Design of RC-active oscillators using composite amplifiers
Abstract
The design of composite opamp Wien-Bridge oscillators is systematically approached by using a general model including amplitude control issues. Two different design criteria are presented and their main features summarized. A general composite opamp topology from which a catalog of structures can be obtained in a systematic way is presented. Experimental data are included illustrating the performance of the proposed design criteria.
Full text
DESIGN
OF
RC-ACTIVE OSCILLATORS USING COMPOSITE AMPLIFIERS
B.
Pb ez-Ve d i,
J.L.
Hue as
and
A.
Rod iguez-Vhzquez
Dep . o Design o Analog Ci cui s, Cen o Nacional de Mic oelec 6nica, Se illa,
SPAIN
Abs ac
The design o composi e opam Wien-B idge
oscilla o s is sys ema ically app oac!ed by using
a
gene al model including ampli ude con ol issues.
Two
di e en design c i e ia a e p esen ed and hei
main ea u es summa ized.
A
gene al composi e
opamp opology is p esen ed om whe e
a
ca alog o
s uc u es can be ob ained in a sys ema ic way.
Expe imen al da a a e included illus a ing he
pe o mance o he p oposed design c i e ia.
In oduc ion
I
is well known ha he ini e gain-bandwid h
(GB) oduc o
o
e a ional ampli ie s (opamp)
deg ac es he high-Eequency beha io o ac i e RC
ci cui s. One o he solu ions p oposed in he
li e a u e is he use o ac i e compensa ion
echniques. Many pape s ha e deal wi h he opic o
p oposing ac i e-compensa ed ampli ie s (hence o h
called
composi e ampli ie s),
see o ins ance
[1,21,
and
a
sys ema ic s udy ha e been epo ed ecen ly [31.
Composi e ampli ie echniques a e no di ec ly
applicable o he design o sinusoidal oscilla o s.
Al hough some ci cui s uc u es ha e been 'us
p oposed [4-81, he e is
a
lack o sys ema ic, his jack
p e en ing om a meaning ul compa ison among he
epo ed solu ions,oand among hem and non-
compensa ed oscilla o s. Besides some app oaches a e
based on o e simpli ied linea models, which a e no
able
o
co ec ly explain da a measu ed on ac ual
p o o ypes.
In his communica ion we will unde ake a
s
s ema ic s udy o he use o composi e ampli ie s o
ie Wien-B idge amil o oscilla o s. Models
including issues ela ei o he he con ol and
s abiliza ion o he ampli ude a e used
o
his pu pose.
Single-opamp Wien- R idge Family
Fig.1 is he block diag am o he Wien-B idge
amily o opamp based RC-ac i e oscilla o s. Fig.2
shows a comple e se o canonical RC s uc u es o
he passi e block (see e e ences in
[9]).
The unc ion
o his block is
o
make he
phase
a ound he loop
o
be
ze o
a a equency
wo=w,
being nonze o a any o he
equency. The unc ion o he ampli ie is, on he
o he hand, wo old. Fi s , i has
o
p o ide
si nal gain
o
make he loop ans e unc ion magni u e
o
be
1
a
w,.
Second, i has
o
include an
adap i e mechanism
making he ampli ie gain o depend on he signal
ampli ude
A
in
such a way ha he c i ical gain alue
is ob ained jus o
a
single ampli ude alue
A,.
Foi
A>A,
he am li ie gain mus be smalle han he
c i ical alue king la ge o he wise. Whe he he
ampli ie ul ills p e ious equi emen s, Fi
.1
would
gene a e
a
quasi-sinusoidal
signal o amp i ude
A,
and equency 0,.
passi e
ne wo k ampli ie
Fig.1:
Block
diag am o he Wien-B idge
amily o oscilla o s.
I
I
I
I
I
I
I
L_______-__-___________________----------------------------l
j
w,=lI(RC)
Fig.2 Canonical RC s uc u es o he
Wien-
R idge amily.
Fig.3(a) shows a con en ional one-opamp
implemen a ion o he ampli ie o Fig.1. Opamp
nonlinea i ies can be exploi ed
o
ge an adap i e gain
and hence
o
s abilize he ampli ude. Fo lowe
dis o ion, i may be howe e mo e con enien
o
use
an AGC ci cui con olling he alue o esis o
R
as
a
unc ion o he opamp signal ampli ude.
No
ma e
how he ampli ude con ol is made, i ideal opam
s
we e a ailable Fig.3(a) would allow us ge
a,=
w,,
8
any alue o wi, by jus making
k
=
3
+e
(0
<
e
<
<
1).
Le us now conside a eal opamp and use he
model o Fig.3(b)
o
desc ibe i s co esponding
small-
signal
beha io . A e some calcula ions he ollowing
esul o he
oscilla ion equency
and he
oscilla ion
condi ion,
espec i ely:
CH
3006-4/91Kxxx)
-
2589
$1
.oO
0
IEEE
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I I
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1:
V,(S)
=
VJS)
-
I
(k
-
l)R
I
m1
I
I
I
I
-
composi e opamp
I
I
I
I
L~~~~~~___~~~~___~~_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l
I
(a)
(b)
Fig.
3:
(a)One-opamp ampli ie , (b)Fi s -o de
These e ua ions o ide a linea iew on he
ope a ion
o?
he oscil a o . They ha e
o
be sligh ly
modi ied
o
accoun o he ampli ude s abiliza ion
mechanism. Le us assume o his pu pose ha
pa ame e
b
abo e
is
con olled by an ampli ude-
dependen adap a ion pa ame e
C(A)
which we de ine
o
be
a
unc ion o he signal ampli ude
as
ollows:
opamp small-signal model.
single opamp
whe e
A,
is he c i ical ampli ude alue (i.e., he
s able oscilla ion ampli ude).
Fo s able sel -s a ing oscilla ions o exis
pa ame e
b
mus ul ill he ollowing se o
condi ions:
b(Q<O
o
A<Ao
b(Q=O
o
A=Ao
Fi s one gua an ees ha o low ampli ude he e will
be
a
pai o imagina y oo s on he igh -hal o he
complex equency plane and hence ha oscilla ions
will sel -s a . Second one allows
o
calcula e he
ampli ude alue o 'which he oo s a e on he
imagina y axis. Finally, he hi d one ensu es he
oo s will c oss he imagina y axis om igh
o
le
o he ampli ude inc easing,
as
i is equi ed o he
oscilla ions
o
be s able. In summa y, (2c)
is
a
much
mo e ealis ic oscilla o condi ion han (2a).
Equa ions
(1)
and
(2)
a e he basic design equa ions
o he one-opamp Wien-B idge oscilla o s. In ac ual
ci cui s he e a e
wo
ways
o
achie e
b
o
depend on
5.
One pssibili is
o
con ol he ampli ie DC gain
k
by
making
ka ,.
&he podsibili y is
o
con ol he opamp
ime cons an
T
by making
~al/ ,.
In bo h cases
nonlinea limi a ion ( o ins ance he slew- a e o he
ime cons an o diodes o
k)
as
well as AGC ci cui s
can be used. Howe e no ma e which echnique is
used ci cui ope a ion is desc ibed wi h easonable
accu acy by
(1)
and
(2)
o equencies up
o
abou .
0.21~
[91.
F om
(1)
i can be seen ha he ac ual oscilla ion
equency de ia es wi h espec
o
he ideal one, he
de ia ion inc easing
as
(o~T)
inc eases. This d awback
can be howe e pa ially o e come in case ampli ude
con ol is made ia
T,
pa ame e
k
emainin ixed.
F om (2) i can be seen ha he c i ical
oi
ake ( he
one
making
b
=O)
u his case does no depend on
U,.
Hence he ac ual and he ideal equency a e ela ed
in
a
linea way
(w,=pwi),
he a io
l
depending only
on
k
and hence being independen on he ampli ie
cha ac e is ics. This
is
a
e y in e es ing ea u e o
single opamp whose only d awback comes om he
ac ha pa ame e
b
de e mining he oscilla o
condi ion
is
s ongly dependen on
wi .
Hence, in case
k
is
selec ed
o
ensu e b>O (sel -s a ing ope a ion) in
wide equency anges,
5,
can be shown
o
exhibi
la ge ana ions om one ex eme
o
he o he o he
ange. This
is
no con enien in p ac ice
as
i
can be
unde s ood om Table
1.
Da a on his able ha e been
measu ed om oscilla o s using he slew- a e
as
he
con ollin mechanism. The wo igh mos columns
co espon i he single-opamp case. Pa ame e dis .
e e s
o
he a io be ween he
i s
and he hi d
ha monics.
k
was selec ed
o
ensu e sel -s a ing
ope a ion in he ange shown, which esul ed in
5,
being e y close
o
uni y o he highe equency and
inc easing
as
he equenc dec eases. Since changes
in
Z,
ha e
o
be abso bed 8y he nonlinea i y, la ge
dis o ion may be expec ed o low equencies,
as
i
is
con i med om he measu ed da a.
Composi e Opamp Osci la o s
Le
us
assume he ampli ie in Fig.1 is made by
using wo opamps and some linea esis o s (see
Fig.4). In he mo e gene al case and usin he opamp
model o Fig.3(b) he ollowing ans e knc ion can
be ob ained o he ampli ie :
(3)
whe e
k,
pl, p2 and
p3
a e con olled by esis o a ios
( hey a e no ypically sepa a ely con ollable) and
a( l,
TZ)
can be ei he
TI
o
~2
depending on he ac ual
composi e opamp s uc u e.
A e some analysis, he ollowing can be ob ained
o pa ame e s woand
b
o he composi e opamp
oscilla o :
3-k
1+-
2590
b=04x
zzp3-o
~~~~~~~~+",~~(3p~-kp,~~+~~+
independen o he opamp ime
cons an s,
which
is
a
I
TZ
(4b)
e y appealing ea u e dese ing u he a en ion.
F om (4b) i can be shown ha by making,
+
a;
01
As
o he one-opamp case, an adap a ion
3p2--kpl1=0
(6)
P
he oscilla ion equency exac ly coincides o
ai
p o iding he ollowing
is
ul illed o he C i ical
alue o he adap a ion pa ame e ,
a ame e
E,
ul illin (2b)
is
assumed
o
be he ehicle
Fo ampli ude con o ia ei he one o he opamp ime
cons an s o he ampli ie pa ame e s
k
and
p,.
Equa ions (2b-C) hence also holds
as
he oscilla o
condi ion, pa ame e
b
o
his
case being
ha
in
(4b).
Ideal gain design c i e ion. Di e en design
c i e ia o com si e
o
amp Wien-B idge can
zS iised by ,a e uG ana yzing
(4).
Since he
pu ose o Cbm osi e
o
amp
is
o app oach he
ped mance o i&al ampi ie s, one possible c i e ion
is
o
y
o
ix
k
o
he ideal alue
3.
As
i can
be
seen
om
(4a)
his
yields equency de ia ions which a e
e y simila
o
he ones o he single-opamp case. The
ad an age o he composi e-opamp case comes om
he oscilla o condi ion. A e some analysis, we ge ,
a
'1
=2
3
3pz(p2-p1-)- -3pzp3
(5)
whe e
i
can be seen ha pa ame e
b
does no
depend,
o
a i sbo de , on
ai.
Hence and
no
ma e
he ampli ude con ol be made ia
,
k
o an o he
p,
pa ame e s, he c i ical alue
o
he aIap a ion
Fa ame e will change only sligh ly o e wide
equency anges.
This
is ad an a ous in compa ison
o
he one-opamp case
as
i can ye con i med om
Table
1.
In he wo le mos columns measu ed da a
ha e been collec ed o a composi e ampli ie
s uc u e wi hpl=1.55,p~=k=3 andp3=kpl and o
he slew- a e o ampli ie
#2
being he ampli ude
con ol mechanism. LM747 dual opamps we e used.
As
i
can be seen, he dis o ion emains p ac ically
unchanged in
he
whole oscilla ion equency
ange.
The e a e se e al obse a ions o be made
conce ning he use o his ideal gain design c i e ion:
1)
Acco ding
o
he i s -o de exp ession o
b,
i
is
no
possible
o
ge s able oscilla ions by con olling ia
he slew- a e o
o
amp
#1
( la l'/o.
Fo
slew- a e
based s able oscil a ions he opamp
#2
should be
he con olling de ice.
2)
I
is possible
o
make
pI
=O
(no phase
compensa ion allowed) wi hou deg ading he
c i e ion ea u es.
3)
Con olling ia
p3
(p3a
5)
yields he oscilla o
equency o be insensi i e o simul aneous
p opo ional changes in he opamp ime cons an s.
Random changes in
zz
canno howe e be abso bed
by he adap a ion mechanism and will hence
in luence he oscilla ion kequency.
No ice inally ha , since
ai
does no in luence he
sign o
b,
i is no possible
o
ge a linea ela ionship
be ween
w,
and
w,,
in opposi ion o wha can be
achie ed o he one-opamp case.
Ideal equency design c i e ion. Some in e es ing
p ope ies can be obse ed in case
k
is no ixed
o
he
ideal alue.
As
a ma e o ac , in [71 he au ho s
p oposed a composi e ampli ie s uc u e we e by
p ope ly selec ing
k
i was possible
o
ge
w,=ai
o
equencies
up
o abou
1.5/~.
T
means ha he
osci1l;ih)n
equency
can
be
madc
o
be
comple ely
(7)
Rega ding he pa ame e de e mining he
oscilla ion condi ion, i is con enien
o
sepa a ely
conside wo di e en cases. One whe e
PI,
pz,
and he
ime cons an s a e ixed acco ding
o
(6)
and he
con ol
is
made ei he ia
k
o p3. Fo
his
case
I
I
esul s,
3n he o he hand i
k
and
p3
a e ixed using
(7)
and
he con ol is made ia any o he o he pa ame e s,
he ollowing can be ob ained:
The e a e some obse a ions applying o his
design c i e ion:
1)
S able ope a ion con olling ia he slew- a e is
only possible o hose s uc u es whe e
a=q,
and
o he con olling de ice being he opamp
#2
( zaT;2'/5). Besides, he oscilla ion condi ion o
his
case is insensi i e
o
p opo ional changes in he
opamp ime cons an s.
2)
Ampli ude con ol ia
~2,
pl
o
p2
(based on (8b))
equi es
k
o
be selec ed
o
ul ill(7) which depends
on equency. Hence his app oach is only
app op ia e o ixed equency applica ions.
3)
Fo ampli ude con ol ia k (kak
E,),
he oscilla ion
condi ion can be made insensi i e
o
bo h andom
and simul aneous changes in he opamp ime
cons an s by eso ing
o
s uc u es ha ing
a=xZ.
O he wise, his condi ion will only be insensi i e
o
simul aneous p opo ional changes.
4) Obse e o ampli ude con ol ia k, he oscilla ion
condi ion
(8a)
depends on equency.
As
a
consequence, la ge a ia ions o he c i ical
alues esul in case
k'(kak'5)
is
selec ed
o
ensu e
sel -s a ing ope a ion in a wide equency ange.
In
case he he adap a ion p ocess
is
implemen ed
by eso ing o nonlinea limi a ion, la e
dis o ions a e hus expec ed o he hig%-
equency edge o he ange.
Pe o mance o he ideal equency c i e ion
is
illus a ed in Table
2
whe e we show expe imen al
esul s o a composi e opamp s uc u e wi h
p1=3.105, p2=k and p3=kpI. LM747 dual opamps
we e used, he con olling de ice being he slew- a e
o he opamp
#2.
As
i
can be seen, de ia ions in
equency a e lowe han
2%
o equencies up
o
1
OOKhz.
2591,
Ideal
equency,
kHz
22.7
49.1
88.4
107.8 105.5
Real
equency,
kHz
22.5
492
88.3
Discussion on
Composi e oDamD s uc u es
Fig.4(a) shows a gene al block diag am o
a
wo
opamps composi e ampli ie . T iangula blocks
co espond
o
opamps while ec angula blocks
ep esen weigh mg by esis o s
as
i
is
illus a ed in
Fig.qb). Swi ches
SI
and
Sp
ha e no be ac ually
im
lemen ed bu ha e been used
o
indica e
ha
wo
di8e en poin s
a?
a ailable
o
be
used
as
he ac ual
ampli ie ou pu .
,-------------------------------------------------
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1
I
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IF
I
1
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I------___----_-____-----
Fig.4: Gene al
block
diag am o
a
wo
Table
3
shows exp essions o
k,
PI,
p2, p3
and
a
as
unc ions o
C,
and
yi
o he wo possible ampli ie
ou pu s. Fo p ope ope a ion o he composi e
ampli ie Wien-B idge, ac ual s uc u es de i ed om
Fig.4 would ul ill he ollowing cons ain s,
opamps composi e ampli ie .
Table
3
"aa
ensu es inpu
o
he composi e opamp will be ia high
impedance nodes.
om Fig.4 wi h (9) and aking in o
accoun Ta%le
3
i
is
no a complica ed ask
o
de i e
com si e ampli ie s uc u es o wo composi e
am ie design c i e ia p esen ed in he ape .
As
i
is
gmons a ed by
he
expe imen al esu s included
in
he
communica ion, s uc u es can be ound
ul illing he c i e ia
o
equencies up
o
abou
0.9~.
Re e ences
[
11
A. Soliman: "Classi ica ion and Gene a ion o
Ac i e Com ensa ed Non-in e ing VCVS
Building BlmLs".
Zn . Jou nal
o
Ci cui Theo y
and Applic.,
Vo1.8, pp 395-405, Oc . 1980.
[21 J.L. Hue as and A. Rod iguez Vbz uez:
"On
he
Ac i e Com ensa ion o Ope a ional Ampli ie s-
Based VCV&.
ZEEE T ans. Ci cui s and Sys ems.
S a in
CAS-29,
p
497-506, July 1982.
W.B. Milhael and
S.
Michael: "Composi e
Ope a ional Ampli ie s: Gene a ion and Fini e-
Gain Applica ions".
ZEEE T ans. on Ci cui s and
Sys ems,
CAS-34, nQ5, pp. 449-459, May 1987.
M.A. Redd
:
"Ope a ional-Ampli ie Ci cui s wi h
Va iable $has, Shi and hei Applica ion o
High-Q Ac i e RC- il e s and RC%scilla o s".
ZEEE T ans. Ci cui s and Sys ems,
CAS-23,
pp
__
384-389, June 1976.
[51A. Budak and
K.
Nay: "Ope a ional Ampli ie
Ci cui s o he Wien-b idge Oscilla o ".
ZEEE
T ans. Ci cui s and Sys ems,
CAS-28, pp 930-934,
Sep embe 1981.
[6]
S.
.Awad: "Ex ending . he F equency Range o a
Wien-B idge Oscilla o using Composi e
Ope a ional Ampli ie s".
ZEEE T ans. on Ins . and
Measu emen ,
o1.38, nQ3, pp. 740-744, June 1989.
[7] A. Rod iguez VBzquez e al.: "High-F equency
Design o he Wien-B idge Oscilla o using
Composi e Ampli ie s".
ZEEE T ans. Ci cui s and
Sys ems,
CAS-34, pp 441-443, Ap il 1987.
[8]
A. Ca losena e al.
:
"An Imp o ed Wien B idge
Oscilla o ".
IEEE T ans. Ci cui s and Sys ems,
CAS-37, pp 543-546, Ap il 1990.
[9] J.L. Hue as e al.: "Analysis and Design o Sel -
Limi ing Single-Opamp RC Oscilla o s".
In .
Jou nal
o
Ci cui Theo y and Applica ions,
~~
Vo1.18, pp.53-69,1990.
[lo]B. Pe ez-Vedu:
"Nonlinea Modeling
o
Ope a ional Ampli ie s Based
RC
Oscilla o s".
PhD disse a ion, Uni e si y o Se ille 1985.
i s one ensu e no pa asi ic poles will be alloca ed in
he igh hal o he complex equency plane
(acco ding
o
he
one pole opamp model). Second one