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Active
Filter
Design Using Operational
Transconductance Amplifiers A Tutorial
Randall L. Geiger and
Edgar
Sânchez-Sinencio
Abstract
Basic properties
of the
Operational
Transconductance
Amplifier
OTA)
discussed.
Applications of the OTA in voltage-contro lled amplifiers,
and impedances are
presented.
A
versatile family
of voltage-
filter
sections suitable
for systematic design requirements is de
The total
number
of components used in these circuits is small,
d the design equations and voltage-co ntrol chara cteristics are attractive.
as well as practical
considerations
of OTA
based
filters using
available bipolar
OTAs are
discussed.
Applications of OTAs
continuous-time
monolithic
filters
are considered.
Introduction
The conventional operational amplifier (op amp) is
filter literature. For design purposes, the as
o °
Rin =
o o
o = 0) is generally made, and large amounts of
pendent of the gain of the op amp. A host of
ilter designs have evolved following this ap
has also become apparent, however , that
a few nondemanding applicat ions), and con
adjusting the filter characteri stics do not exist.
With the realization that the B JT and MOS F E T are
current, or transresistance) in place of a voltage
c active device in a filter structure?
This question is currently difficult to answer for
re is a near void in the literature
active filter structures employing the alternative
3080
and
M
13600
and transresistance amplifiers such as the
M 3 900
[ l ] - [ 5 ] .
Comparisons of some characteris
of these amplifiers were recently discussed by
In this paper, basic first- and second-order struc
operational
transconductance amplifier:
OTA)
are discussed. It is shown that these structures offer
improvements in design simplicity and program-
mability when compared to op amp based structures
as well as reduced component count.
Many of the basic OTA based structures use only
OTAs and capacitors and, hence, are attractive for in
tegration. Component count of these structures is
often very low (e.g., second-order biquadratic filters
can
be constructed with two OTAs and two capaci
tors) when compared to V C V S designs. Convenient
internal or external voltage or current control of filter
characteristics is attainable with these designs. They
are attractive for frequency referenced (e.g., master/
slave)
applications. Several groups have recently uti
lized OTAs in continuous-time monolithic filter struc
tures
[ 2 8 ] - [ 4 0 ] .
From a practical viewpoint, the high-frequency
performance of discrete bipolar
O TA s ,
such as the
CA
3 0 8 0 ,
is quite good. The transconductance gain,
g
m
, can be varied over several decades by adjusting an
external dc bias current, J
A B C
. The major limitation of
existing OTAs is the restricted differential
input
volt
age swing required to maintain lineari ty [5]. For the
CA 3 0 8 0 , it is limited to about 30 mV p-p to maintain a
reasonable degree of linearity.
Although feedback structures in which the sen
sitivity of the filter parameters are reduced (as is the
goal in op amp based filter design) will be discussed,
major emphasis will be placed upon those structures
in which the standard filter parameters of interest are
directly proportional to
g
m
of the OTA. Thus , the
g
m
will be a design parameter much as are resistors and
capacitors.
S i n c e the transconductance gain of the
OTA is assumed proportional to an external dc bias
current, external control of the filter parameters via
the bias current can be obtained.
Most exist ing work on OTA based filter design ap
proached the problem by either concentrating
upon
applying feedback to make the filter characteristics
independent of the transconductance gain or modify
ing existing op amp structures by the inclusion of
some additional passive components and
O TA s .
In ei
ther
case,
the circuits were typically component in
tense and cumbersome to tune. Some of the earlier
works are listed in the
Re f s . [ 6 ] - [ 1 6 ] .
Some of the
most practical circuits can be found in the manufac
turer s application notes
[ 3 ] - [ 5 ] .
OTA Model
The
symbol used for the OTA is shown in Fig. 1,
along with the ideal small signal equivalent circuit.
8755-3996/85/0300-0020$ .00 © 1985
IEEE
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Fig. 1 OTA. (a) Symbol, (b) Equivale nt circuit of
ideal
OTA.
Th e
transconductance gain, g
m
, is assum ed propor
tional* to 7 A B C . The proportionality constant
h
is de
pendent
upon
temperature , d evice geometry, and the
process [2].
gm = WA BC (1)
Th e
output
current is given by
h = gm(v + - ν - )
(2)
As shown in the mod el, the input and output imped
ances in the model assume ideal values of infinity.
Current control of the transconductance gain can be
directly obtained with control of J
A B C
.
Since
tech
niques abound for creating a current proportional to a
given voltage , voltage contro l of the O TA gain can
also be attained throu gh the
J A B C
input. Throughout
this paper, when reference is made to either the cur
rent o r voltage con trollabilit y of OTA bas ed circuits , it
is
assumed to be attained via control of g
m
by 7
A B C
.
Basic OTA Building Blocks
Some of the basi c OTA buildin g bloc ks [6] are intro
duced in this section. A
brief
discussion about these
circuits follows.
Voltage amplifiers using OTAs are sho wn in Fig. 2,
along with voltage gain and
output
impedance ex
pressions. T he basic inverting and noninvertin g con
figurations of
Figs.
2a and 2b have a voltage gain
directly
proportional to g
m /
which makes current
(vol
tage) control of the gain via J
A B C
straightforward. Fur
thermore, observe that a differential amplifier can be
easily obtained by using both input terminals of the
OTA
in
Figs.
2a or 2b. The major limitation of these
circuits
is the relatively high
output
impedance.
I A B C
Z 0 R L
(a)
V
(b)
(c)
z
o ' °
(d)
Re
8m 1—
Ï
abc
V|
i
gm R
ι
Ri+R 2
0
(e)
-oVo
Vo.Q» R|»*t>
Vi i+g
m
R,
7 . R|+
R
2
* °
l+QmRi
(f)
*A
linear
dependence on bias
current
is
typically obtained
for
bipolar
OTAs
and MOS configurations operating in weak inversion.
MOS structures operating in the
saturation
region typically exhibit
a quadratic dependence on 7A B C .
Fig. 2 Voltage
amplifiers,
(a) Basic
inverting,
(b) Basic
noninverting.
(c) Feedback amplifier, (d) Noninverting feedback amplifier, (e) Buf
fered amplifier, (f) Buffered VCVC
feedback,
(g) All OTA amplifiers.
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A
voltage buffer, such as used in F igs . 2c and 2d, is
output impedance.* Al
not the same. The performance differences are due
effects of parasitics in the
cir
Specifically, the parasitic output capacitance of
in Fig. 2c, along with instrumen tation para
parallel the resistor
R
L
in discrete component
thus
causing a
roll-off
in the frequency re
output capacitance of the OTA is connected
the null port of an op amp and
thus
has negli
effects when the op amp functions properly.
instrum entation parasitics will typically ap
output of the op amp and
not have a major effect on the performance.
with conventional amplifier design using resis
bandwidth
of these
warrants consideration. For the circuits of
2c and 2d , the major factor limiting the band
is generally the finite gain
bandwidth
product
the op amps . If the op amps are modele d by the
roll-off model, A(s) =
GB/s,
and
are assumed ideal, it follows that the band
of the circuits of Fig. 2c and Fig. 2d is GB,
penden t of the voltage gain of the amplifier.
can be contrasted to the bandw idths of GBl Κ
d
G B / 1
+
Κ
for the basic single op amp noninvert
Κ
and
-K,
Note that the circuits of F igs . 2a and 2b differ only
labeling of the " + " and "
—
terminals. In all
+ " and " - " t erminals of the OTA will result on ly in
g
m
coefficient in any equat ion
The
circuits of F igs . 2e and 2f are feedback struc
g
m
.
By interchanging the
and - termina ls of the OTA , very large gains can be
g
m
R
1
approa ches 1 (as Z
0
approaches in
Gain is nonlinearly related to
g
m
.
Control
g
m
is reduced in these structures wh en com
F igs . 2a and 2b. If compo
made essentially indepe ndent of
g
m
(as in the con
output
impedances can be made
small.
The
amplifier of Fig. 2g is attractive since it contai ns
*An alternative to the op amp buffer is the Darlington pair,
is included in the same package in some commercial OTAs
3 0 9 4 , LM 13600) .
tained with either
g
ml
or
g
ml
.
The total adjustment
range of the gain of this structure is double (in dB)
that attainable with the single OTA structures consid
ered in F igs . 2a and 2b. Furthermor e, if both OTAs
are in the same chip, the variations with temperature
of
the
g
m
s
are cancell ed.
Several
standard controlled impedance elements
are shown in Fig. 3, along with the
input
impedance
expression. These controlled impedances can be used
in place of passive counterparts (when applicable) in
active RC
structures to attain voltage control of the
filter
characteristics or as building blocks in OTA
structures.
Th e
circuit of Fig. 3a is a grounded Voltage Variable
Resistor ( W R ) . The circuit of Fig. 3b behaves as a
floating W R , provided
g
ml
and
g
m2
are matched . If a
mismatch occurs, the structure can be modeled with
a floating W R be twee n termina ls 1 and 2 of value
g
mV
along with a voltage depen dent current source of
value (g
ml
-g
m2
)
Vi
driving node 2.
The
circuit of Fig. 3c acts as a scaled W R . Higher
impedances are possible
than
with the simple struc
ture
of Fig. 3a, at the expense of the additional re
sistors.
A voltage variable impedance inverter is shown in
Fig. 3d. Note the doubling of the adjus tment range of
this circuit, as with the amplifier of
Fig.
2g. Of special
interest is the case where this circuit is loaded with a
capacitor. In this case, a synthetic inductor is ob
tained. T he doubling of the adjustment range is
par
ticularly attractive for the synthetic inductor since
cutoff frequencies in active filter structures generally
involve inductor values raised to the 1/2 power. By
making
g
ml
= g
m2
and adjusting both simultaneously,
first-order rather
than
quadratic control of cutoff fre
quencies is possible.
A floating impedan ce inverter is shown in Fig. 3e.
Note that it is necessary to match
g
m2
and
g
m3
for
proper operation. The circuit of Fig. 3f serves as an
impedance multiplier. That of Fig. 3g behaves as a
super inductor and that of Fig. 3h as a
FDNR.
First-Order Filter Structures
A
voltage variable integrator structure with a differ
ential
input
is shown in Fig. 4a. The integrator serves
as the basic building block in many filter st ruct ures .
Two different lossy integrators (first-order lowpass
fil
ters)
are shown in F igs . 4b and 4c. The circuit of Fig.
4b has a loss that is fixed by the
RC
product and a
gain controllable by
g
m
.
The circuit of Fig. 4c offers
considerably more flexibility. The pole frequency can
be adjusted by
g
m2
(interchanging the
input
terminals
of
OTA 2 actua lly allows the pole to ente r the right
hal f plane), and the dc gain can be subsequently ad
justed by
g
ml
.
It shou ld be noted that the struc ture of
Fig.
4c cont ains no resisto rs and can be obtained from
the circuit of Fig. 4b by replacing the resistor
R
with
the controlled impedance of Fig. 3a. Another lossy
integrator without adjustable gain but with adjustable
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Π
8m
α )
9 m
'•HE
(c)
1
Γ Π |
I
z L
9 m
2
h
Z
:
ni| m L
~2Τ
Χ
gm
Zin©
(b)
χ
Ι Ϊ Ι |
(d)
r
3 m 2
3
m 3
iti4
7 Z
L
g
m39m4
z
iB
-
s
2
C | C 2
(f)
Z « n 2 C | C 2 g
g
ι
^SUPER
INDUCTOR
(g)
(h)
Fig.
3 Controlled impedan ce elements. a) Single-ended voltage variable resistor VVR). b) Floating VVR. c)
Scaled
VVR. id) Voltage variable
impedance inverter e) Voltage variable floating impedance f) Impedan ce multiplier g) Super inductor h)
FDNR.
pole location and a very simple structure is shown in
ig 5a.
When
designing cascaded integrator-based filter
structures it may be the case that the
input
imped
ance
to some stages is not infinite. If that is the
case
a unity gain buffer would be required for coup
ling since the output impedances of all integrators in
ig 4 are nonz ero . Note however that no buffer is
needed for the cascade of any of the integrators of
ig 4 since the input impedance to each circuit is
ideally
infinite.
First-order filters can be readily built using OTAs.
Considerable flexibility in controlling those specific
filter
characteristics that are usually of interest is pos
sible with these struct ures. Several first-order voltage-
controlled
filters are show n in Fig. 5 and a functional
plot of the transfer charact eristics as a function of the
transconductance gains is shown in Fig. 6.
Vi ,
is An.
V | , - V |
2
sC
(o)
Vi
ViO-
c)
3
V
0
C Î
f R o
Vq 9mR
Vj s R C +
(b)
V
0
Qm
V |
sC +
g
m 2
Fig. 4 Integrator structures, a) Simple, b) Lossy, c) Adjustable.
2 3
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1985
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c
2
VjO-
» m 2
τ
(h)
a
Qm\ s C 2
V|
8 s C
|
+ C
2
) + g
m
+ g
m 2
( i )
5
First-order voltage-controlled filters, (a) Lowpass, fixed dc gain pole adjustable, (b) Lowpass fixed pole, adjustable dc gain, (c) Highpass, fixed high-
frequency gain, adjustable pole, (d)
Shelving
equalizer, fixed high-frequency gain, fixed pole, adjustable zero, (e)
Shelving
equalizer, fixed high-
frequency gain, fixed zero, adjustable pole, (f) Lowpass filter adjustable pole and zero, fixed ration, (g)
Shelving
equalizer, independently adjustable
pole and zero, (h) Lowpass or highpass filter, adjustable zero and pole, fixed ratio or independent adjustment, (i) Phase shifter, adjustable with gm.
4
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6 Transfer characteristics for first-order structures of Fig. 5. (a) Circuit of Fig. 5a. (b) Circuit of Fig. 5b. (c) Circuit of Fig. 5c. (d) Circuit of Fig. 5d.
(e) Circuit of Fig. 5e. (f) Circuit of Fig. 5f. (g) Circuit of Fig. 5g. (h) Circuit of Fig. 5h. (i) Circuit of Fig. 5i.
Circuit
Type
Input
Conditions
Transfer
Function
Κ gml = gml = gm
«Ό Q
w
0
Adjustable
Lowpass
w
0
Adjustable
Bandpass
w 0 Adjustable
Highpass
w 0
Adjustable
Notch
Vi
=
VA
V B
and
Vc Grounded
Vi =
v
B
V
A
and V
G
Grounded
Vi = V
c
V
A
and Vß Grounded
Vi
v
A
v
c
V B Grounded
gmlgml
S
2 C C 2 + SCig
m2
+ gmlgml
y Q c 2
SCigml
gm
S
2
Ci C
2
+ SCig
m2
+ gmlgml
y c , c
2
S
2
Ci C
2
gm
S
2 C i C 2 + SCigm2 + gmlgml
y c , c
2
S
2 C C 2 + gmlgml
gm
S 2Ci C 2 SCxgml + gmlgml
c ,
IL
c ,
C i
6
Table Transfer functions for biquadratic structure of Fig. 7a.
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-ο Vo2
±
c
2
*>v r
( c )
sense that only four components are needed to obtain
second-order transfer functions. The
output
voltage,
V
0
,
is given by the expression
s^QQVc +
sC
lgm2
V
B
+
s ^ Q + s C m̂ 2 + gmlgm2
(4)
The
transfer function for the specific excitat ions at
VAf Vb
a R
d
Vc
are listed in the Table. Note that for
8mi
=
8mi
= 8m > the lowpa ss, bandp ass, highpass,
and notch versions of this circuit all behave as ω
0
ad
justable circuits with fixed pole Q's. The pole Q's are
determ ined by the capacitor ratio, which can be accu
rately maintained in monolithic designs . It is interest
ing to note that the zeros of the notch circuit also
move in a constant-
Q
(i.e. along the
jw
axis) manner
with the poles, as
g
m is adjusted.
Occasionally, it is desirable to have circuits in which
ω 0 an d
Q
of the poles can be independent ly adjusted.
Two
circuits with these characteristics are shown in
Fig. 7b [18], [19] , [24] and Fig. 7c [18], [24]. The out
put voltages for these circuits are, respectively,
_ s
2
C
x
C
2
V
c + sClgm2VB +
8τ η \8η ΰ Υ A
s
2
C,C
2 + sC^g^R + g
and
_ s2CxC2Vc
+ sC
x
g
m2
V
B
+ g
ml
g
m2
V
A
s ^ Q +
sg^C, + g
(5)
(6)
The
circuits of F igs . 7b and 7c can be also used to
implement lowpass, bandpass, highpass, and notch
transfer functi ons through the proper selection of the
inputs
as for the circuit of Fig. 7a.
In the circuit of Fig. 7b, the expressions for ω
0
and
Q of the poles of the circuit are given by
8m\8m2
Q C
2
and
Q =
ι
g
m3
R
V
c
l g
Sml
(7)
(8)
The
poles can be moved in a constant- Q manner if
gm3
is
fixed, and if
g
ml
= g
m2
= g
m is adjusted; where as
movement in a constant ω
0
manner is attainable if
g
m3
is adjusted when
g
ml an d
g
m2 remain constant. The
independe nt adjustment of ω
0
and
Q
is apparent.
For the circuit of
F ig .
7c, the ex pression s for ω
0
and
Q of the poles become
8ml8m2
Q C
2
n = ι / Q \J g m l g m 2
u / c
J g
m3
(9)
(10)
Fig. 7
Second-order
filter structures.
ω 0 can be adjusted linearly with
g
ml
= g
m2
= g
m and
g
m3
const ant. Suc h movem ent is often termed con
stant
bandwidth
movement. If
g
mV
g
m2
,
and
g
m3 are
adjusted simultaneously, constant-Q pole movement
is possible . Adjusting
g
m3 (for
Q >
Vi) moves the poles
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ous circuits has been split to allow for adjusting the
pole-zero ratio. The transfer function of the circuit is
given by
Fig. 8 Elliptic
filter structure.
jw axis in the
The circuit of Fig. 7d has an output given by
VçC^s
2 +
Vßg^sC,
+ g
ml
g
m2
V
A
s ^ Q + s C ^ m 3 + g
ml m2
e ω
0
and Q of the poles are, respectively,
ml m2
Qc2
Q
=
8m3
(11)
(12)
(13)
s term in the nu
equals that in the denominator, adjustment
of
version of this circuit with g ml = gm2 = gm
result in a constant bandwidth, constant gain
For monolithic structures, it may prove useful to
the resistor in Fig. 7b with the OTA structure
f Fig. 3a. Likewise, if the bandwidth adjustment
g
m3
is not nee ded , it may be desirab le to replace
TA shown in
Fig.
7c with a fixed resis tor in
applications.
Phase equalizers are also possible with the struc
Fig.
7. For example, interchanging the
+ and " - " terminals of the first two OTAs in Fig.
, setting VA = VB = Vc = Vt, and making gml = gm2
g
m3
= g
m
results in a second-order g
m
adjustable
The circuit of Fig. 8 has both poles and zeros that
n
be adjusted simultaneously in a constant-Q man
2 in the previ-
Ci
c 2 + c
3
S
+
gml/ClCl
s
2
+ sgm2/(C 2 + C3 ) +
gmlgJC^C,
+ C3 )
(14)
This circuit has applications in higher-order voltage-
controlled
elliptic filters. For higher-order structures
obtained by cascading these second-order blocks, all
g
m
s would be made equal and adjusted simultane
ously.
Buffering between stages using a standard
unity gain buffer is required to prevent interstage
loading. Modifications of the other circuits in
Fig.
7 to
obtain ω 0 and Q adjustable features is also possible.
Although the ratio of the zero location to pole location
can
be controlled with the C 2 /C 3 ratio in discrete de
signs, this may pose some problems in monolithic
structures. One convenient way to control the pole-
zero ratio is to insert the voltage-controlled amplifier
of Fig. 2g between the points χ and x ' in Fig. 8 and
use the transconductance gain of either of these addi
tional OTAs as the c ontrol variable.
The final second-order structure considered here is
the general biquad of Fig. 9. The output for this cir
cuit is given by
_
s
2
C C
2
y
c
+ sCxgm±vB + gm2gm5vA
Smlgml
(15)
The potential for tuning the ω 0 and Q for both the
poles and zeros (when V, = V
A
= V
B
= V
c
) to any
desired value should be apparent. Although some
what co mponen t inte nse, it can be argued that if there
Fig.
9
General
biquadratic
structure.
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is
to be capability for completely arbitrary location of
a
pair of poles and a pair of zeros via adjustment of
the transconductance gain of the OTA, then at least
4
degrees of freedom and, hen ce, 4 OTAs are re
quired. This circuit uses on ly one more than the mini
mum The capability for various types of pole and/or
zero movement through the simultan eous adjustment
of
two or more of the transc onduc tance gains should
also
be apparent. Many other biquadratic structures,
some of which
offer
more
flexibility
at the expense of
additional complexity, also exist but are not discussed
here.
Emphasis in this section has been placed entirely
upon
second-order structures in which the desired
filter characteristics depend directly
upon
the trans
conductance gain of the OTA. Very simple structures
in whic h the filter characte risti cs are adjustab le
through
the parameter g
m
resulted. As stated in the
introduction, gm is readily con trollable by a dc bias
current over a wide range of values, thus making
these circuits directly applicable to voltage-controlled
applications. Several of the more recent works on
OTA
applications [ 1 8 ] - [ 2 4 ] have followed this ap
proach. Most of the earlier works [ 7 ] - [ 1 6 ] and the
cir
cuits presen ted in the manufacturer's application not es
[ 3 ] - [ 5 ] concentrated upon topologies in which the fil
ter characteristic s are independe nt or only mildly de
pendent upon the transc onducta nce gain. Most of
these structures are very complicated, very compo
nent-intense, and require tuning algorithms that are
unwieldy. Alternatives to these earlier designs using
conventional operational amplifiers have proven to be
much better.
Practical
Considerations
Although all circuits presented up to this point in
this pape r are pract ical with ideal opera tional trans
conducta nce amplifiers, existing discrete OTAs are far
from ideal. As menti oned in the introduction, the
Fig. 10 Signal conditioner for OTAs.
M A R C H 1985
Fig.
11
Macromodel
of
bias current port
on
bipolar
OTA.
major
limiting factor with commercially available
OTAs is the limited differential input voltage swing.
Recent activity in the literature has concentrated
upon
designing OTAs with improved input character
istics [ 2 7 ] - [ 2 8 ] . Signifi cant improvements in perfor
mance over what is currently available with discrete
OTAs have bee n demonst rated. An alternative is to
use voltage attenuators and buffers at the
input
of ex
isting
OTAs.
This technique is often suggested in the
manufacturer's application note s and is illustrated in
Fig.
10. This techniq ue can be used to obtain reason
able signal swings with all circuits discussed up to
this point. Although such circuits are useful, a rather
high price is paid for this modification. First, the
cir
cuit requires many more components. Second, the
finite
bandwidth of the op amps will limit the
fre
quenc y respo nse of the OTA structures. Finally, the
attenuation of the input signal to the OTA causes a
serious loss in dynamic range. From a topological
point of view, some OTA based structures are inher
ently more susceptible to differential voltage limita
tions than others. This parallels the concern for op
amp based active RC and switched-capacitor struc
tures that the signal amplitudes at the output of inter
nal op amps assume acceptable values. These consid
erations become more serious for high Q and high
dynamic range applications.
A
macro model of the bias current ( JA B C )
input
port
of
a typical bipolar OTA is shown in
Fig.
11 . This actu
ally forms part of an internal current mirror that is
discussed later. Several schemes for controlling the
current /
A B C
and, thus, the g
m
of the OTA by an exter
nal control voltage, Vc, are sho wn in Fig. 12. The first
circuit is the simplest but is very sensitive to small
changes of V
c
as V
c
approaches .6v + V . In the sec
ond circuit, the control voltage is referenced to zero,
but the small V c is sensitive to mismatches between
the B-Ε voltage of the transistor and the forward di
ode voltage drop. In the circuit of Fig. 12c , the control
voltage is also refe renced to ground and is not depen
dent
upon
the matching or cancellation of voltages
across
external forward biased pn junctions. The
zener diode is used to maintain the common mode
voltage at a reasonable level. The frequency response
of
the op amp is not of concern here since it is used
only in the dc control path. It should be noted that the
29
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8/20/2019 OTA Structures2
11/13
Fig 12 Schemes for obtaining voltage control with the OTA.
i < 4
I ABC.
1
lABCn
Rn
1
b)
ÏABC
ABC
VRET
F/g 23 Schemes for
simultaneous
g
m adjustment
I r e f
J ABC I I
ABC?
l A B C n
<
6V-
Fig.
Ï 4 Smg / e
input-multiple output
bias
current
generator for
monolithic applications
Fig 15 g
m
attenuator
V c for all
shown in Fig. 12. Since 7 A B C can typically be
over several decades all schemes will be
V c toward the low
I A B C range. Logarithmic amplifiers
I
A B C with an external control
f the wide adjustmen t range of 7
A B C
is to be
utilized.
Man y of the filter circuits discusse d in the previous
of this paper require the simultaneous ad-
gm s. Several schemes for achiev-
n in Fig. 13. In the first circuit it is
to adjust the gm s by trimming the resistors for a
gm. The circuit is quite sens itive to the slight dif-
ferences
in the voltage V d of Fig. 11a for small values
of
7 A B C . The circuit of Fig. 13b again has V c referenced
to ground and is essentially indep enden t of the match-
ing of Vd for the individual
OTAs.
The scheme of Fig.
13 c is useful if an external single package pnp current
mirror with η outputs is available. A discrete compo
nent version of this mirror would not be practical.
For
integrated circuit applications, the amplifier
bias currents of several OTAs are particularly easy
to match and control. For monolithic applications,
the simultaneous adjustment of the gain of a large
number of OTAs with a single dc bias current can be
easily
attained by using a single input-multiple out
put current mirror such as is show n in Fig. 14. This
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12/13
structure actually
replaces
the bias current mirrors on
each of the OTAs . The transcond uctance gains can be
ratioed, if desired, by correspondingly ratioing the
emitter areas (or
width
length ratio for MOS struc
tures) in the outputs of the current mirror.
With conventional operational amplifiers, the slew
rate, input impedance, output impedance, and maxi
mum output current are essentially fixed at the de
sign stage. For OTAs, it is genera lly the case that these
parameters are either proportional or inversely pro
portional to
I
A B C
.
Thus adjusting g
m
via 7
A B C
causes all
of these parasitic parameters to change accordingly.
Although the user shou ld be cognizant of the c hanges
in these parameters, the problems they present
are manageable. The output capacitance of an OTA
does cause concern at low
output
currents and high
frequencies.
Much as in the design of conventional op amp
based circuits, the designer must allow for a dc bias
current path for both input terminals of the OTA. Al
though the amplifier of Fig. 15 serves as an effective
g
m
attenuator , which will prove useful in some appli
cations, the circuit is useless since the required
input
bias current will cause an accumulation of charge on
the capacitors and eve ntual sa turation of the OTA.
The
reader should be cautioned that more compli
cated circuits with the same problem are suggested in
the literature [17].
Numerous nonlinear applications of OTA struc
tures exist . Suffice it to say that s ince the amplif ier
bias current , 7
A B C
, can be considered as a third signal
input, simple multipliers , modulators, and a host of
other nonlinear circuits are possible. The reader is
referred to the application notes for a discussion
of some of the nonlinear applications. Some of the
structures that use only OTAs and capac itors show
promise for monolithic applications in MOS or bi
polar processes. The circuits should offer high-
frequency continuous-time capabilities. Either exter
nal voltage-control or an internal reference circuit to
compensate for process and temperature variations
will be necessary to make these circuits practical in
demanding applications.
Finally,
it should be noted that some of the filter
structures presented earlier in this paper have a non-
infinite
input
impedance, and that the
output
imped
ance is generally quite high. Cascading of such struc
tures will require interstage buffer amplifiers, which
will tend to degrade the bandwidth of the overall filter
structures.
Output
buffers are also generally required
to drive external loads.
Conclusions
A group
of voltage-contro lled circuits using the
OTA as the basic active element have been presen ted.
The
chara cteri stics of thes e circuits are adjusted with
the externally accessible dc amplifier bias current .
Most of these circuits utilize a very small number
of components. Applications include amplifiers,
controlled impedances, and filters. Higher-order
continuous-time voltage-controlled filters such as the
common Butterworth, Chebyschev, and Elliptic types
can be obtained. In addition to the voltage-control
characteri stics , the OTA base d circuits show promise
for
high-frequency applications where conventional
op amp based circuits become
bandwidth
limited.
The
major factor limiting the perfo rmance of OTA
based filters using commercially available OTAs is the
severely limited differential
input
voltage capability
inherent with conventional differential amplifier in
put stage s. Recent research results suggested signifi
cant improvements in the
input
characteristics of
OTAs
can be attained [ 2 7 ] - [ 2 8 ] .
References
[1 ] H. A. Wittling er, Applicatio ns of the CA308 0 and CA308 0A
High Performance Operational Transconduct ance Ampli
fiers, RCA Application Note 1CAN-6668.
[2 ]
C. F. Wheat ley and H . A. Wittlinger, OTA Obsoletes OR
AMP ,
P. Nat. Econ. Conf. pp .
1 5 2 - 1 5 7 ,
Dec. 1969.
[3 ] RCA Electronic Compon ents , Linear Integrated Circuits, Model
CA306 0 :
Data File 404, Mar. 1970.
[4 ] National Semiconductor, Linear Applications Handbook, 1980.
[5 ] RCA Solid-State Division, Data Book, Linear Integrated Circuits,
File No. 47 5, Mar. 1975 .
[6 ] M. Bialko and R. W. New comb , Generati on of All Finite Lin
ea r Circuits Using the Integrated DVCCS, IEEE
Trans, on Cir
cuit Theory,
vol. CT-18 , pp . 7 3 3 - 7 3 6 , Nov. 1971.
[7 ] M. Bialko, W. Sienko, and R. W. New comb, Active Synthesis
Using the DVCCS/DVCVS, Int. J. of Circuits Theory App.,
vol. 2, pp. 2 3 - 2 8 , 1974.
[8 ] S.
Franco ,
Use Transconduc tance Amplifier to Make Pro
grammable Active
Fi l ters ,
Electronic Design,
vol. 24, pp. 9 8 -
101 ,
Sept. 1976.
[9 ] F. Atiya, A. Soliman, and T. Saadawi, Active RC Bandp ass
an d Low pass Filters Using the DVCC S/DVCVS, Electron.
Lett. vol. 12, pp. 3 6 0 - 3 6 1 , July 1976.
[10] F. Anda y, On the Analys is and Synthesis of Active Networ ks
Containing DVCCS/DVCVS, Proc.
IEEE,
pp .
3 7 5 - 3 7 6 ,
Mar.
1976 .
[11] F. S. Atiy a, A. M. Soliman, and T. N. Saadawi, Active RC
Nominum Phase Network Using the DVCCS/DVCVS, Proc.
IEEE,
vol. 65, pp.
1 6 0 6 - 1 6 0 7 ,
Nov. 1977.
[12] A. M. Soliman, A Gro und ed Inducta nce Simulation Using
the DVCCS/DVCVS, Proc.
IEEE,
vol. 66, pp.
10 8 9 - 1 0 9 1 ,
Sept. 1978.
[13]
R. Nandi, New Ideal Active Inductance and Frequency-
Depende nt Negative Resistance Using DVCCS/DVCVS: Ap
plications in Sinusoidal-Oscillator Realization, Electron. Lett.,
vol. 14, pp. 5 5 1 - 5 5 3 , Aug. 1978.
[14] I. M. Filanovsky and K. A. Str omsmoe , More Active-RC Fil
ters
Using DVCCS/DVCVS,
Electron.
Lett., vol. 15 pp. 46 6-
467 , Aug. 1979.
[15] D. Patrana bis and A. Paul, Floating Ideal Induc tor with One
DVCCS,
Electron. Lett., vol. 15, pp. 5 4 5 - 5 4 6 , Aug. 1979.
[16] T. Deliyannis, Active RC Filters Using an Operati onal Trans
conductance Amplifier and an Operational Amplifier, Int. J.
Circuit Theory Appl, vol. 8, pp. 3 9 - 5 4 , Jan. 1980.
[17] A. Urba s and J. Osiwski, High-F requ ency Realization of
C-OTA Second-Order Active Filters, Proc. IEEEIISCAS,
pp .
1 1 0 6 - 1 1 0 9 ,
1982.
[18] H. S. Malvar, Electronica lly Contr olled Active Filters with
Operational
Transc onduc tance Amplifiers, IEEE Trans. Cir
cuits
Syst., vol. CAS-29, pp. 3 3 3 - 3 3 6 , May 1982.
M A R C H 1985
31
-
8/20/2019 OTA Structures2
13/13
R. L. Geiger and J. Ferrell, Voltage Controlled Filter Design
Using Operational Transconductance Amplifiers, Proc.
IEEE/
ISCAS,
pp . 5 9 4 - 5 9 7 , May 1983.
A. R. Saha and R. Nandi, Integrable Tunable Sinusoid Os
cillator Using DVCCS, Electron.
Lett.,
vol. 19, pp.
7 4 5 - 7 4 6 ,
Sept. 1983.
G. M. Wierzba and S. Esmelioglu, 'Techniques for Designing
Enhanced-Gain-Bandwidth-Product Circuits, Proc.
26th Mid
west Symp. on Circuits and Syst.,
pp .
6 0 2 - 6 0 6 .
Aug. 1983.
R. W. Newcomb and S. T. Liu, A Voltage Tunable Active-R
Filter ,"
Proc.
IEEE/ISCAS,
pp .
4 0 9 - 4 1 2 ,
May 1984.
J. Hoyle and E. Sânchez-Sinencio, Sinusoidal Quadrature
OTA Oscillators, Proc.
27th Midwest Symp. on Circuits and
Syst.,
June 1984.
H. S. Malvar, Electronically Controlled Active Active-C Fil
ters
and Equalizers with Operational Transconductance Am
plifiers, IEEE
Trans. Circuits Syst.,
vol. CAS-3 1, pp.
6 4 5 - 6 4 9 ,
July
1984.
F. Krummenacher, High-Voltage Gain CMOS OTA for Micro-
power SC Filters,
Electron. Lett.,
vol. 17, pp.
1 6 0 - 1 6 2 ,
Feb.
1981.
M. G. Degrauwe, J. Rijmenants , E . A. Vittoz, and J. deMan,
Adaptive Biasing CMOS Amplifiers,
IEEE J. Solid-State Cir
cuits,
vol. SC-17, pp.
5 2 2 - 5 2 8 ,
June 1982.
K. D. Peterson and R. L. Geiger, CMOS OTA Struct ures with
Improved Linearity, Proc.
27th Midwest Symp. on Circuits and
Syst.,
June 1984.
A. N edungadi and T. R. Viswanathan, Design of Linear
CMOS Transconductance Elements, IEEE
Trans, on Circuits
an d
Syst.,
vol. CAS-3 1, pp.
8 9 1 - 8 9 4 ,
Oct. 1984.
K. S. Tan and P. R. Gray, Fully Integrated Analog Filters Using
Bipolar-JFET
Technology, IEEE
J. Solid-State Circuits,
vol.
SC-12, pp . 8 1 4 - 8 2 1 , Dec. 1978.
A. P. Nedungadi and P. E.
Allen,
A CMOS Integrator for
Continuous-Time Monolithic Filters, Proc.
IEEE/ISCAS,
vol.
2,
pp .
9 3 2 - 9 3 5 ,
May 1984.
G. Tröster and W. Langheinrich, Monolithic Cont inuous -
Time Analogue Filters in NMOS Technology,
Proc. IEEE/
ISCAS,
vol. 2, pp. 9 2 4 - 9 2 7 , May 1984.
H. Khorramab adi and P. R. Gray High-F requency CMOS
Continuous-Time
Fi l ter s ,"
Proc.
IEEE/ISCAS,
vol. 3, pp. 14 98 -
1501 ,
May 1984.
K. Fukahori, A Bipolar Voltage-Controll ed Turnable Filter,
IEEE ] Solid-State Circuits, vol. SC-16, pp. 7 2 9 - 7 3 7 , Dec. 1981.
K. W. Moulding, Fully Integrated Selectivity at
High
Fre
quency Using
Gyra tors ," IEEE Trans. Broadcast.
Telev.
Reg.,
vol.
BTR-19,
pp .
1 7 6 - 1 7 9 ,
Aug. 1973.
H. O. Voorman and A. Biesheuvel, An Electronic Gyrator,
IEEE ]
Solid-State Circuits,
vol. SC-7 pp.
4 6 9 - 4 7 4 ,
Dec. 1972.
K. W.
Moulding
and P. J Ranking, Experience with High-
Frequency
Gyrator Filters Including a New
Video
Delay-Line
IC , " Proc.
6th
European
Conf. on Circuit
Theory
and
Design,
pp. 9 5 - 9 8 , Sept. 1983.
J O. Voorman, W. H. A. Bruls, and J P.
Barth ,
Bipolar
In teg ra
tion of Analog Gyrator and Laguerre Type F ilters (Transcon-
d u c t a n c e - C a p a c i t o r Filters), Proc.
6th
European
Conf. on Cir
cuit
Theory and Design,
pp .
1 0 8 - 1 1 3 ,
Sept. 1983.
J O. Voorman, W. H. A. Brüls, and P. J
Barth ,
Integration of
Analog Filters in a Bipolar Process,
IEEE ] of Solid-State Cir
cuits,
vol. SC-17, pp.
7 1 3 - 7 2 2 ,
Aug. 1982.
K. W. Moulding, J R. Quarterly, P. J Rankin, R. S. Thom pson,
and G. A. Wilson, Gyrator Video Filter IC with Automatic
Tuning, IEEE
J
of Solid-State Circuits,
vol. SC-15 , pp . 9 6 3 - 9 6 8 ,
Dec. 1980.
V. W. Burgger, B.
J
Hosticka, and G. S. Moschytz, A Com
parison of Semiconductor Controlled Sources for the
Design
of Active RC Impedances,
Int. ] . of Circuit
Theory
and Appl.,
vol. 10, pp.
2 7 - 4 2 ,
1982.
Randall
L. Geiger Edgar Sânchez-Sinencio
Randall L. Geiger was born in Lexington, Nebraska, on May 17,
1949 .
He received the B.S. degree in electrical engineering and the
M.S.
degree in mathematics from the University of Nebraska, Lin
coln, in 1972 and 1973 , respectively. He received the Ph.D . degree
in electrical engineering from Colorado State University , Fort Col
lins, in 1977.
In 1977, Dr. Geiger joined the Faculty of the Department of Elec
trical
Engineering at Texas A&M Univers ity, College Station, and
current l y
holds the rank of Associate Professor. His present re
search
is in the areas of integrated circuit design and active circuits.
He received the Meril B. Reed Best Paper Award at the 1982 Mid
west Sympos ium on Circuits and Systems, served as Conference
C h a i r m a n at the 1983 UGIM conference, and is currently serving as
an Associate Editor for the
IEEE
Transactions
for Circuits and Systems.
Dr. Geiger is a member of Eta Kapp a Nu, Sigma Xi, Pi Mu Ep
silon, and Sigma Tau; he is also a Senior Member of the IEEE.
E d g a r Sânchez-Sinencio was born in Mexico City, Mexico, on
October 27, 1944. He received the degree in communications and
electronic engineering (profes sional degree) from the National
Polytechnic Institute of Mexico, Mexico City; the
M . S . E . E .
degree
from Stanford University, California; and the Ph. D. degree from
the University of Illinois at Champaign-Urbana, in 1966, 1970, and
1973 , respectively.
During his graduate studies, he was awarded with fellowships
from the United Nat ions Educational, Scientific, and Cultural Or
ganization; the Mexican Atomic Energy Commiss ion; and the Con-
sejo Nacional de Ciencia y Tecnologia of Mexico. From January
1965 to March 1967, he worked with the Mexican Atomic Energy
Commi ssion, as a Design Engineer. In April 1967 , he joined the
Petroleum Institute of Mexico, where he was associated with
the design of instrumentation equipment until August 1967. He
worked as a Research Assistant at the Coordinated Science
Labora
tory
at the University of Illinois from September 1971 to August
1973.
In 1974, Dr. Sânchez-Sinencio held an industrial post-doctoral
position with the Central Research Laboratories, Nippon Electric
Company, Ltd., Kawasaki,
J a p a n .
F r o m 1976 to 1983, he was the
Head of the Departm ent of Electronics at the Instituto Nacional
de Astrofisica, Optica y Electronica (INAOE), Puebla, Mexico.
Dr.
Sânchez-Sinencio was a Visiting Professor in the Departme nt of
Electrical Engineering at Texas A&M University during the ac a
demic years of 1 9 7 9 - 1 9 8 0 and
1 9 8 3 - 1 9 8 4 ,
w here he is currently a
Professor. He was the General Chairman of the 1983 26th Midwest
Symposium on Circuits and Systems . He is the coauthor of the
book Switched-Capacitor
Circuits
(Van Nostrand-Reinhold, 1984) . Dr.
Sânchez-Sinencio's present interests are in the areas of active filter
design,
solid-state circuits, and computer-aided circuit
design.
He
is a Senior Member of the
IEEE.
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