3.4330
VDS
DsP
I
Go(mA)
-13.5647 -6.1563
0
4.4445
8.0884
Pd(V0s) 0.4408 0.7215
1
1.1855
1.3934
handled by a CAD p og am. Ou wo k has been
ocused owa ds ge ing a model o
SPICE,
whose
use -de ined non1 inea i ies ha e o be exp essed
in polynomial o m.
The e a e se e al me hods o
i
a polynomial
o a se o da a. Ou choice is he one desc ibed
by Hayes
(5)
in which he sum o he squa es o
he esidual e o is minimized by using a sum o
o hogonal polynomials. O he algo i hms as well
as comme icial so wa e can be used o his
pu pose.
Fo simula ing class
A
ope a ion we need o
ge da a a
VT
<
i
<
and ca y ou he
i ing o pg( l) and
C
(??I?
in his ange. How-
e e , o class
B
and ?ope a ion
i
migh no be
necessa y o ake measu emen s in he whole ange
o alues o i. This is because we know
be o ehand ha p
(0)
=
0
o i
<
VT
and ha
Cgs( l) beha es smoo&hly in his ange. Ad an age
is aken o bo h ac s o
limi
he measu emen
ange o
VT
<
i
<
lmax. In ou case we a e
in e es ed in class
B
ope a ion and ou de ice
has
VT
=
-lV
and lmax
=
0.4V which ou
class
B
ange
-2.4
5
l
5
0.4.
Ex apola ion o pg below he pinch-o
ol age consis s o adding ze os a disc e e
alues o
.
Figu e
5
shows he p ocess o ou
pa icula Ease (5.4uA ms e o wi h a 10 deg ee
polynomi a1
)
.
makes
x:poin s o i 1ine: i iw polynomial
70
60
50
Ids(mA)
40
30
20
IO
0
-in
-4
-3
-2
-1
0
0.5
l ( ol s)
FIGURE
5:
POLYNOMIAL FITTING OF
THE
TRANSFER
CURVE
No e ha o he lowe alues o i, pg( l) is
qui e di e en om ze o. This is a ypical
cha ac e is ic o polynomial i ing, i.e. he
(absolu e) e o ends o be highe a he
ex emes o he i ing in e al. The e o e, we
can expec o ha e he highes ela i e e o s a
he le mos ex eme o he ans e cha ac e is-
ic whe e he cu en s a e small bu he i ing
e o can be high. To a oid his e ec , a ew
ze os we e added a alues o i less han -2.4V.
Ex apola ion
o
Cgs( l) is mo e in ol ed.
Fi s , a coe icien
m
has o be ound o
i
he measu ed alues o
Cgs
o he exp ession
which can be la e used o ind
Cgs
o 1
<
VT.
Figu e
6
summa izes his p ocess o ou
pa icula case (m
=
0.474).
A
3.8
F ms
is ob ained wi h an
8
deg ee polynomial.
0
0.5
VI
( ol s)
x
:
measu ed alues
0:
ex apola ed
alues
line: i ing
polynomial
FIGURE
6:
FOLYNOMIAL FITTING
OF
CgS(V1)
AT
VdS-VDSQ'2V
? o
Finally, Pd(Vds) has o be in e pola ed o
he alues shown in Table
2
and he poin pd(0)
=
0.
No e ha since in e pola ion is a pa icula
case o polynomial i ing, he same so wa e ha
has been used o
i
p ( i) and Cgs( l) can now
be used o in e pola e pdq ds)-
111. EXPERIMENTAL RESULTS
Measu emen s a
10
GHz
on
a
SONY
MODFET
2SK677H5 we e made o con i m he h ee basic
nonlinea e ec s:
0
Nonlinea i y in
Cgs
o
o
Nonlinea dependence o Ids wi h Vds
Nonlinea dependence o Ids wi h 1
The accu acy o he nonlinea beha io o Cps( l)
was checked by measu ing he la ge signal
11
and
compa ing
i
wi h simula ed da a. This is shown
in Figu e 7, whe e he measu ed class
A
and
class
B
S11
a e compa ed o he calcula ed ones
o wo alues o inciden powe .
349
FIGURE
7:
LARGE SIGNAL
SI
1
Vas
-
-0.31V
0
Measu ed Class
B
Vos
-3V
as
-
-l
Slmulaled Class
B
1
PIN
lnln
-
-5.86
dBm PIN
-
9.14
dBm
-The
a ows lndlcale
Ihe
change In
S11
wilh Inc easing PIN
Simila ly, he la ge signal S22 is expec ed
o be sensi i e o he nonlinea dependence o
Ids wi h Vds. Figu e 8 shows compa i i e esul s
o his pa ame e a wo bias le els. (This
pa ame e showed low sensi i i y
o
he inciden
powe ).
FIGURE
8:
LARGE SIGNAL
S22
Measu ed) VoS
-
3V
;
VGs
-
-0.31V
Simula ed
-1ncldenl Powe : PI i
-
4.14dBm
-The
a ow Indica es
he
change
In
S22
wilh lnc easlng
Vos
Finally, he accu acy in he modeled ans e
cha ac e is ic was checked by compa ing he
measu ed DC cu en gene a ed in class
B
ope a ion
o he calcula ed alue. This is shown in Figu e 9
and again, good ag eemen is ound.
IV.
CONCLUSIONS
x:
measu ed
solid 1im:calcula ed
Cu en in
mh
-8
-4
0
4
Powe inciden in
dBm
P1GUQ.E
9:
DC
"T
GENERATED
IN
CIASS
8
OPERATION
V.
REFERENCES
K.
Josin, T. Mimu a,
Y.
Yamashi a,
K.
Kosemu a and T.,, Sai o, "Noise Pe o mance
o
Mic owa e HEMT, IEEE MTT-S In . Symp. Dig.
June 1983.
W.
Cu ice, "GaAs MESFET Modeling and
Non1 inea
CAD,"
IEEE
T-MTT, Feb ua y 1988.
F. Diamond and
M.
La i on, "Measu emen
o
Ex insic Se ies Elemen s o a !ic owa e FET
Unde Ze o Cu en Condi ions, P oc. 12 h
Eu opean Mic owa e Con e ence (Finland),
Sep embe 1982.
C.
Raushe and
H.
A. Willing, "Simula ion o
Nonlinea FET Pe o mance Using a Quasi-
S a ic Model," IEEE T-MTT, Oc obe 1979.
J.
C.
Hayes, Edi o , "Nume ical App oxima ion
o
Func ions and Da a," A hlone P ess, 1970.
FET modeling can be done wi h li le ha dwa e
and common so wa e. The p oposed model does no
make any assump ion as o he physical s uc u e
o
he FET, and he
CAD
simula ions a e in good
ag eemen wi h la ge signal measu emen s.
350