NONLINEAR TIME-DOMAIN MACROMODELING OF OTA CIKCUITS
B.
Pe ez-Ve du
,
J.
C uz
7,
B. Lina es-Ba anco
S,
A. Rod iguez-Vazquez
,
J.L. Hue as
and E. Sanchez-Sinencio
$
D o. Elec 6nica y Elec omagne ismo, Uni e sidad de Se illa. 41012-Se illa. SPAIN
#Texas
A&M
Uni em y, Dep . o Elec ical Enginee ing, College S a ion, TX 77843, USA
ABSTRACT
ape we p esen an accu a e nonlinea
mac omode: o he OTA which is sui able o he
ansien simula ion o OTA-based
CMOS
analog
in eg a ed ci cui s.
As
compa ed
o
de ice-le el OTA
models, he p oposed mac omodel is ad an a eous in
e ms o CPU ime. Besides, in ci cui s wi % many
OTAs, i does no ha e he p oblems o con e gence
ha he de ice-le el has. All he mac omodel
pa ame e s can be calcula ed om measu emen s
made
a
he OTA e minals. Expe imen al esul s om
a
3pm
CMOS OTA p o o ype as well as simula ion
esul s om de ice-le el models a e included and
compa ed
o
simula ion esul s om he mac omodel.
In
his
INTRODUCTION
Fo many yea s he con en ional ol age
Val Ampli ie (opamp) has been he wo kho se
o analog ci cui design. Recen ly, he
0
e a ional
T ansconduc ance Ampli ie (0TA)jas been
aemons a ed
o
be posn ially ad an ageous o he
syn hesis o high- equency analog building blocks [l-
41. One eason o his
is
ha ansconduc ance
am
li ie s do no ha e any high in e nal impedance
no e, hence no equi ing in e nal compensa ion
capaci o s and he eby yielding la ge bandwid hs
ha
he opamp. Ano he appealing ea u e o he
OTA
is
ha i s ansconduc ance gain can be ex e nally
con olled, he eby allowing p og ammable
applica ions. These p e ious ea u es ha e mo i a ed
an in e es in he applica ion o he OTA o he
syn hesis o con inuous- ime analog ci cui s, ei he o
linea
[5,61
o o nonlinea [7,81 a plica ions. These
e o s un pa allel
o
he p oposal
o
new
CMOS
OTA
implemen a ions ha a e capable o linea ope a ion in
la ge inpu ol age anges [1,3,4,9]. The ul ima e goal
is he implemen a ion o high- e uency con inuous-
ime analog ci cui s in ully monoli%ic o m.
The design o in eg a ed ci cui s ely on he
e icien
use
o
an app op ia e se o CAD ools. In
pa icula , elec ical simula ion ools (like SPICE21
a e essen ial o he design o analog in eg a ed
ci cui s. Al hough elec ical simula ion can be done
using de ice-le el models, eso ing
o
mac omodels is
a common s a egy
o
educe he CPU- ime e ui ed in
simula ing complex analog sys ems. Se e al opamp
mac omodels ha e been epo ed in he pas (see
e e ences in
[lo]).
Howe e , li le ha e been s ill done
abou
OTA
mac omodeling, he ew con ibu inns
1441
ISCAS
'89
exis ing [11,121 no being speci ically ocused on he
inclusion o he mac omodel in a elec ical simula ion
ool. I es ic s ou abili y
o
p ope ly analyze complex
OTA-based analog in eg a ed ci cui s.
In
his pape we
o e come his d awback by p esen ing an OTA
mac omodel which is sui able o he ime-domain
simula ion o OTA-based CMOS analog ci cui s.
OTA MACROMODEL
OTA
speci ica ions and pa ame e s
Figu e
1
shows a gene ic CMOS OTA a chi ec u e
consis ing
o
an inpu ansconduc ance s age ollowed
by cu en mi o s 121. The inpu s age pe o ms he
co e ope a ion o di e en ial- ol age o cu en
con e sion while he cu en mi o s a e used
o
s ee
he ou pu cu en s o he di e en ial ampli ie
o
a
high impedance ou pu node. Se e al ypes
o
cu en
mi o s
[131 and ansconduc ance
s a
es [1,3,4,91 can
be
used
in
Fig.1, he eby esul ing in a oad ca alog o
p ac ical OTA implemen a ions.
I
ESPEJOS
P
I
Figu e
1:
Gene ic CMOS OTA block diag am
The ideal model o Fig.1 is a linea di e en ial-
ol age-con olled cu en -sou ce, he only pa ame e
equi ed
o
desc ibe his ideal model being he DC
ansconduc ance gain o he OTA,
g,.
The beha io o
p ac ical
OTAs
de ia e om wha is expec ed using he
ideal model in di e en ways.
In
he ollowing he e is
a lis o he pa ame e s and speci ica ions o be
conside ed in he p oposed mac omodel.
DC small-signal OTA ansconduc ance gain
e
Inpu ca aci ance
V,,
Inpu eg ed o se ol age
CH2692-2/89/0000-1441
$1.00
0
1989
IEEE
u iic
im na i n
can
~e
m aineu
mo n
u -.
w.
henne n JenKins.
-~
(217)
333-4789
Linea egion (less han
1%
de ia ion) o he
ol age
o
cu en con e sion
Nonsa u a ed egion o he ol age o
cu en con e sion
Maximum ou pu cu en
Minimum ou pu cu en
High- equency pole
Maximum ou pu ol age
Minimum ou pu ol age
Delay
o
he op ol age-sa u a ion s a e
Delay o he bo om ol age-sa u a ion
s a e
Minimum ou pu cu en in he op ol age-
sa u a ion s a e
Maximum ou pu cu en in he bo om
ol age-sa u a ion s a e
Ou pu Resis ance
Ou pu Capaci ance
Each pa ame e abo e is di ec ly ela ed o he
co esponding OTA speci ica ion and can
be
calcula ed
om ex e nal measu emen s a he OTA e minals.
Mac omodel a chi ec u e
Figu e 2 shows he block diag am o he p oposed
mac omodel consis ing o ou s ages. The di e en
s ages a e connec ed by ol age-con olled sou ces.
,A~ A
s age
ln e media
s age
Figu e
2:
Mac omodel a chi ec u e
All he nonlinea i ies in he mac omodel a e
implemen ed using analog swi ches,
as
i is done in
[
101
o he opamp. The con ol s age in Fig.2 gene a es
he h eshold signals equi ed o con olling he
analog swi ches. The inpu s age includes he inpu
impedance, o se ol age and
CMRR.
I s
implemen a ion is simila
o
he co esponding s age
in
[lo].
Figu e 3a shows he implemen a ion o he
in e media e s age. The condi ions o each analog
swi ch
o
be
a
he posi ion
0
a e gi en in he i s ow
o Table
1;
he co espondin condi ions o he posi ion
0
a e included in he seconi ow.
The in e media e s age is d i en by he ou pu
ol age o he inpu s age,V,, and de elops an ou pu
ol age
Vb.
Analysis gi es he ollowing dynamic
equa ion o desc ibe he inpu -ou pu ope a ion o
Fig.3a:
dVb
'b
c
-
+-
=I(V
)
I
d
H,
whe e
I(VJ
is he nonlinea unc ion depic ed in
Fig.3b. When pa icula ized o small-signal, his
equa ion accoun s o he DC ansconduc ance gain
(pa ame e
gml
in he lis abo e) also p o iding a
sin le ole app oach
[2]
o
he hi h equenc beha io
o &e 'BTA (pa ame e
o1
=I/R, !,i
The nonsnea i ies
in he OTA ol age
o
cu en con e sion a e modeled
by he ans e cha ac e is ics
o
Fig.3b ( ia he
pa ame e s
IH+,
18-,
8,
-,
Sl+,82-,
&+).
I(",)
3a
3b
Figu e
3:
a)In e media e
s age,
b)DC
OTA
ans e cha ac e is ic
Table
1:
Swi ching condi ions o Pig.3a
(Zb=
VdR,)
The ou u s age is shown in Fig.4. The swi ching
condi ions
&
he analog swi ches used in
his
s age a e
gi en in Table 2. As o Table
1,
he i s ow
co esponds
o
he posi ion
0.
Besides, he swi ches
LS
and
LIZ
exhibi
a
con olable delay in he
0
o
0
ansi ion.
+-
Figu e
4:
Ou pu
s age
The ou pu s age
is
d i en by he ou pu ol age o
he in e media e s age,
b,
and models he ou pu
impedance and he ou pu ol age sa u a ion
1442
cha ac e is ics, including he limi a ions on he
a ailable cu en when he ou pu ol age
is
a
sa u a ion, and he ime delays appea ing when he
OTA
is
d i en ou o he ol age sa u a ion s a es
(pa ame e s
Is-,
Is+,TD-
and
TD+).
V,>Eg+
V.,>Es+
Vu<&-
V,,<Is-
lb<Io
ls-<Io
1b>I0
Is+>Io
Table
2
Swi ching condi ions o
Fig.4
(I*&
VdRI)
Mos o he elemen alues o he mac omodel can
be di ec ly calcula ed om measu emen s.
RP
is
included
o
a oid he cu en sou ces om being in
open ci cui a any ime and mus
be
selec ed la ge
enough.
MACROMODEL PERFORMANCE
Figu e
5
is a mic opho og a h o a
CMOS
3pm
double me al p o o ype
o
he &'A a chi ec u e o
Fig.1, whe e we ha e used enhanced Wilson cu en
mi o s
[
131 and he ex ended- ange di e en ial
ampli ie o Fig.6 [l].
Figu e
5
CMOS 3pm
O A
p o o ype
1
1
Figu e
6:
Linea ized di e en ial pai
I1
I
Di e en measu emen s ha e been made on he es
ci cui o Fig.'la, whe e he o o ype o Fig.5 is
connec ed
o
se e al ancilla y ogchip com
Figu es 8a,c show wo osciloscope dispczE m he
es ci cui s o Fig.7a. Figu es 8b,d show he
co esponding wa e o ms ob ained by simula ion using
DIANA [14] and he OTA mac omodel. Figu es 8a.b
a e o
C,,
=
33pF,
GI.
=
1lR~
=
0,
he
signal d i ing he
es
ci cui being
a
5Khz sinusoidal wa e o m.On he
1443
o he hand, Figs.8c,d a e o
CL
=
200pF,
RL
=
212KQ
and a squa e inpu signal.
7a 7b
Figu e 7: Tes s ci cui s
Ru
=
50KQ)
8a
n
E
a
-
!4
s-
0
5
E
4
P
-
0
5
In
..
1....1....1....1
8d
'
'
7~10-~
8~10'~ 9~10'~
lo5
Figu e
8:
Expe imen al e sus simula ed wa es
~
~__~
~
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im na i n
can
~e
m aineu
mo n
u -.
w.
henne n
JenKins.
-~
(217)
333-4789
P e ious igu es shows a e y close ag eemen
be ween expe imen al and simula ion esul s. The
o e shoo s in he expe imen al wa e o ms a e due
o
he eac i e beha io o he expe imen al se up.
The pe o mance o he new mac omodel has been
also compa ed
o
ha o de ice-le el models.
B
he
way o example, Fig.9a shows se e al wa e& ms
ob ained when simula ing he es ci cui o Fig.7b by
using SPICE2 and de ice-le el models. The
co esponding esul s when using ou mac omodel in
DIANA a e shown in Fig.9b. The OTAs o his
example used a con en ional noncompensa ed
di e en ial ampli ie and enhanced Wilson cu en
mi o s. As i can be seen, he ag eemen be ween he
mac omodel and he de ice-le el model is e y good.
Howe e , he o me is much mo e e icien in e ms o
CPU- ime han he la e . Conce ning his poin , ou
expe ience o his and many o he examples and
simula ion uns gi es a a io n=TdT which anges
be ween
4
and
30,
whe e
TD
is he CPU- ime o he
de ice-le el model and
T,
is
he co esponding ime o
he mac omodel.
n
9b
Figu e
9
Simula ion esul s
o
Pig.7b
a) De ice-le el model,
b)
Mac omodel
ol ages:O.l ol sld ;
cu en s
10pA/d
1)lSCUSSION
OF HESULTS
A mac omodel o he OTA has been p esen ed
whose ea u es can be summa ized in he ollowing
poin s:
1)
I
is a la ge signal nonlinea mac omodel.
2)
I
models he inpu -ou pu beha io
o
he OTA,
hus being adequa e o di e en OTA
implemen a ions ( o ins ance, wo di e en
OTAs a e conside ed in he sec ion on
mac omodel pe o mance).
3)
All he nonlinea i ies in he new mac omodel
a e simula ed using h eshold unc ions [lo].
4) The mac omodel pa ame e s can be calcula ed
om measu emen s made a he OTA e minals.
5)
I yields easonably accu a e simula ions,
p o iding impo an ad an ages in e ms o
CPU- ime sa ing.
6) Besides he educed CPU- ime, he mac omodel
in ci cui s wi h many OTAs does no ha e he
se ious p oblem o con e gence (in SPICES) ha
he de ice-le el model has.
Fu u e esea ch will ocus on he inpu s age and
common mode e ec s. Also, a classi ica ion o a la ge
ca alog o OTA a chi ec u es will be done. Finally,
equency-domain mac omodels will be de elopped.
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111
I21
[31
141
I51
161
171
[SI
[91
I101
1111
I121
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