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Electrnica 3
Oscillators and Multivibrators
Mestrado Integrado emEngenharia Electrotcnica e de Computadores
Telecomunicaes, Eletrnica e Computadores
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Oscillators Summary
LC basic oscillator
Barkhausen criterion
Ring oscillator
Multivibrators
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Harmonic oscillators An oscillator can be defined as a device that generates a
sinusoidal or any other type of repetitive signal.
An harmonic oscillator is generally characterized by being
capable of generating a sinusoidal signal, or nearly
sinusoidal, with a well defined frequency.
In contrast, the rest of the oscillators group is given the name
of relaxation oscillators.
The most important features associated to an oscillator are:amplitude and frequency stability, output power and harmonic
content (a variation in frequency is called drift)
3
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Oscillators
Tuned oscillator - LC resonant circuit
L C
[ ] real;,02ideal;,0
sin
0;0
0
5,022
0210
2
0
2
021
2
0
2
021
2
02
2
2
2
2
2
00
jjssss
jsss
tVeVeVv
vdt
vd
LC
v
dt
vd
dt
vdLC
dt
dvC
dt
dL
dt
diLv
tjtj
L
LLLL
LLLL
=>=++
==+
=+=
=+=+
=
==
vL
energy
LC Oscillator: low phase noise, large area
Power is usually supplied by DC bias to the devices that convert
the bias power into signal power in the form of a negative,
nonlinear conductance or as regenerative feedback.
jL -j/C
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Oscillators
( )
( ) ( )
( )LC
LCGLGLss
kei
idt
diGL
dt
idLC
VL
vLdt
di
iidt
diGL
dt
idLC
iiii
stL
LLL
CL
NLLL
NLRC
2
4,
0
10
10
I0i,conditionsInitial
2
21
2
2
0
0L
2
2
=
=
=++
==
=
=++
=++L
C
vL
energy
R
[ ]
0)()(
real;,
02
0201
0
5,022
021
02
02
+=
=
>=++
ttSinKtCosKeti
jjss
ss
tL
iN
set iN=0 to obtain a homogeneous
equation in the inductor current.
A trial solution of the form iL=Kest
leads to the characteristic equation
Case (GL)2-4LC
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Harmonic oscillators
6
LC
Rs
LC RPQL>5
RP=QL2Rs
Assuming some initial energy inthe system, the natural response
is a sinusoidal signal with
frequency:
With magnitude dumping of:
2411Q
o =
Qo
2 =
221 4
11
2,
Qj
Qpp o
o =
CRQ
LC
Po
o
=
=1
How to keep a sustained oscillation?
Active mode: Using an active element
that replaces the dissipated energy in
Rs (or Rp). Some sort of feedback is
needed.
a sort of negative resistor is needed.
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Harmonic oscillators
7
LC Rs
-Rs
+
-
R1
R2
R3
3
2
1
3
2
1
RRRR
RR
Riv
i =
=
LC RP-R
p
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Oscillators
Barkhausen Criterion
H(s)
G(s)
Vi(s) Vo(s)
)()(1
)(
)(
)(
sGsH
sH
sV
sV
i
o
+=
)()(1
)(
)(
)(
sGsH
sH
sV
sV
i
o
+=
1 ( ) ( ) 0 ( ) ( ) 1H s G s H s G s+ = =
180)()(
1)()(
00
00
0
=
=
=
jGjH
jGjH
js
Self-sustaining oscillation
the loop gain slightly exceeds unity at the resonant frequency,
the phase shift around the loop is n2 rad (where n is an integer),
the oscillation is sustained even if Vi=0.
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Oscillators
Barkhausen criterion regenerative feedback
The inverting amplifier grants a rad (180 deg.) phase shift. To meet
the requirements of the second criterion, the filter block provides anadditional rad phase shift for a total of 2 rad (360 deg.) around the
entire loop.
By design, the filter block inherently provides the phase shift in addition to
providing a coupling network to and from the amplifier.
The filter block also sets the frequency of oscillation, using a tuned circuit(inductor and capacitor) or crystal.
The amplifier provides for the replacement of the dissipated energy.
G
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H(f)
G(f)
vof
|GH|>1
saturation
-
++
Oscillators
Vi(s)
Vo(s)
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Harmonic oscillators
Tuned oscillator
11
C RP
R3=
L
RPv1
voAv
It is possible after a simple inspection tofind the right conditions for oscillation.
For a null phase in the system, L and C
should not be noticed during oscillation.That happens at the resonant frequency,
(infinite impedance):
For a sustained oscillation the losses atRp needs to be compensated. That is
accomplished if the amplifier is able to
replace that energy by sensing v1 and by
trying to keep its function (sinusoid).Once there is an attenuation of from
the output to v1, Av=2!
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Harmonic Oscillator
12
+
-
Wien-Bridge oscillator
R2
R
R
C
C
R1( ) ( )
+
+=
CRCRj
R
R
jjA oo
0
0
1
2
13
1
1
2;1
1
2 ==R
R
RCo
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Oscillation control
It is impossible to impose the exact conditions for oscillation.
The solution passes by giving a gain > 1 when the signal has a
small amplitude, and a gain < 1 for the large portion of the
signal. Eventually a sustained oscillation is obtained.
13
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Harmonic oscillator
14
+
-
R22
R
R
C
C
R1
R22
( ) ( ) 1=oo jjA
( ) ( ) 1>oo jjA
Low signal level
In-between state
High signal level
( ) ( ) 1
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Harmonic Oscillator
15
Phase delay based oscillator
+
-C
R
C C
R
R
KR
Negative feedback. To
verify the Barkhausen
criterion a total shift of 180
is needed, at a single welldefined frequency. Then three
singularities are imposed
(together of a gain equal to
one).
( ) ( )
( ) ( )
29;6
11
1561
32
===+++
= KRC
SRCsRCsRC
KssA o
j
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Oscillators
Can this circuit be an oscillator?
1
1
+2700
+900
+1800
1
+2700
+900
+1800
1
+1800
18001
H1
H1H2
H2
If gm1RP1gm2RP2 1, the circuit oscillates
1 2
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Oscillators
Ring oscillator
INV1
INV3
INV2
Easy to integrate, high phase noise
Rarely used in RF systems
Often used in high speed data links
tp
N stages with delay t
2N=T
A B C
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Oscillators
Ring oscillatorINV
1INV
3INV
2
3
0
3
0
( )
1
AH s
s
=
+
1
1
32
0
3
0=
+
osc
A
01
s
A)s(A oi
+= inverter gain
Open-loop gain
Design requirements:
The 3 inverters intrinsically
ensure a 180 phase shift gain.
The frequency dependentphase must provide another 180
shift.
Sinusoidal oscillation.
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Quadrature Oscillator
19
==+
)(
1)(0)(
)(2
2
tv
k
tvtv
t
tvk
+
-
R+
-
R
C
+
-
R
CR
The solution of this
equation is a sinusoid
sin((1/k)t)cos((1/k)t)
K=RC
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Quadrature Oscillator
20
+
-
C
+
-
2R
2R
2R
2R
Non-inverting integrator
Integrator (invertor)
Amplitude control made
at this stage.
The adjustment can place
the poles into the right side.
2R
C
v
v/2R
The output of the firstintegrator presents a typical
1% distortion. The sin(.) is
even better because of the
extra filtering performed by
the second integrator.
sin((1/k)t)
cos((1/k)t)
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Oscillators
Regenerative feedback basic architecture of transistor based
oscillators
LC 1/G-1
Vx
GmVx
Z(j)
+ -1 -Gm Z(j)+
+
Barkhausen criterion for oscillation at resonance frequency
GmZ(j0)=1
Assuming Gm is purely real, Z(j0) must also be purely real
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Oscillators
Regenerative feedback
Issue GmRp needs to exactly equal 1
Magnitude condition achieved
making |GmRp|=1
+ -1 -Gm Z(j)+
+
Rp
0
90
-90
0
+ -1 Z(j)+
+-Gm 0 0 20 30
Transistors transconductance is non-linear and presents
saturation characteristics
Harmonics are produced but are filtered out by the resonant circuit
The Barkhausen criterion must be verified at fundamental frequency
L
C
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Colpitts oscillator
Tuned oscillator Negative feedback but three singularities
23
C1R
vo(t)
C2
L
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Colpitts oscillator
24
C1R
vo(t)
C2
L
v(t) v(t)( ) ( )
( )( )
( ) ( ) ( ) ( ) ( )tvLCstvtv
sCsL
sCtv
tvsCR
tvtvsCtvg
oo
oom
+=+
=
++=
2
2
2
2
21
11
1
1
2
21
21
1
C
CRg
CC
CCL
m
o
=
+
=This is the exact value for
oscillation. In reality, one
do gmR > C2/C1 and let the
transistor non-linearity toshape the magnitude.
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Colpitts oscillator
25
Choong-Yul Cha, and Sang-Gug Lee
A Complementary Colpitts Oscillator in CMOS TechnologyIEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
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Hartley Oscillator
26
L1 R
vo(t)C
v(t) v(t)
L2
( )
2
1
21
1
LLRg
LLC
m
o
=
+=
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Simplified analysis
Hartley oscillator
27
L1 R
vo(t)
CL2
vo(t)
v1(t)
Z= for
( )21
1
LLCo
+
=
To compensate losses : Vo=-gmRV1.
Then:
( )12
22
2
1
2
22
2
111
RVgCL
CLVVCLs
CLsV mo =+=
At the resonant frequency:
This is true if: gmR=L1/L2
( )112
1 RVgL
L
V m
=
C l ill
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Crystal oscillator
The circuit shows two resonant frequencies. Within the seriesresonance the equivalent impedance of the crystal is very
small (Rs).
The second resonance frequency is defined by the LC series in
parallel with Cp. Under these circumstances, the equivalent
impedance is very high.
28
LCC
CC
ps
ps
p
+
1
Cp
CsLRs
R
L
RCQ s
s
==
1
Cp: shunt capacitance
Cs: motional capacitance
L: motional inductance
R: motional resistance
s
sLC
1=
C l ill
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Crystal oscillator
29
~
The concept of electromechanic
resonance can be understood as an
RLC circuit.
Rs
Cs
LCp
Capacitor between
plates
Crystal mass
Elasticity
Friction
Rs is very small => Q is a large
value (Q> 20.000 are typical values)
Symbol
C t l ill t
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Crystal oscillator
30
ws
wp
w
X
Inductive
Capacitive
Very small difference
(Cs
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Crystal Oscillator
31
C1C2
Filtering avoids resonance of the
harmonics.
Pierce oscillator
T d O ill t
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Tuned Oscillator
Differential LC tuned oscillator
L1 L2
C1 C2
I
/VO
VO
This type of oscillator structure is quite popular in current
CMOS implementations
Simple topology Differential implementation (good for feeding differential
circuits)
Good phase noise performance can be achieved
L1 L2Cp1 Cp2
I
/VOVO
Rp2Rp1
O ill t
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Oscillators
L1Cp1
I
/VO
VOVS
L1Cp1
I
VOVS
-1
Rp1Rp1 L1Cp1
VO
Rp1
-1/Gm1
Design tank to achieve high Q
Choose I bias for large swing, preventing saturation
Transistor size adequate to obtain proper -1/Gm value- usually |GmRp|>1 to ensure start-up
Differential LC tunned oscillator
O ill t
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Oscillators
L1 L2
C1 C2
I
/VOVO
I2I1
I1
I
I/2
TI/2
2I/
Fundamental component is:
I1(t)=2/.I.sin(0t)
Resulting oscillator amplitude:A=2/ .I.sin(0t)*Rp
Differential LC tunned oscillator
Oscillators
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Frequency stability
Oscillators
See also:Sedra and Smith, Microelectronic Circuits
Multivibrators
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Multivibrators
One-shot (monostable) - an electronic device thatemits a single pulse when triggered.
Free-running (astable) - an electronic device thatoscillates between two stable states (high and low).
Commonly called a clock in digital systems.
Latch (bistable) - an electronic device that has two
stable states (high and low) and must be triggered to
jump from one to the other. Also called a flip-flop.
Commonly used as temporary memory.
Multivibrators
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Multivibrators
Monostable / One-shot - The one-shot, or monostablemultivibrator, presents only one stable state. When triggered,
it goes to its unstable state for a predetermined length of time,
then returns to its stable state.
Trigger
CEXTREXT
+V
CX
RX/CX
Q
QFor most one-shots, the length of time inthe unstable state (tW) is determined by an
external RC circuit.
tW
Trigger
Q
Multivibrators
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Multivibrators
Monostable /One-shot - Non-retriggerable one-shots do notrespond to any triggers that occur during the unstablestate. Retriggerable one-shots respond to any trigger, evenif it occurs in the unstable state. If it occurs during theunstable state, the state is extended by an amount equal tothe pulse width.
Retriggers
tW
Trigger
Q
Retriggerable one-shot:
Triggers
derived
from ac
Missing trigger
due to power
failure
tW
Power failure indication
tW
tW
Retriggers RetriggersQ
Multivibrators
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Multivibrators Monostable/One-shot
Example
See also:Sedra and Smith, Microelectronic Circuits
Multivibrators
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Multivibrators
Monostable /One-shot - Example
T Recovery time( ) ( )
( ) ( ) ( )
( ) ( )CRR
Trcy
DDDDD
CRR
T
DDTHi
RC
t
SFFC
on
on
eVVV
eVVVtv
eVVVtv
+
+
+=+
==
=
1
12
02,01
See also:Sedra and Smith, Microelectronic Circuits
Multivibrators
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Multivibrators
+
-
R2
R1
Av
Vref
viSchmitt trigger
vi
vo
AL
AH
THHref VARR
RV =+= 21
1
vi
vo
-A
A
TLLref VARR
RV =
+=
21
1
vi
vo
AL
AH
Hysteresys
VTL VTH
vc
41
Multivibrators
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Multivibrators
+
-
R2
R1 vovi
Schmitt trigger no inversor
vi
AL
AH
LTH AR
RV
2
1=HTL AR
RV
2
1=
vi
vo
AL
AH
Actual characteristic
of a comparator
42
Multivibrators
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Multivibrators
Sedra, Smith
Microelectronic Circuits
t1 t2
21
1
21
1 ;RR
RVV
RR
RVV OLTL
OHTH
+=
+=
+=+=
2
1221
2ln2
R
RRttT
Assuming
|VOH| = |VOL|
If R1 = 0.86R2, then T = 2RC and
where
= RC
RCf 2
1=
Astable or Relaxation Oscillator VOH
VOL
Oscillators and Multivibrators
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Oscillators and Multivibrators
Bibliography Sedra, Smith, Microlectronic Circuits, Oxford University Press.
Johns, David;Analog integrated circuit design. ISBN: 0-471-14448-7.
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