Oscillator design.ppt

8/18/2019 Oscillator design.ppt

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ECES 352 Winter 2007

Oscillator


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Objectives

* Describe the basic concept of an oscillator

* Discuss the basic principles of operation of an oscillator

* Analyze the operation of RC and LC oscillators

* Describe the operation of the basic relaxation oscillator circuits


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Introduction

* Oscillator is an electronic circuit that generates a periodic avefor!

on its output ithout an external signal source" It is used to convert dc

to ac"* Oscillators are circuits that produce a continuous signal of so!e type

ithout the need of an input"

* #hese signals serve a variety of purposes"

* Co!!unications syste!s$ digital syste!s %including co!puters&$ and

test e'uip!ent !a(e use of oscillators


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Introduction

* An oscillator is a circuit that produces a repetitive signal

fro! a dc voltage"

* #he feedbac( oscillator relies on a positive feedbac( of

the output to !aintain the oscillations"

* #he relaxation oscillator !a(es use of an RC ti!ing

circuit to generate a nonsinusoidal signal such as s'uareave

Sinewave

Squarewave

Sawtoothwave


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#ypes of oscillators

)" RC oscillators

ien +ridge

,hase-.hift

/" LC oscillators

0artley

Colpitts

Crystal1" 2nijunction 3 relaxation oscillators


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+asic principles for oscillation

* An oscillator is an a!plifier ith positive feedbac("

(1) f se V V V +=

(2) o f βV V =( ) ( ) (3) os f seo βV V AV V A AV V +=+==


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* #he closed loop gain is4

( ) ( )os f seo

βV V AV V A AV V

+=+==

oso V A AV V β +=( ) so AV V A =− β 1

( ) Aβ A

V

V A

s

o f −

=≡1


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* In general A and β are functions of fre'uency and thus !ay be rittenas5 is (non as loop gain

( ) ( ) ( )

( ) ( )s β s A1

s As

V

V s A

s

o f

−==

( ) ( )s β s A


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* riting the loop gain beco!es5

* Replacing s ith jω

* and

( ) ( ) ( ) s s β AsT =

( ) ( )

( )sT 1s A

s A f −=

( ) ( )

( ) jωT 1

jω A jω A

f −=

( ) ( ) ( ) jω β jω A jωT =


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* At a specific fre'uency f 6

* At this fre'uency$ the closed loop gain5

ill be infinite$ i"e" the circuit ill have finite output for zero input

signal - oscillation

( ) ( ) ( ) 1000 == jω β jω A jωT

( )

( )

( ) ( )00

0

0 jω β jω A1

jω A

jω A f −=


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* #hus$ the condition for sinusoidal oscillation of fre'uency is f 6

* #his is (non as +ar(hausen criterion"

* #he fre'uency of oscillation is solely deter!ined by the phase

characteristic of the feedbac( loop 7 the loop oscillates at the

fre'uency for hich the phase is zero"

( ) ( ) 100 = jω β jω A


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* #he feedbac( oscillator is idely used for generation of sine ave

signals"

* #he positive %in phase& feedbac( arrange!ent !aintains theoscillations"

* #he feedbac( gain !ust be (ept to unity to (eep the output fro!

distorting"


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Design Criteria for Oscillators

)" #he !agnitude of the loop gain !ust be unity or slightly larger

7 +ar(haussen criterion

/" #otal phase shift$φ of the loop gain !us t be 8x196: here 8;6$ )$/$ <

1= Aβ


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RC Oscillators

* RC feedbac( oscillators are generally li!ited to fre'uencies of ) =0z

or less"

* #he types of RC oscillators that e ill discuss are the ien-bridge

and the phase-shift


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ien-bridge Oscillator

* It is a lo fre'uency oscillator hich ranges fro! a fe (0z to )

=0z"


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* #he loop gain for the oscillator is5

* here5

* and5

( ) ( ) ( )

+

+==

s p

p

Z Z

Z

R

Rs β s AsT

1

21

sRC

R Z p +

=1

sC

sRC Z s

+= 1


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* 0ence5

* .ubstituting for s5

* >or oscillation fre'uency f 65

( )( )

++

+=

RC /j RC j R

R jT

66)

/6

)1

))

ω ω ω

( )

( )

++

+=

/sRC sRC R

RsT

13

11

1

2

( )

( )

++

+=

RC /j RC j R

R jT

ω ω

ω

)1

))

)

/


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* .ince at the fre'uency of oscillation$ T % jω & !ust be real %for zero phase condition&$ the i!aginary co!ponent !ust be zero5

* hich gives us5

6)

6

6 =+ RC j

RC jω

ω

RC

)6 =ω


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* >ro! the previous e'uation5

* the !agnitude condition is5

or

+=

1

)))

)

/

R

R

( )( )

++

+=

RC /j RC j R

R jT

66)

/6

)1

))

ω ω ω

/

)

/ =

R

R

To ensure oscillation, the ratio R2/ R1 must be

slightl greater than 2!


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* ith the ratio5

* then5

K ; 1 ensures the loop gain of unity 7 oscillation K ? 1 4 groing oscillations

K @ 1 4 decreasing oscillations

/)

/ = R

R

1))

/ =+≡ R

R K


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,hase-.hift Oscillator

* #he phase shift oscillator utilizes three RC circuits to provide )6B

phase shift that hen coupled ith the )6B of the op-a!p itself

provides the necessary feedbac( to sustain oscillations"* #he gain !ust be at least / to !aintain the oscillations"

* #he fre'uency of resonance for the this type is si!ilar to any RC

circuit oscillator4

RC f r

9/

)

π =


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vi v

1v

1

v

2 v

2

v

3 v

o

C C

C

R R

R R2

iv

sRC

sRC v

+

=)

)

iv sRC

sRC v

/

/)

+=

iv

sRC

sRC v

1

1

)

+

=

1

1

)&%

+==

sRC

sRC s

v

v

i

β

R R

vv s A o /

1

&% ==


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* Loop gain$ #%s&4

* .et s;j

1

/

)&%&%&%

+

==

sRC

sRC

R

R s s A sT β

[ ] [ ]///////

/

1

/

11)&&%%&%

)&%

C R RC jC R RC RC j

R R jT

RC j

RC j

R

R jT

ω ω ω ω ω ω

ω

ω ω

−+−

−=

+

=


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* #o satisfy condition #%jo&;)$ real co!ponent !ust be zero since the

nu!erator is purely i!aginary"

* the oscillation fre'uency4

* Apply o in e'uation4

* #o satisfy condition #%jo&;)

61) /// =− C Rω

RC 1

)

6 =ω

[ ]

−=

−+

−=

A

)

&13)%1&13%6

&13)&%13%&% //

R

R

j

j

R

R jT oω

A/ =

R

R The gain greater than ", the circuit #ills$ontaneousl begin oscillating % sustain

oscillations


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RC f o

9/

)

π = // =

R

RThe gain must be at least

2& to maintain the

oscillations


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LC Oscillators

* 2se transistors and LC tuned circuits or crystals in their feedbac(

netor("

* >or hundreds of (0z to hundreds of =0z fre'uency range"* xa!ine Colpitts$ 0artley and crystal oscillator"


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Colpitts Oscillator

* #he Colpitts oscillator is a type

of oscillator that uses an LCcircuit in the feed-bac( loop"

* #he feedbac( netor( is !ade

up of a pair of tapped tapped capacitorscapacitors

(C (C 11 and C and C 22 ) ) and an inductor Lan inductor L to produce a feedbac( necessary

for oscillations"

* #he output voltage is developed

across C)"

* #he feedbac( voltage is

developed across C/"


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Colpitts Oscillator

* ECL at the output node4

* voltage divider produces4

* substitute e'%/& into e'%)&4

6))

/)

=+

+++

sC sL

V V g RV

sC

V o gsm

oo

o gs V

sL sC

sC V •

+=

/

/

)

)

( ) 6)) )//

/ =

++++ sC R

LC s sC g V mo

- ' %)&

- ' %/&


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Colpitts Oscillator

* Assu!e that oscillation has started$ then FoG6

* Let s;jH

* both real i!aginary co!ponent !ust be zero I!aginary co!ponent4

( ) 6)

/)

/

/

/)

1

=

+++++ R g C C s R LC s

C LC s m

( )[ ] 6) /)//)//

=−++

++ C LC C C j

R

LC

R g m ω ω

ω

+

=

/)

/)

)

C C

C C

L

oω - ' %1&


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Colpitts Oscillator

* both real i!aginary co!ponent !ust be zero

I!aginary co!ponent4

* Co!bining '%1& and '%J&4

* to initiate oscillations spontaneously4

R g

R LC m )

/

/

+=ω

R g C

C m=

)

/

>

)

/

C

C R g m

- ' %J&


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0artley Oscillator

* #he 0artley oscillator

is al!ost identical tothe Colpitts oscillator"

* #he pri!ary

difference is that the

feedbac( netor( of

the 0artley oscillator

uses tapped tapped inductorsinductors

(L(L11 and Land L22 ) ) and aa single capacitor C single capacitor C "


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0artley Oscillator

* the analysis of 0artley oscillator is identical to that Colpitts oscillator"

* the fre'uency of oscillation4

( )C L Lo

/)

)

+=ω


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Crystal Oscillator

* =ost co!!unications and digital applications re'uire the

use of oscillators ith extre!ely stable outputextre!ely stable output" Crystal

oscillators are invented to overco!e the output fluctuationoutput fluctuation experienced by conventional oscillators"

* Crystals used in electronic applications consist of a 'uartz

afer held beteen to !etal plates and housed in a a

pac(age as shon in >ig" %a& and %b&"


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Crystal Oscillator

* ,iezoelectric ffect

#he 'uartz crystal is !ade of silicon oxide %.iO/& and exhibits a

property called the pieoelectric pieoelectric

hen a changing an alternating voltage is applied across the

crystal$ it vibrates at the fre'uency of the applied voltage" In the

other ord$ the fre'uency of the applied ac voltage is e'ual to the

natural resonant fre'uency of the crystal"

#he thinner the crystal$ higher its fre'uency of vibration" #his

pheno!enon is called piezoelectric effect"


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Crystal Oscillator

* Characteristic of Kuartz Crystal

#he crystal can have to resonant

fre'uencies5

One is the series resonance fre'uency f )

hich occurs hen L ; C" At this

fre'uency$ crystal offers a very loi!pedance to the external circuit here M

; R"

#he other is the parallel resonance %or

antiresonance& fre'uency f / hich occurs

hen reactance of the series leg e'ualsthe reactance of C=" At this fre'uency$

crystal offers a very high i!pedance to

the external circuit

R

L

C

CM


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Crystal Oscillator

* #he crystal is connected as a series ele!ent in the feedbac( path fro!

collector to the base so that it is excited in the series-resonance !ode

BJ

T FE

T

l ill


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Crystal Oscillator

* .ince$ in series resonance$ crystal i!pedance is the s!allest that

causes the crystal provides the largest positive feedbac("

* Resistors R )$ R /$ and R D provide a voltage-divider stabilized dc

bias circuit" Capacitor CD provides ac bypass of the e!itter

resistor$ R D to avoid degeneration"

* #he R>C coil provides dc collector load and also prevents any

ac signal fro! entering the dc supply"

* #he coupling capacitor CC has negligible reactance at circuit

operating fre'uency but bloc(s any dc flo beteen collector

and base"

* #he oscillation fre'uency e'uals the series-resonance fre'uency

of the crystal and is given by4

C

o LC

f π /

)=

2 ij i O ill


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2nijunction Oscillator

* #he unijunction transistor

can be used in hat is

called a rela!ationrela!ationoscillator oscillator as shon by

basic circuit as follo"

* #he unijunction oscillator

provides a pulse signal

suitable for digital-circuit

applications"

* Resistor R # and capacitor

C# are the ti!ing

co!ponents that set the

circuit oscillating rate

UJ

T

2 ij i O ill


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* .atooth ave

appears at the e!itter

of the transistor"

* #his ave shos the

gradual increase of

capacitor voltage

2 ij i O ill


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* #he oscillating fre'uency is calculated as follos4

* here$ N ; the unijunction transistor intrinsic stand- off ratio

* #ypically$ a unijunction transistor has a stand-off ratio fro! 6"J to 6"9

( )[ ]η −≅ )3)ln)

T T

oC R f

O ill


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ECES 352 Winter 2007 '2

Oscillators

* eebac* am$li+ier but +reuenc e$enent +eebac*

* -ositi.e +eebac*, i!e! + ( ) ( ) 0

* scillator gain e+ine b

* scillation conition at 4 o (ar*hausen6s criterion) + (o) 4

( ) ( )

&%&%) s A s

s A s A

f

f β +

=

&%&%&%

)&%&%&%&%&%&%

oo f o

joo f oo f o

Aof p"ase

e A A L o

ω ω β ω φ

ω ω β ω ω β ω ω φ

=

===

( ) ( )

&%&%) s A s

s A s A

f

f β −=

i + id O ill t


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ien +ridge Oscillator

* ase on o$ am$

* Combination o+ 6s an C6s in

+eebac* loo$ so +eebac* +actor+ has a +reuenc e$enence!

* nalsis assumes o$ am$ is ieal!

8ain is .er large

9n$ut currents are negligibl

small (9: 9; 0)! 9n$ut terminals are .irtuall

shorte (etermine +eebac* +actor!

>etermine gain #ith +eebac*!

* Shunt?shunt con+iguration!


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ECES 352 Winter 2007 ''



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@1


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ECES 352 Winter 2007 'B


( )

r f

r rf

r r f

A

A A

sCR sCR

sCR

R

R

sCR sCR

sCR R

R

R

sCR

sC

A sCR

sC A

β

β

+=

++

+−=

+++

+

+−=

+−=

)

isfeedbac(ain ith

&)%)

&)%

))

)

)

/)

/

/)

/

Aoo$ 8ain

scillation conition

( )

/)1

))

usingelyappropriat

and resistors theselecting by)getcane#hen$

)

fre'uencynoscillatio at the 6ter!i!aginary#hen

)1

))

)1

))1)

)

/))

&)%)

Reriting

)&)%)onlyneed#hen

6" since isalreadyIt")A6 toe'ual of ,hase

)

/

)

/

/)

)

/

)

/

///

)

/

///

)

/

/

)

/

/

)

/

o

==

+

=

==

=

−+

+=

++

+=

++

+=

+++

+=

++

+=

=++

+=

<

R

Ror

R

R

R R A

RC

CRCR j

R

R

sCR sCR

R

R

RC s sCR

sCR

R

R

RC s sCR sCR

sCR

R

R

sCR sCR

sCR

R

R A

sCR sCR

sCR

R

R A

A A

r f

o

r f

r f

r f r f

β

ω ω

ω ω

β

β

β β

i + id O ill t l


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ien +ridge Oscillator - xa!ple

scillator s$eci+ications o41D10B ra/s

K K R

K

srad !n C R

RC n C

o

o

/6&)6%/

get eR /R sincethen$)6R Choosing

)66&3)6)%)6

))

) fro!then$)6 econveniencfor.electing

/

)/)

9

====

Ω===

==

ω

ω

i + id O ill t


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ECES 352 Winter 2007 '"


inal note No input signal is needed. oise at the esire oscillation +reuenc

#ill li*el be $resent at the in$ut an #hen $ic*e u$ b the oscillator #hen

the >C $o#er is turne on, it #ill start the oscillator an the out$ut #ill

uic*l builu$ to an acce$table le.el!



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ECES 352 Winter 2007 '&

ien +ridge Oscillator* nce oscillations start, a limiting circuit is neee to $re.ent

them +rom gro#ing too large in am$litue

,hase .hift Oscillator


50/56

ECES 352 Winter 2007 50


* ase on o$ am$ using in.erting in$ut

* Combination o+ 6s an C6s in

+eebac* loo$ so get aitional $hase

shi+t! Target 1"0o to get oscillation!

* nalsis assumes o$ am$ is ieal!


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R R

so R

R

C R

RRC RRC

* RRC

) L(*

so ) L(*

RC so

CRCR

CRCR j

RRC

CRCR j

CR j

sCR sCR

sCR

V

V A L

sCR sCR sCR

V

f

f f f

o

f

o

o

f f

f

f

o

)/

))/1

)

JJ

get eforngsubstituti and)J

)need also ens$oscillatioget#o

1

))1

so fre'uencyoneatthisachievecan*e

zero" togo toter!i!aginarytheneed ens$oscillatioget#o

)

1J&%

)J

1

)

&%

)J1

&%&%&%

gain loop for thegete

&%

)J1F

gRearrangin

//

///

6

//

6

6

o

//

/

/

6

/

=

===

==

=

===

−+

=

−−

−=

=

++

−===

++−=

ω

ω

ω ω ω

ω

ω

ω ω

ω

ω ω

ω

ω ω β ω



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Colpitts LC-#uned Oscillator

* >eedbac( a!plifier ith inductor L andcapacitors C) and C/ in feedbac( netor("

>eedbac( is fre'uency dependent" Ai! to adjust co!ponents to get

positive feedbac( and oscillation"

Output ta(en at collector Fo"

8o input needed$ noise at oscillation

fre'uency ωo is pic(ed up anda!plified"

* R +) and R +/ are biasing resistors"

* R>C is R> Cho(e %inductor& to allo dccurrent flo for transistor biasing$ but to

bloc( ac current flo to ac ground"* .i!plified circuit shon at !idband

fre'uencies here large e!itter bypasscapacitor C and base capacitor C+ are

shorts and transistor capacitances %Cπ andCµ& are opens"

C+

C


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Colpitts LC-#uned Oscillator *


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ECES 352 Winter 2007 5'


* #o get oscillations$ both the real and i!aginary parts

of this e'uation !ust be set e'ual to zero"

* >ro! the i!aginary part e get the expression for

the oscillation fre'uency

* >ro! the real part$ e get the condition on the ratio

of C/3C)

( )[ ] 6) /)1

/)/

/

=−++

−+ C LC C C j

R LC

R g m ω ω ω

( )

+

=+=

=−+

/)

/)/)

/)

/)1

/)

)

6

C C

C C L

C LC

C C

C LC C C

o

oo

ω

ω ω

R g C

C

C

C

C LC

C C LC LC R g

R LC

R g

m

om

om

=

+=

+==+

=−+

)

/

)

/

/)

/)//

/

/

/

))

6)

ω

ω

Colpitts LC #uned Oscillator


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* iven4

Design oscillator at )Q6 =0z

#ransistor g! ; )66 !A3F$ R ; 6"Q E

* Design4

.elect L; Q6 n0$ then calculate C/$ and then C)

( ) srad ! ! f o 3)6J")6)Q6// A9 === π π ω

Q6&Q"6&%3)66%)

/ === K V mA R g C C

m

p p C

C

p ! !n+ C

C

LC

C

C

LC C LC

C C

o

o

/1Q6

)16$)

Q6

)16$))6)1")&Q6)%&)6J"%Q6

))

)

))

/)

/A)

///

)

/

//)

/)

===

==+=

+=

+=

+=

−

ω

ω

xa!ple

.u!!ary of Oscillator Design


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.u!!ary of Oscillator Design

* Sho#n ho# +eebac* can be use #ithreacti.e com$onents (ca$acitors) in the+eebac* $ath!

* Can be use to achie.e $ositi.e +eebac*! With a$$ro$riate choice o+ the resistor

si=es, can get +eebac* signal in $hase#ith the in$ut signal!

esulting circuit can $rouce largeam$litue sinusoial oscillations!

* >emonstrate three oscillator circuits Wien rige oscillator -hase Shi+t oscillator Col$itts AC?Tune oscillator

* >eri.e euations +or calculating resistor anca$acitor si=es to $rouce oscillations at theesire oscillator +reuenc!

* He result scillator esign e$ens$rimaril on com$onents in +eebac*net#or*, i!e! not on the am$li+ier6scharacteristics!

Wien rige scillator

-hase Shi+t scillator

Col$itts AC?Tune scillator

Oscillator design.ppt

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Transcript of Oscillator design.ppt