ece 145b / 218b, notes set 9: oscillators, part 1. · oscillators, part 1. mark rodwell university...

class notes, M. Rodwell, copyrighted 2012

ECE 145B / 218B, notes set 9: Oscillators, Part 1.

Mark Rodwell

University of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax


Oscillator Design

Noise Phase Oscillator

Amplitude Oscillator

VCOs :Tuning and Varactors

Topologies Oscillator Standard""

Examples Specific

approachport -2 General

design oscillatorport -One

Theoryn OscillatioAbout Comments General


Stability

? 1an greater th of magnitude theIs

viewpoint(S) Reflection

?part real negative a have )( Does

viewpointImpedance

? plane-s of halfright in lieany Do

)(/)()(or ,)(/)(in poles Find

port-or twoport -One analysis. nodalby circuit Analyze

:eoryNetwork th

? plane-s of halfright in lieany Do

poles. loop-closed ofpart real Find

margin. phase find :methodsNyquist & Bode

theorysystem control Classical

: versionsequivalentmany :theoryStability

Oscillatorinput zeroh output wit zero-non :yInstabilit

in

in

genout

jZ

sIsVsZsVsV


Stability: LaPlace Transform / Eigenvalue Method

...)exp()exp()exp()(

:response Impulse

)...)(()(

)...)(()(

...1

...1)(

)(etc)(

)(or

)(

)(or

)(

)(

function.transfer limit signal-small in etc.) (circuits, system Physical

332211

321

32122

21

2

211

tsktsktskth

ssssss

ssssssc

sasa

sbsbcsH

sHsI

sV

sa

sb

sV

sV

ppp

ppp

zzz

in

in

gen

out

system. unstable

limit.ut grow witho will)exp( then

)positive( plane-s of halfright in lie polesany If

:complex )(generally are Poles

tsk

js

pii

pi

pipipi


Unstable system if any pole has positive real part

system. stable

decays. )exp(

negative ;

ts

js

pi

pipipipi

system. unstable

grows. )exp(

positive ;

ts

js

pi

pipipipi


LaPlace vs. Fourier Analysis of Oscillators

)()(not ),(

computing toourselves resrictedalready have we

)()()( ie. reactance, and resistance

of composed being impedancean ofspeak When we

analysis.complex in studied is This lie.

poles theplanecomplex theof sidein which certain be to

n integratiocontour from derived Theorems usemust we

, )(or )( computing toourselvesrestrict weIf

clear. is LHPor RHP in the sfrequencie

pole theoflocation ),( impedancesor

)( functions transfer computingIn

jZsZjZ

jjXjRjZ

jZjH

sZ

sH

unstable !

stable ?

unstable ?

must look

at phase of

H(j)

stable !

stable ?

unstable ?

must look

at phase of

H(j)

careful. bemust We


One-Port Oscillator Analysis: Series Impedance

|||| i.e. , ||||

requiresn oscillatio then ,0 If

0)( if Oscillates

0/)/2(1

0)(1

0)/1(

1212

1

21

22

2

21

21

GGRR

R

RR

ss

LCsRRsC

sCRRsLI

nn


One-Port Oscillator Analysis: Parallel Admittance

|||| i.e. , ||||

requiresn oscillatio then ,0 If

0)( if Oscillates

0)(1

0)/1(

1212

1

21

2

21

21

RRGG

G

GG

LCsGGsL

sLGGsCV


Stability: A Paradox

(????) |||| i.e. , ||||

requiresn oscillatio then ,0 If :Parallel

1212

1

RRGG

G

(???) |||| i.e. , ||||

requiresn oscillatio then ,0 If :Series

1212

1

GGRR

R

parallel.or series isnetwork theif lcannot tel We???Which

networks. parallel and series

betweenn distinctio no is thereelements, reactive theinclude weUnless

.*time*or with *frequency*

eitherith behavior w calculatecannot weand frequency,with

variationno hasnetwork theelements, reactive theinclude weUnless

stable. iscircuit above r theask whethe tosmeaningles isIt


A Mixed Resonant Network: What Criterion ?

0/1/1

/1/1 :So

0

0

/1/1

/1/1

1

2

2

1

1

2

sLGsL

sLsLsCG

V

V

sLGsL

sLsLsCG

0)||(1

01

0

011

0111

0/1/1/1/1

21

22

21

21

12

12

12

21

12

1

2

2112

1

3

21

2

12

1

2

2

12

RR

LCRs

RR

LRRCs

GG

LCGs

GG

GLG

GG

Cs

LCGsLGGCsGG

LCLGsLGLGLCsLGLGs

sLGLCssLG

sLsLsLGsLsCG

0)||(

if Oscillates

21

21

RR

LRRC

2/1

2

21

Frequencyn Oscillatio

LCR

RRn


A Mixed Resonant Network (2)

CGLR nn and

:elements Q-high assume Now

21

0/1 2

12 LCsRLCRs

0/ if Oscillates

)(

12

2/1

RLCR

LCn


Impedance Point of View

CjGLjLRYY

CjGjY

LjLRjZjY

RLjjZ

RLCRLC

020

22

01activeload

020load

0

0

22

010active0active

0

100active

0

12

2/1

0

/1/

admittance Total

)(

:frequency at admittance Load

/1/)(/1)(

:frequency at admittance device Active

)(

:frequency at impedance device Active

0/ if Oscillates ,)(

before. ascriterion same theis This

.0/Re need n,oscillatioFor 2

22

011 GLRGGGYY activeloadactiveload


Impedance Point of View

0)( if Oscillates

0)(by definedfrequency n Oscillatio

)()(

impedance Total

)(

:frequency at Load

)(

:frequency at device Active

load

load

loadload

loadload0load

0

0active

0

RR

XX

XXjRRZ

jXRjZ

jXRjZ

active

active

activeactivetotal

activeactive


Admittance Point of View

0)( if Oscillates

0)(by definedfrequency n Oscillatio

)()(

admittance Total

)(

:frequency at Load

)(

:frequency at device Active

load

load

loadload

loadload0load

0

0active

0

GG

BB

BBjGGY

jGGjG

jBGjY

active

active

activeactivetotal

activeactive


Equivalence of Impedance and Admittance Methods

paradox.stability theregarding comments theagain torefer Please

).(! followy necessaril toseemnot does thisQ,-high *not* are impedances theIf

0 implies 0then

Q,-high are impedances theif :nobservatioKey

negative. is then ,1/ i.e. Q,high are impedances theif So,

02

then , and , If

But

11

222222

2222

activeloadactiveload

total

XR

total

activeload

loadactive

loadload

loadload

activeactive

activeactive

loadactive

loadactivetotal

GGRR

GRXQ

X

R

X

R

XR

R

XRR

RG

RRRR

XXX

XR

jXR

XR

jXR

ZZYYY


Simple Negative-Resistance Oscillator

etc. , model order toin drawn bemust circuit aldifferenti Full

shown. is modelcircuit -half simplified-Over

gdC


Common-Base Colpitts Oscillator

21

1

2

21

1

1

2

21

1

11

2

21

1

121

1

2121

1

21

211

21

1

1

20

)(1

)/(1

)/(

(2)

model-T BJT simplified (1)

:Assume

tedious.is analysis General

CC

gC

CC

C

Cj

g

CC

gC

V

Vg

V

I

CC

C

Cj

g

CC

C

CCj

g

CC

C

CjCjg

CCC

gCjCj

Cj

V

V

Cr

mmmem

c

m

m

mm

e

e

econductanc

Negative

ignore) will(we

component inductive small



21

11

CC

gCG m

21

11

CC

gCG m

21

11

CC

gCG m

2

21

1

21

1

2

21

1

21

isr transistoby the provided

econductanc negative overall The

. transformseries-parallel a then and

parallel-series aby analyzed becan

and ,, involvingnetwork The

CC

Cg

CC

CgG

CC

CgG

rCC

mmneg

mp

e

2

21

1

CC

CgG mp

21

21

CC

CCCeq

negG



2

21

1

21

1

CC

Cg

CC

CgG mmneg

21

21

CC

CCCeq

ingunderstandfirst for Good

e.approximatextremely wasAnalysis


Common-Collector Colpitts Oscillator

Colpitts

collector-common in the results

collector the toground theMoving

analysis. in theabritrary is

node ground theofLocation

emitter. or the base the

eitherat criterion admittance

impedance/ apply thecan We

y.differentl

connectedhowever *is* load The


Common-Emitter Colpitts Oscillator

commentsSimilar


Clapp Oscillator

crystal. quartz

resonant) (series aby replaced are and if oscillator Pierce

thebecomes right) the(toion configuratemitter -common The

frequencyn oscillatio samechangednot hasr transistothe

topresentednetwork impedance then theunchanged, is If

)/1( have now We

. and n combinatio series with theReplace

/1with

,oscillator Colpitts theStart with

2

1

31

32

1

LC

B

CjLjjB

CL

LjjB

tune

ootune

otune


Hartley Oscillator

elements bias e with thesassociated resonance parasiticfor Watch

blocking. DC ofaddition requiring bias, DCr transistoecircuit th-short inductors The

. and inductors through isFeeback

form. emitter)collector,(base, -commonin aboveshown isnetwork signal-small AC The

21 LL

ece 145b / 218b, notes set 9: oscillators, part 1. · oscillators, part 1. mark rodwell university...

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