Oc obe 20, 1998 5:14 pm 1
Ve y Wide Range Tunable CMOS/Bipola
Cu en Mi o s wi h Vol age Clamped Inpu
Te esa Se ano-Go a edona1, Be nabé Lina es-Ba anco1, and And eas G. And eou2
1 Na ional Mic oelec onics Cen e (CNM), Ed. CICA, A . Reina Me cedes s/n, 41012 Se illa,
SPAIN, Phone: 34-5-4239923, Fax: 34-5-4231832, E-mail: [email p o ec ed]
2 Dep . o Elec ical and Compu e Enginee ing, The Johns Hopkins Uni e si y,
Bal imo e, Ma yland, USA
Abs ac
In low powe cu en mode signal p ocessing ci cui s i is many imes equi ed o use cu en
mi o s o eplica e and ampli y/a enua e cu en signals, and o clamp he ol age o nodes
wi h high pa asi ic capaci ances so ha he smalles cu en s do no in oduce unaccep able
delays. The use o unable ac i e-inpu cu en mi o s would mee bo h equi emen s. In
con en ional ac i e inpu cu en mi o s s abili y compensa ion is equi ed. Fu he mo e,
once s abilized, inpu cu en canno be made a bi a ily small. In his pape we in oduce wo
new ac i e-inpu cu en mi o s ha clamp hei inpu node o a gi en ol age. One o hem
does no equi e compensa ion, while he o he may equi e unde some ci cums ances, bu o
bo h inpu cu en may ake any alue. The mi o s can ope a e wi h hei ansis o s biased
in s ong in e sion, weak in e sion o e en as CMOS compa ible la e al bipola de ices. I
biased in weak in e sion o as la e al bipola s, he cu en mi o gain can be uned o e a e y
wide ange. Acco ding o he expe imen al measu emen s p o ided in his pape , inpu cu en
may spawn beyond nine decades, and cu en mi o gain can be uned o e 11 decades. As an
applica ion example a sinusoidal gm-C based VCO has been ab ica ed whose oscilla ion
equency could be uned o o e 7 decades be ween 74mHz and 1MHz.
I. In oduc ion
When using cu en mode signal p ocessing VLSI ci cui s i is no unusual ha a e y wide ange
o cu en le els ha e o be handled. Fo example, when building low powe silicon e inas, ligh
in ensi y is di ec ly and (app oxima ely) linea ly ans o med in o cu en [1]-[2]. Silicon e inas can
sense up o six decades o ligh le els, which yields also six decades o cu en le els a he
pho o ecep o s ou pu . I is imp ac ical o pe mi ha his cu en would con ol di ec ly he ime
cons an o he comple e sys em. This would make a silicon e ina be as o high ambien ligh , bu
six o de s o magni ude slowe o low ambien ligh . This is no ealis ic, and a way o speed up hese
delays is by clamping he ol ages o hose nodes wi h high pa asi ic capaci ances. Since cu en
mi o s a e necessa y elemen s o cu en mode signal p ocessing ci cui s, a e y compac solu ion is
o use cu en mi o s ha clamp hei inpu ol ages. These cu en mi o s a e usually e e ed o as
ac i e inpu cu en mi o s [3]-[4].
In he nex Sec ion he con en ional ac i e inpu cu en mi o is analyzed and i is shown why i
needs compensa ion, why compensa ion depends on he mi o inpu cu en , and why his cu en
canno be made a bi a ily small. In Sec ion III wo new sou ce d i en ac i e inpu cu en mi o
opologies a e in oduced and s abili y is analyzed. One o he mi o s does no equi e compensa ion
and he o he may equi e unde some ci cums ances. Howe e , o bo h s uc u es, inpu cu en can
be made a bi a ily small wi hou ende ing uns able beha io . Sec ion IV p o ides some in ui ion
Submi ed o IEEE T ansac ions on Ci cui s and Sys ems, Pa I on Ap il 24, 1998. Re ised e sion
submi ed on July 31, 1998. Accep ed on Sep embe 4, 1998. Final e sion submi ed on Oc obe 20, 1998.
Oc obe 20, 1998 5:14 pm 2
ega ding dynamic beha io o he mi o s. Sec ion V shows how o make he mi o s o ha e a
con inuously adjus able gain unable o e a e y la ge ange. Sec ion VI s udies loading e ec s. In
Sec ion VII i is shown how o ex end he mi o ing ope a ions o bipola ansis o s using he CMOS
compa ible la e al bipola ansis o s, and inally in Sec ion VII expe imen al measu emen s a e
p o ided ha show he inpu cu en s spawning beyond six decades and he cu en mi o gains
being adjus ed o e 11 decades. As an applica ion example, he i s mi o is used o make a cons an
linea inpu ange OTA whose ansconduc ance is unable o o e 7 decades. This OTA is hen used
in a sinusoidal VCO whose oscilla ing equency could be uned om o .
II. Con en ional Ac i e Inpu Cu en Mi o
The con en ional ac i e-inpu cu en mi o [3] is shown in Fig. 1(a). By ed awing i s inpu
s age as shown in Fig. 1(b), one ecognizes a s anda d (uncompensa ed) 2-s age CMOS ope a ional
ampli ie [5], connec ed in a uni y-gain nega i e eedback con igu a ion. The i s s age o he opamp
is he di e en ial inpu ampli ie o Fig. 1(a), and he second (in e ing) s age consis s o ansis o
M1 and cu en sou ce . I is well known ha his s uc u e needs compensa ion [5], and ha he
compensa ion ci cui y depends on he alue o he second s age bias cu en . Fu he mo e, i
esul s imp ac ical o compensa e when has o be a ied o e many decades and eaches e y low
alues.
Fo he di e en ial inpu ol age ampli ie he OTA in Fig. 2(a) can be used. OTAs a e
compensa ed by hei load capaci ance . An OTA connec ed in uni y gain eedback con igu a ion
(as in Fig. 2(b)) has he small signal equi alen ci cui shown in Fig. 2(c), whe e elemen
models he ansconduc ance gain o he OTA and i s ou pu conduc ance. T ansconduc ance
gm-C
74mHz
1MHz
Iin
1
2
Cp
M1
V
CLAMP
V
CLAMP
Iin
1
2
M1M2
CpIo
(a)
2
Cp
M1
Iin
1
CA
V
CLAMP
gm1 1go1
Cpa
goa
2
(s)
gm
1 2
gd1
C
Cp
(c)
(b) (d)
Fig. 1: Con en ional ac i e inpu cu en mi o , (a) ci cui schema ic ep esen a ion, (b) inpu
s age d awn as a 2-s age opamp, (c) small signal equi alen ci cui o mi o inpu s age, (d)
compensa ed ci cui .
Iin
Iin
Iin
Cpa
gms( )
goa
Oc obe 20, 1998 5:14 pm 3
is equency dependen because o he delay in oduced by he pa asi ic capaci ances o he
OTA in e nal nodes. This delay can be modeled as [6]
(1)
whe e is he DC ansconduc ance gain o he OTA and models i s delay. This yields he
ollowing s abili y condi ion o he ci cui in Fig. 2(c)
(2)
Using his model o he OTA wi h he s abili y condi ion o eq. (2), i is possible o analyze he
s abili y o he ci cui in Fig. 1(b), whose small signal equi alen ci cui is shown in Fig. 1(c).
T ansis o is modeled by elemen s , and , while he OTA is modeled by
, and he node pa asi ic capaci ance . A e s aigh o wa d
analysis i is easy o see ha , i eq. (2) is sa is ied, imposing he condi ion
(3)
gua an ees s abili y. Bu his equi es, a leas , ha which imposes a lowe bound on he
alue o (and ) in Fig. 1(b). In p ac ice, he ci cui is usually compensa ed as shown in Fig.
1(d) [3], by adding a uni y gain ol age bu e and a compensa ion capaci o . Eq. (3) would
change o
(4)
Bu again, canno be made a bi a ily small.
in
-
in
+
bias
V
ou
Cpa
bias
I
(a)
ou
Cpa
in
(b)
goa ou
gm(s)( in- ou )
pa
C
(c)
Fig. 2: (a) OTA s uc u e sui able o he di e en ial inpu ol age ampli ie .(b) Uni y gain eedback
con igu a ion, and (c) small signal equi alen ci cui .
gms( )
gms( ) gma 1s
ωa
------–
 
 
=
gma
ωa
Cpa
gma
ωa
---------
>
M1
gm1
go1
Cgd1
gms( ) gma 1s/ωa
–( )=
goa
1
Cpa
Cgd1gm1gma
–( ) gm1gma
ωa
------------------
>
gm1gma
>
gm1
Iin
CA
gm1Cgd1CA
+( ) gm1gma
ωa
------------------ gmaCgd1
+>
gm1
Oc obe 20, 1998 5:14 pm 4
The wo new ac i e inpu cu en mi o opologies in oduced in his pape do no ha e his
p oblem: (and consequen ly, ) can be made a bi a ily small. In he nex Sec ion hese mi o s
a e in oduced and analyzed.
III. Two New Ac i e Inpu Cu en Mi o s
A. Fi s Topology
The i s al e na i e ci cui o he one in Fig. 1(a) is shown in Fig. 3(a), whe e he OTA ou pu
d i es he sou ce o ansis o ins ead o i s ga e. The OTA mus be able o sink wice he
maximum expec ed alue o , which imposes an impo an design cons ain o he OTA: in
Fig. 2(a) mus be, a leas , wice he maximum ope a ion cu en o he mi o 1. The mi o inpu s age
can be ed awn as shown in Fig. 3(b), which can be conside ed o be a special wo s age opamp
connec ed in uni y gain eedback con igu a ion. No e ha he second s age o his opamp is a posi i e
gain ol age ampli ie , as opposed o he case o Fig. 1(b). Neglec ing body e ec o ansis o ,
he absolu e gain alue o his second s age would be iden ical o ha o Fig. 1(b). Also no e, ha he
inpu node o his second s age is he sou ce o ansis o which is a low impedance node. This
makes he ci cui o Fig. 1(b) o ha e a single dominan pole, and consequen ly i s beha io is
quali a i ely simila o a single s age opamp in uni y gain eedback con igu a ion. To analyze he
s abili y condi ions o his ci cui , le us eso o i s small signal equi alen ci cui , shown in Fig.
3(c). I s cha ac e is ics equa ion is
1. E en ually, special OTAs ha ope a e in a ype o class AB mode [7] could be used o op imize powe consump ion.
gm1
Iin
M1
Iin
Ibias
M1
M1
V
CLAMP
Iin
2
M1
1
M2
CpIo
(d)
gm
1 1
2
(s)
m
goa
gpa
Co1
gp
C
1 2
(c)
V
CLAMP
Iin
2
M1
1
M2
V
G
Io
Cp
(a)
Iin
2
Cp
M1
1
V
G
V
CLAMP
(b)
Fig. 3: Fi s new ac i e inpu cu en mi o opology, (a) ci cui schema ic ep esen a ion, (b) inpu s age
d awn as a 2-s age opamp, (c) small signal equi alen ci cui . (d) Second cu en mi o opology.
Oc obe 20, 1998 5:14 pm 5
(5)
Since he OTA is assumed o be compensa ed, eq. (2) is sa is ied, and he las e m o coe icien b in
eq. (5) is posi i e. Howe e , b migh s ill become nega i e. The ollowing condi ion gua an ees a
posi i e b coe icien
(6)
This can be achie ed by ei he adding an ex a capaci ance a node o by making he OTA o ha e
a smalle delay (la ge ) o lowe . No e ha he igh hand side o eq. (6) is an inc easing
unc ion o . Consequen ly, once eq. (6) is sa is ied o he maximum possible (maximum
) s abili y is gua an eed o any smalle alue o (and ).
I eq. (6) canno be sa is ied, ano he way o achie e compensa ion o his opology is by adding
a compensa ion capaci o be ween nodes and in Fig. 3. This yields he ollowing
cha ac e is ics equa ion
(7)
I eq. (2) is sa is ied, coe icien a is posi i e as well as he second e m o coe icien b.
Consequen ly, s abili y is gua an eed i
(8)
I he igh hand side o eq. (8) is nega i e, is no necessa y and eq. (6) esul s. I he igh hand
side o eq. (8) is posi i e, hen should sa is y eq. (8) o he la ges alue o (o ). Once
his is assu ed, eq. (8) emains alid o any smalle alue o (o ).
B. Second Topology
Ano he al e na i e ac i e inpu cu en mi o is he one shown in Fig. 3(d). No e ha in his case
ansis o is connec ed as a diode a ound he nega i e eedback loop o he ampli ie , and ac s
simply as a passi e de ice. The e o e, i he di e en ial ol age ampli ie is al eady compensa ed o
uni y gain eedback, he ci cui should always be s able. This can be e i ied by pe o ming a simila
analysis o ha o he i s opology.
C. Discussion
The s abili y analyses o bo h opologies a e alid whe he ansis o s and a e biased in
hei weak o s ong in e sion egions o ope a ion. This allows he cu en mi o s o ope a e o a
as2bs c+ + 0=
a CpCpa
=
b goa gm1
+( ) Cp
gm1gma
ωa
------------------– go1Cpa
gma
ωa
---------–
 
 
 
+=
c gm1gma
=







Cp
gmagm1
ωagoa gm1
+( )
-------------------------------------
>
2
ωa
gma
gm1
gm1
Iin
gm1
Iin
CA
1
2
as2bs c+ + 0=
a CpCpa CACpCpa
gma
ωa
---------–+
 
 
 
+=
b Cpgoa gm1
+( ) go1Cpa
gma
ωa
---------–
 
 
  gma CA
gm1
ωa
---------–
 
 
 
+ +=
c gm1gma
=







CAgm11
ωa
------ Cp
gma
---------–
 
 
  Cp
goa
gma
---------
–>
CA
CA
gm1
Iin
gm1
Iin
M1
M1
M2

Oc obe 20, 1998 5:14 pm 6
e y wide ange o cu en s: om alues equal o junc ion leakage cu en s up o he maximum
cu en he OTA migh be able o sink. Also, ca e needs o be aken o a oid ha he OTA ou pu
ol age eaches i s minimum (o maximum, o p- ype cu en mi o s) alue by adjus ing o
a sa e enough le el.
The s abili y ad an ages o hese wo new opologies wi h espec o he con en ional one o
Sec ion II, come om he ac ha he di e en ial ol age ampli ie is loaded by a low impedance
node, which makes he whole ci cui o beha e simila o a single pole (o one-dominan pole) sys em.
Al hough he Topology 1 cu en mi o migh equi e s abili y compensa ion, i has ce ain
ad an ages o e he Topology 2 one, as will be seen h oughou he pape : i is as e o e y low
cu en s and i can be ope a ed in bipola mode by simply ebiasing cons an global ol ages.
IV. T ansien Response
A. Fi s Topology
The ci cums ances unde which he cu en mi o will be slowes is when inpu cu en is
smalles (in he o ange). In hese cases ansis o is ope a ing in weak in e sion and i is
sa e o conside he OTA ac ing as an ins an aneous de ice ha does no in oduce any delay. I his is
he case, he la ge signal ansien esponse o he ci cui in Fig. 3(b) can be compu ed by modeling
he mi o inpu s age as shown in Fig. 4(a) bu wi h . I and model he OTA and
is he cu en h ough ansis o , s aigh o wa d analysis
yields he ollowing s a e equa ion
(9)
whe e is he OTA ol age gain. I changes in a s ep ashion om o , he
solu ion o eq. (9) can be w i en as
(10)
whe e,
(11)
I we de ine as he delay ime i akes o o each , hen
(12)
No e ha i is su icien ly la ge can be easonably small, e en o low alues o .
As inc eases he ci cui will espond as e and he delay in oduced by he OTA will s a o be
app eciable. In his case, he ci cui shown in Fig. 4(a) wi h can be used o analyze i s
ansien esponse. The esul ing s a e equa ion does no ha e an analy ical solu ion, hus in o de o
ob ain an es ima ion o he delay in he cu en mi o one can eso o i s small signal equi alen
ci cui , and conside makes a “li le” s ep. Neglec ing he OTA in e nal delay1 (cha ac e ized by
VCLAMP
nA
pA
M1
Cpa 0=
gma
goa
IM1IS1VG1 1
–( ) /nUT
{ }exp=
M1
Iin IM1
Cp
goaA
--------------I
˙M1Cp
nUT
A
----------I
˙M1
IM1
--------
+ +=
A gma/goa
=
Iin
Ic
Ic
IM1 ( )
IcIM1 ( )–[ ] 1ε+
------------------------------------------- Ic
Ic Ic
–[ ] 1ε+
---------------------------------e /τ1
=
τ1
CpnUT
A Ic
----------------- ,εIc
goanUT
------------------= =
d1
IM1 ( )
RIc
d1τ1R
--- 1 –
1R–
------------
 
 1ε+
ln=
A
τ1
Ic
Ic
Cpa 0≠
Iin
Oc obe 20, 1998 5:14 pm 7
) he ollowing cha ac e is ics equa ion ( alid o weak and s ong in e sion) esul s o he ci cui
d awn in Fig. 3(c),
(13)
The oo s o his equa ion a e gi en by
(14)
I wo complex poles esul and he ansien has an associa ed ime cons an o he
o de o . I he poles a e eal, he dominan ime cons an may ange om ( o high alues
o ) o ( o small alues o ). No e ha o e y small alues o (
and ) i ollows ha and , and he esul ing ime cons an is , as de i ed
p e iously using he la ge signal i s o de model. On he o he hand, o e y la ge (and )
alues is also small and a dominan i s o de dynamics esul s wi h ime cons an
. Consequen ly, o bo h e y small and e y la ge he e a e no complex
poles and he dynamics is domina ed by a single eal pole. The maximum alue o is
eached o (assuming ), and is . The e o e, i
can be sa is ied, no complex poles (and no inging) will appea o he whole inpu
cu en ange.
I a compensa ion capaci o is used, he esul ing equa ion would be
1. The e ec o migh be included, al hough he main delay in oduced by he OTA is gi en by loaded by
and o he loads.
ωa
gma
Cpa
oa
gpa
C
1
V
G1
Iin 2
Cp
M1
2CLAMP
-V
ma
g( )
(a)
oa
g
1
pa
C
gs
C1
M1
Iin
2
Cp
2CLAMP
-V
ma
g( )
(b)
Fig. 4: Equi alen ci cui s o compu ing ansien analysis i OTA delay canno be neglec ed, o (a) i s new
opology and o (b) second new opology.
ωa
s2s
τ3
----- 1
τ1τa
----------+ + 0=
1
τ3
----- goa gm1
+
Cpa
----------------------- go1
Cp
--------+=
1
τ1
----- gm1A
Cp
---------------
=
1
τa
----- goa
Cpa
---------
=









so1
2τ3
--------– 1 1 4 τ3
2
τ1τa
----------
–±=
τ3
2/τ1τa1/4>
2τ3
2τ3
τ3
2/τ1τa
τ1τa/τ3
τ3
2/τ1τa
Iin
gm10≈
go10≈
τ3
2/τ1τa1«
τaτ3
≈
τ1
Iin
gm1
τ3
2/τ1τa
τ1τa/τ3Cp/gma
≈
Iin
Iin
τ3
2/τ1τa
gm1goa
=
gm1/Cpa go1/Cp
»
A Cpa/4Cp
A Cp/Cpa
<
CA
Oc obe 20, 1998 5:14 pm 8
(15)
whe e and wi h a, b and c gi en by eq. (7). Again, he associa ed dominan
ime cons an would ake a alue be ween and . Fo e y small and e y la ge he e is
a dominan eal pole o ime cons an ha p oduces a i s o de dynamics. Fo e y small
i esul s , while o e y la ge i is . The maximum
alue is eached o , o which wo eal poles esul bo h o
simila ime cons an s a ound .
B. Second Topology
Fo he cu en mi o o Fig. 3(d) simila analyses can be done. Fo e y small inpu cu en s,
such ha he OTA can be conside ed o espond ins an aneously, he ollowing s a e equa ion esul s
(assuming and )
(16)
Consequen ly, eqs. (10)-(12) would also be alid o his mi o as long as is subs i u ed by
.
I he OTA migh no longe be conside ed o espond ins an aneously, o i is no negligible
wi h espec o , an es ima ion o he delays can be ob ained om he small signal equi alen
ci cui o Fig. 3(d) wi h . Rou ine analysis yields he ollowing cha ac e is ics equa ion ( alid
o weak and s ong in e sion)
(17)
Consequen ly, he se ling o he mi o has a dominan ime cons an ha can ange be ween alues
o he o de o and . Fo e y small and e y la ge alues (and assuming
) i ollows ha and a dominan i s o de dynamics esul s wi h
e ec i e ime cons an . Fo e y small his ime cons an is , while o e y
la ge i is . The maximum alue o is
eached o . The e o e, i can be sa is ied no complex poles
will appea .
C. Simula ions
Ex ensi e Hspice ansien esponse simula ions ha e been pe o med on bo h opology cu en
mi o s o con i m he p e ious analyses. Sizes o ansis o s and we e se o
and he in e nal bias cu en o he OTA was . An inpu node capaci ance o
was conside ed and inpu cu en was changed in a s ep ashion om o . The alue
s2s
τ3'
------ 1
τa'
------
 
 2
+ + 0=
τ3'a/b=
τa'( ) 2a/c=
2τ3'
τ'a
2/τ3'
Iin
τ'a
2/τ3'
Iin
τ'a
2/τ3'τ1CA/gm1
+≈
Iin
τ'a
2/τ3'Cp/gma
≈
2τ3'/τa
( ) 2
gm1goa gmaCA/Cp
+≈
1/τ3' 2 goa/CAgma/Cp
+( )=
Cpa 0≈
Cgs10≈
Iin IM1
Cp
goa A 1+( )
------------------------------I
˙M1
CpnUT
A 1+
-----------------I
˙M1
IM1
--------
+ +=
A
A 1+
Cgs1
Cp
ωa0=
s2s
τ4
----- 1
τ5
2
-----+ + 0=
1
τ4
----- Cgs1Cp
+
Ce
2
-----------------------goa
Cpa Cp
+
Ce
2
---------------------gm1
Cgs1
Ce
2
-----------gma
+ +=
1
τ5
2
----- gmagm1
Ce
2
------------------
=
Ce
2CpCgs1CpCpa Cgs1Cpa
+ +=









2τ4
τ5
2/τ4
Iin
CpCpa Cgs1
,»
2τ4/τ5
( ) 21«
τ5
2/τ4
Iin
τ1Cgs1/gm1
+
Iin
Cp/gma
2τ4/τ5
( ) 2Cgs1Cpa
+( ) /Cgs1Cp/A
+( )=
gm1goa gmaCgs1/Cp
+=
A Cpa Cp
<
M1
M2
150µm5µm×
20µA
Cp1pF=
Ic
2Ic
Oc obe 20, 1998 5:14 pm 9
o was swep loga i hmically om o . The ou pu o he cu en mi o was connec ed
o a ol age sou ce equal o . The cu en h ough his ol age sou ce was
ime-no malized o , whe e is he ime a which has eached 63.2% o i s o al
excu sion alue (assuming a i s -o de -like esponse). Fig. 5(a) shows he simula ed ou pu
wa e o ms, whe e he ampli ude has also been no malized wi h espec o ,
(18)
In Fig. 5(b), o he ace wi h ci cles, he co esponding alues o as a unc ion o a e
ep esen ed o Topology 1 wi h . As discussed p e iously in Sec ion IV.A, o e y small
cu en s he ime cons an is in e sely p opo ional o cu en le el (see eq. (11)), while o la ge
cu en s he ime cons an ends o se le o a cons an alue (see discussion a e eq. (14)). Fo
be ween and he mi o ou pu cu en s ep esponse showed inging (p esence o
complex conjuga e poles), while ou side his ange no inging is obse ed (absence o complex
conjuga e poles). This was also p edic ed by he heo e ical discussion a e eq. (14). E en ually,
inging could be educed o supp essed by imp o ing he ci cui phase ma gin by adding he
compensa ion capaci ance men ioned in Sec ion III.A. Howe e , may inc ease he delays o
he comple e ange o inpu cu en s.
The same simula ions we e epea ed o he second opology. The esul ing alues o as a
unc ion o a e ep esen ed in Fig. 5(b) using he ace wi h as e isks. Again o e y small cu en s
he ime cons an is in e sely p opo ional o cu en and ends o se le o la ge cu en s (as p edic ed
in Sec ion IV.B). P esence o complex conjuga e poles was obse ed o be ween and
, as an icipa ed by he discussion a e eq. (17). No e ha o he lowe cu en s ange he
esul ing alues o a e abou wice han hose o Topology 1. This is because o Topology 2 he
inpu node capaci ance includes now also he sub h eshold ga e- o-bulk capaci ance o
ansis o . Fo ga e oxide hickness and ga e a ea his
capaci ance is [8]. The e o e, in his example, he e ec i e
Fig. 5: T ansien Analyses Simula ion Resul s. (a) Time and Ampli ude No malized T ansien Responses o
Topology 1 Cu en Mi o wi h Uni y Gain, (b) Ex ac ed alues o τn o bo h Topologies wi h Uni y Gain
and Sweeping he Gain.
(a) (b)
10−11 10−10 10−9 10−8 10−7 10−6 10−5
10−8
10−7
10−6
10−5
10−4
Iou
τ n
opology 1, gain=1
opology 2, gain=1
opology 1, Iin=10 nA
opology 2, Iin=10 nA
Ic
10pA
10µA
VCLAMP 2.5V=
Io ( )
Io /τn
( )
τn
Io
Ic
Io /τn
( ) Ic
–
Ic
-------------------------------
τn
Ic
CA0=
Ic
2nA
100nA
CA
CA
τn
Ic
Ic
10nA
100nA
τn
Cp
Cgb
M1
ox 10nm=
A150 5µm2
×=
Cgb 0.4Aεox/ ox 1.05pF= =
Cp
Oc obe 20, 1998 5:14 pm 16
Fo he ab ica ed p o o ype VCO he capaci o alue is . When using con en ional
CMOS OTAs o sinusoidal VCOs, hei equency uning ange is limi ed o li le mo e han
one decade [6]. The eason is ha o uning he VCO equency, OTA ansconduc ances ha e o be
changed. I he OTA ansconduc ance is adjus ed h ough i s di e en ial pai bias cu en hen
he linea ange o he OTA is educed as i s ansconduc ance (and ) is lowe ed. I a linea ange
abo e is desi ed, ansconduc ance uning is limi ed o li le mo e han one decade. The
ansconduc ance o he OTA in Fig. 9 can be uned while main aining i s cu en (and linea
ange) cons an . The wo op Topology-1 PMOS cu en mi o s a e uned simul aneously h ough
con ol ol age and a e able o change he OTA ansconduc ance o o e 7 decades. Fig. 10(b)
shows he expe imen ally ob ained ela ionship be ween oscilla ion equency and con ol ol age
o he sinusoidal VCO. The minimum equency ha could be measu ed was
, while he maximum was . Fig. 11 shows he measu ed
sinusoidal wa e o ms o hese wo limi si ua ions.
To show he e ec o OTA linea inpu ange deg ada ion, le us eso o Fig. 12. Classically, he
OTA ansconduc ance is uned by changing i s di e en ial pai ail bias cu en . Fig. 12(a)
shows he measu ed cu es o he OTA o Fig. 9 ( ) when using cu en
o uning and lea ing cons an . Fig. 12(b) shows he cu es , which a e he
i s de i a i es o hose in Fig. 12(a) no malized wi h espec o (de ined as he slopes a
o Fig. 12(a)). The wides bell-shape cu e co esponds o he maximum and maximum . As
is dec eased he bells become na owe (less inpu ange) un il he di e en ial pai ansis o s a e
ully biased in weak in e sion and he linea inpu ange emains cons an (be ween one o wo ).
In Fig. 12(a) and Fig. 12(b) he la ges measu ed ansconduc ance is , while he
minimum is . I ins ead o using o une we use hen he cu es shown
in Fig. 12(c) and Fig. 12(d) a e measu ed. Fig. 12(c) shows and Fig. 12(d) shows
. In Fig. 12(c) and Fig. 12(d) he la ges measu ed ansconduc ance is
, while he minimum is . No e ha now he OTA inpu ange is
main ained cons an . As a esul , he OTA beha es almos linea ly om o
which means ha low dis o ion sinusoids o peak- o-peak ampli ude can be ob ained wi h
he VCO o Fig. 10 o he whole equency ange, as can be seen in Fig. 11.
Fig. 11: Measu ed VCO ou pu s o minimum (73.94mHz) and maximum (1.015MHz) equencies.
Ve ical scale is 50mV/di and ho izon al scales a e 2s/di o le ace and 200ns/di o igh ace.
C10pF=
gm-C
Iss
Iss
200mV
Iss
VG2
VG2
min 73.96mHz=
max 1.015MHz=
gm
ISS
Iou Vin
( ) /ISS
Vin V+V-
–=
ISS
VG2
I'ou Vin
( ) /gm
gm
Vin 0=
ISS
gm
ISS
nUT
gm30.0µA/V=
gm60.4pA/V=
ISS
gm
VG2
Iou Vin
( ) /Iou
max
I'ou Vin
( ) /gm
gm30.0µA/V=
gm40.0pA/V=
100mV–
100mV+
200mV

Oc obe 20, 1998 5:14 pm 17
IX. Conclusions
Two new ac i e-inpu cu en mi o s uc u es a e in oduced. The no el y esides in ha he
ac i e ampli ie d i es ansis o sou ces ins ead o ga es. This allows he ampli ie o be connec ed in
a nega i e eedback loop con igu a ion, ins ead o posi i e. The i s p oposed opology migh equi e
compensa ion, while he second does no need i . Bo h opologies beha e much be e om a s abili y
poin o iew han he con en ional ac i e inpu cu en mi o . This is because he ampli ie ou pu is
connec ed o a low impedance node. The consequence is ha he mi o s emain s able o a bi a ily
small ope a ion cu en s, hus allowing cu en anges o many decades. Expe imen al measu emen s
e eal ha he cu en s in ol ed can a y o e 9 decades, and ha he gain o hese cu en mi o s
can be con inuously uned o e 11 decades while main aining 1% linea i y e o in he mi o ing
ope a ion. The mi o s can be used ei he wi h hei ansis o s biased as MOS o as CMOS
compa ible la e al bipola de ices. Expe imen al esul s ha e been p o ided. As an applica ion
example a sinusoidal VCO has been ab ica ed and es ed. I s equency could be con inuously
uned o o e 7 decades h ough a single con ol ol age. To ou knowledge his has ne e been
achie ed be o e o CMOS sinusoidal VCOs.
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Vin (Vol s)
gm (No malized)
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Vin (Vol s)
Iou (No malized)
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Vin (Vol s)
Iou (No malized)
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Vin (Vol s)
gm (No malized)
(a) (b)
(c) (d)
Fig. 12: Expe imen ally measu ed dependence o OTA linea inpu ange on ansconduc ance uning. Fo
di e en ial pai ail bias cu en (ISS) uning, linea ange dec eases as ansconduc ance dec eases: (a)
no malized OTA ou pu cu en (Iou /ISS) as a unc ion o di e en ial inpu ol age, (b) no malized i s
de i a i e o p e ious cu e. Fo uning h ough he op Topology-1 cu en mi o s: (c) no malized OTA
ou pu cu en , (d) no malized i s de i a i e o p e ious cu e.
gm-C
Oc obe 20, 1998 5:14 pm 18
X. Acknowledgemen s
This wo k was pa ially suppo ed by an ONR Mul idisciplina y Uni e si y Resea ch Ini ia i e
(MURI) o Au oma ed Vision and Sensing Sys ems N00014-95-1-0409.
XI. Re e ences
[1] Ca e Mead, Analog VLSI and Neu al Sys ems, Addison-Wesley, 1989.
[2] A. G. And eou, R. C. Mei zle , K. S ohbehn, and K. A. Boahen, “Analog VLSI Neu omo phic
Image Acquisi ion and P e-p ocessing Sys ems,” Neu al Ne wo ks, ol. 8, No. 7/8, pp. 1323-
1347, 1995.
[3] D. G. Nai n and A. T. Salama, “A Ra io-Independen Algo i hmic Analog- o-Digi al Con e e
Combining Cu en Mode and Dynamic Techniques,” IEEE T ans. Ci c. & Sys ., ol. 37, No. 3,
pp. 319-325, Ma ch 1990.
[4] T. Se ano and B. Lina es-Ba anco, “The Ac i e-Inpu Regula ed-Cascode Cu en Mi o ,”
IEEE T ans. Ci c. & Sys . Pa I, ol. 41, No. 6, pp. 464-467, June 1994.
[5] P. E. Allen and D. R. Holbe g, CMOS Analog Design, Hol -Rineha and Wins on Inc., New
Yo k 1987.
[6] Be nabé Lina es-Ba anco, Angel Rod íguez-Vázquez, José L. Hue as, and Edga Sánchez-
Sinencio, “On he Gene a ion Design and Tuning o OTA-C High F equency Sinusoidal
Oscilla o s,” IEE P oceedings-Pa G, Ci cui s De ices and Sys ems, ol. 139, No. 5, pp. 557-
568, Oc obe 1992.
[7] M. G. Deg auwe, J. Rijmenan s, E. A. Vi oz, and H. J. De Man, “Adap i e Biasing CMOS
Ampli ie s,” IEEE Jou nal o solid-S a e Ci cui s, ol. SC-17, No. 3, pp. 522-528, June 1982.
[8] Y. P. Tsi idis, Ope a ion and Modeling o he MOS T ansis o , McG aw-Hill, New-Yo k, 1987.
[9] X. A egui , CMOS Compa ible Bipola La e al T ansis o , PhD Disse a ion, EPFL,
Swi ze land, 1985.