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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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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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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


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


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



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Bibliography Sedra, Smith, Microlectronic Circuits, Oxford University Press.

Johns, David;Analog integrated circuit design. ISBN: 0-471-14448-7.

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