OTA Structures2

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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

0

I E E E C I R C U I T S AND D E V I C E S M A G A Z I N E


2/13

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.

M A R C H 1985

21


3/13

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

I E E E C I R C U I T S AN D D E V I C E S M A G A Z I N E

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4/13

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

M A R C H

1985


5/13

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

IEEE C IR C UIT S A ND DEV IC ES MA GA ZINE


6/13


7/13

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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C I R C U I T S A N D D E V I C E S M A G A Z I N E


8/13

-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

M A R C H 1985

27


9/13

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.

IEEE C IRCU ITS A N D D E V I C E S MA GA ZINE

8


10/13

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


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

I E E E C IR C U I T S A N D D E V I C E S M A G A Z I N E


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


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.

2

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OTA Structures2