© RAJ~"~U'MAR SRI~/AS~~VA,

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SOFTWARE

CONTR~LLED

^{DELTAPWMiNvERTER S}

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© RAJ~"~U'MAR SRI~/AS~~VA,

^{B.Se.,B.Tech.}

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.Fa~ult.y~^ofEngin~ering,andApplied Science

, Me,morial·Univ,erSit.)'of Newfoundla.nd' .~,/~

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copies.o e.the fUia.,

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zero-hysteresis,bang-bangtype ofcontrollers,.Such .ystems'arcwi4elyusedin

coIl].lllU~icatio.p: _{-' .} ~JlId,.;Dlltrume~t:tion·-·apPliJ:a:UODs fo~ cn'~i~g b~d-limit~

^ana:

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ratio

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-:.,'-con_trolaD~loworde~hemcn le att enuation ofmodu1.:Io~cdout put arcsomc,.of\ho- ,'

a.tt~acti·~etatur~ o~ d~i~modulation ~~i~h

^'c'an

b~' employe~

^involtage

'~ntrol'

^•

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..'ofInvertersandi,~~.ti~el'3. ^{,, '.}">;~~

•Delt1L.

~~ci~l~t~d vol~age ~urc,e iriv~~~~~,-T~Plem'ented '·b~·.:a~~~~~~~~s>-~

.'bave

sh.o~~ 'i~~~v~d' ~~f~rmanc'~ over~conv~~tio:nal P~M invert~~,

^{,Howev.or. .' -,:;;}

software

'~ntroll~ d~lta modut~ted

^{inverters.require}

less,'~o~pie:i, controt~i'~~'i': ;~i

try

a.~d ofJe~~ ~asi~;~~ri~ro,1 Of',~;~:p~amet~. ~.b ·~ht!iS is 'th'~ ~~Ud.r ~'~

^{the .}

:~',~ l

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-perrorm~n~'e

^orvoltage

so~~ee inv~~!S

^using

dia-ete~t, typ~ ~f

delta rOOdulation ',' ..

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Contibuo~s

^{time·variablesof}dJ.!itll. modulatOrs

tran9fo~med'

^{'into .}

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ti~e ~~~ai.n A~,Abl~

^to

~enera~'swit~hing ~avdo~m; .to co~.trol

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sin~h~ ':::j

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ph~e^.voltage~~rce,.inverter. Three tYPei ordelta m~~ula.tion.^stmtCpelare'

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^results

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a. modulati~n'

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2.4.3

O~eri08d

Characteristic ,",1

. .' 2:5

AP'~l1cation" or\?~ Te~hDiqu~ I n lnvert~rs :~

c~~

^3:

SOFJ~LEMENTATION ^OF

3" DMsy.te:EL~:p~~:~I , ON ^'

3',1.1 HardLimitei, . . 3.1.2 ~Digital to Analog Converter. 3.1.3. lnte,;ator...· --

) 4'

. 3.1.4 Erro,rD,':te~tor\, I' .3.2'OMSrstem De9lgn \

3.2.1'.OM,SystemRequ~~ents _3.2.2.,".P'\V.M,Cont rolRe~",~emeQts 3.3So(twareImplementatioo',of"DM Strategies

.. 3.3.1 Linear Delta Modulato r '. .~

,. 3.3.ili.'·,'A1gorlthmDeSign.

j\. .: .

.'a.3.1b_:p~()p.am

Fl ow

Char,\ .' .

,

~:3:3.2·

^{:'Ei"p'onential}

Oeita Mtod~latdr

^•

3.3.211.:Alg~rithm^{Deeiga.:1,·-'.\ .}

L

3.3.2b.PrOgfam:Flow··Chart 3.3.3.v-5igtryll.Delta

Mo1u.lak~

^{I, •}

.,...

3.~.3a ·.,

^Algorithm

-~

^Design"

J ,. ' . '

"3.3.3b Program Flow

Ch~

^{" c.}

. ~L ' ! RE~tiLTOFS~TED\iELTA ^{MODULATED r STEMS, .}

4.1

~C IDPU~"ResPQD"~~

^{. """- ' :\}

"{ SystemResponseonParameterVarlat!oP9

4.~,1

Variatio n'in

In~t

Frequency\\

4.12 VariationinSamplingFrequency 4.2.3 VariationinSte~^{Size(.6.) ,}

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118' .156

'185 1~~, ^•

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158· "

.:.6~· 163.

'".,165

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6.1"Sumrrl&ry

·6.2'_CODClu,~i.~~~_

6,3-Recommend'a~i9DI"forFurtherResearch."

,:.APPENDI)(: PR'f'RAMLISTINGS.

Linear DeltaModul~tor

ExpODeDti~-DeltaM?dul.ator Si~.aDelta

A:ie:dulator

."~ . . , :,. :" 'I ^'," " <"''''T rf'"'"'':' ''V>':''' :':'~"';"i",,"'C' : '. '""':':'1 .:' "

^;,,,,,,1,

::,'!f;.~<~T~,,\.

;:;;',~;

CHAPTER 5:~ERlMENTAL RESUL~OF SOFTWARE : ••

, . , CONTROLLE~DELTA.MODULATED SYSTEMS eo

· _ . ' 0

. ,,1 '

5,1 OperatIOnalCbaracteristies of QifrerentOMTechnique!. 6.1.1

~

OutputandHarmonic Content·

..I

5,1.2 r:l)mber or Commut.,iorl..,J ·

' I

5.1.3 AvailableVoltage .

5.2Single-PhaSeIDvert~r withResistive and Motor.Load 53 Merits of SoftwareCont

. ^'.

rolledDMItverters

. . ,

CHAPrnR.: SUMMARYAND CONCLUSIONS

'I

I . •. :. ', ' . ..

Calculatlon,ofNumberof Commutations in a Linear~e~t~Modulated Inverter. ) . Calculation"ofNumberof Commutations.ia an"

·ExponentialDelta ModulatedInverter...

CdculatloD orNumber1)rCo~uiaiiobs

in"

S~gmaDel,ta,~odula~ed ~~_.~~.~~~~_-.::

" \

\FourierSeriesAiialysi9~r ~he^OutputWav~(o~~.r.,a:·"

\L~earDeltaModul~tor

;:i'~f - ,' .

"1¹'. .

\Fourie~-Series'·~aIisb,or.lhe .o'_utput Wa,::~ronn ~i ^{an '}

r:,:·"

\~~nential}~elt"Modula?:or. ~ ".-~ ^{fl " ' "}

r ···· I . \.

'\ o' ",. , :: _{,,:~ , ~,\: "} ,:.A".,:~!),·: , ^{.. l>}

•43'

l ' " \ " .

-t:

37

46·

47 '8 11 I ' 16

'Is

",.

~

",

. .

.20.

"33.

-'-22 Page.

•30

.<

I

_I

,.. ..

_.

} . Figurep tle

L1STOFFIGURES

Line u.Delu.Modulator

.

.

~

·I~Ung Cbaru~fisfj:o,r~~.M ..

l. .', ' oVerlOad

Cbara.eteristieolLOM,~:

'Exponcllti,uDelt~Modula'to'r IdlingCheracteristlc of~DM

.

^.

IdlingW~ver~rni'~rEDM. .

"LnM

' / ~i~~te~a~~

^..'

.

^at'the

Inp~t' .

·Sigm aDeltaModuJalDr ", ' / '.

. .. .. .

IdliD~Cb~-,:teristicofSDM

·Rectan gul ar WaveMOQulator

. .

^.

.

Singh!PhaseBridgeI,D;erter -Transfercbar~teristicoC•Hafd'Limi~r

'Input

~d ~;tp~t Wav~r~'r~

^.ofa

~~f

~n.itImpulseRes~ns~~~r.~bH Gain'and PhaseCh~acteristieof ZOH

·Frequeh.cy~e'~~~s~of an IdeelIn~gra.tor

'no.O~.AMP..lntegr.ator

. . . ...- -

,

s-domeinRepresenta~onofOP-AMPIntegrator", 3.6

Fig.No.

3.7

·3.4 .3.5' 2.1 2.2 2.3,

< ,2.4.

2.5 2.6 2.7 2.8. 2.'

2.10 2.11

.3.1'

3.21 3.3

9~

.'\'4.5 '-,'.-.LDM:Waver~rms

. .

^{, '} Cot^'r=^\40Hz

4.6

··LDM

Wavdoi-;;ns.rOt'r=125Hz .

·~.7:; J;ri;;;.;i{:;>,:_~?'~ ~~v:~r~.~~,8,(~~ ^r

^{=20 Hz}

'48:'·""· ~·~·' 'v·, EDM WaveformsCort=40Hz

-":,,,;,.~'"'.

i-~e'queni:~ Re~,~nse.or aP~sive

^{RCIntegrator\}

~.D.~~~~ -R~;;es~ntatio~ o~

^.a

P~;i~e

^{RCIn·tegro.tor}

".MlcroproeesecrBesedo.e"t~.Modulaiedin~erter LOMin.e-Dcmain

.4.2 4,3

4.4"

~

"

,:~i~ re ntle'

1:,pa:sive:RCIptegrator.

~' ".'Plow

..

0

. iagrarn

o(

^..

LOM

^{. .}

'.~D.M:inz-Dornain:

FI~w.D.i~a.m

or

EI?M.

.~DM.in.z-Domain FlqwD.i~am^ofSDM

'...,

.; ' :.

". - ',: .

C~MWa.veCorm,tcrDCInput

,

'_1ED M"Wa~e~o~R!'s(or,I?CInpu t. SD~ ~4ve'rorms(o~DC~nput.

'L~M ~ave'~orm~ r~r

^r=

^{2 0}

^{'H z}

-.••;Y,

·.~~ge 49-···

,0,

" 51 56' ,57

5Q

" .

,M

,1)2

"

⁶³

65 68 68 60

71 71 7' 7' 73 73

\

Fig,"No. Figu rentle I?ag~

4.11. .SOMWavefo rm s·rorl

==

40He-" 74

4.12

.~D~

^{WaveCor ms(or(= 125}

H~ '

⁷⁵

"',

^{4.13 LDM}'.\'avero~s(or r,'=1600Hz 76

" ~'

~.;

4.14 LDMWa~etormsfort,~4800Ih. 77

4.15· LDM Waveformsforr,=20 KHz 77

:1:16 •

^{EDMWaveformsfor}r, :::::1600""'fil: 78

",1,17 EDMW~verorms^torr,'='4800,H~ ^,78

',1.1 8 ~'W ave(o qll9' Iorr.=20KHz 7'

·:-'4.Ht SDMWaveforrns (or 1'.

=

1600 Hz 7.

~,2" ^{', ,} \

SD M_Wevercr m efort,

==

.4800.Hz' 6.

j ,80Mw,v<!a~~ra'!:trh' ^6.

LDM Waveformsfor6. 0.2- .',.- ../ 82, 4",23

' " " , '1 ' ;,"

8'

oLDM Waveformsr~rtJ. 0;7,.

4.24 LDMWaverorm~r~r^tJ.~^{3.0:• 83}

-. " ' .

^--' _.'

7"""4.25 ROM WaveformstortJ.=0.2 83

4.26 EDM

W~ve~~;~s.

^CorA=:=0;7

"

I

4.27. EDM~~rormsto;~'1:::::3.0 ^~ 84

. , -

SoM.W.a vetormslor~

=

0.2-

'#

8DM WaveformsforA

==

0.7

..

^{' Fig.No.} Fi.gure TIUe Page 4.31 H"a.rmoni c Con tentof LDMou tput1=20 liz 88 4.32 -cvm oni CCon tento !LDM outputf=40lIz 88

4.33 .armoni~Con tentofLDMoutpull= 1251h 8. ~ 4.34 ran;;onicContent ofEDMoulp ut

r

⁼ 20IIi 8.

4.351 Hermcrric Conten t of EDMoutput( =40 liz 00 4.36 Harmon ic Contento!EDMoutputt

=

125liz 00

" .

4.37 Harmonic C:n-tentof

~DM

^output

^r

^{=21)Hz 01}

\ .

4.38·· Humon-{e Con te ntof 8D.Moutp~tf~40 Hz OJ 4",ag.: HarmonicContentofSDt.;1Qutp,"!tf=125lIz 02

5.1; , . ,-.

_LDMIuputan~"OutP~t-¥(~vCr~~m9^ror'>

f=:.20, 40,60,Hz -. . 05

,.5,lb LDM-Jnputand'OutputWa~cro~msfor

'.=:= 80,~rO,:12~, ~.z. 00 \,

" S.le "L DM Inpu t"and-Outputweverorm efor

t

=

140 ;160.180,Hz '7

5.211. EDMInput,~~'O~tputWavefor ms for

.

^{r=-20, 40,.60,}

^'H!.

⁰⁸

5.2b •EDM Input and Outputwevcrormeror.

.r=,~~,'100,)20,"Ifr. 00

S.2c EDM Input andOutput.Waveform s for

.r

^=/4',160;ISO, Hz

,I ,

'00

S.3a· 80M'Input~dOutputWaveforms'for.'

r":'"20,40,60,H~

1

^'01

102

'

. .

5Ac Power Spectrum or LOM Outputat.

f=.145,160,180 Hz

113

116

P aif/

1Q3

105

106,

10 7

108

')

'100

110

, _t

l l PowerSpedrum'oCLOM'D.utput"at.

r=20,40,60 Hz' Figure1lt!e

SOM Input.andOu tputWavefo rmsfor r='140;160 , 180,Hz

Pow erSpect r um ofLOM Output.at r=80,100,120 Hz ' -

Power SpectrumatEDMOu tpu tat.

r=:= 2D,40,60Hz" . " .1

'Po~r^{Spectru m}

o r

^{EDMOutputat.. ' \.'}

t=·80,100,-120 Hz .' . .

. \ ' . ~

PowerSpectr,u m"ot ED'MOutR,u tat ,'f

=

180and 200 Hz

P~wer SpeCtfU~'

^cf

SD~'I"o"~tPut

^at

f.-=20,40,60HI,.,....:

Pow~;

^SpecfzumoC

8 DM _OutP~t d

t.";~o,l~O,-i?oHi. .

~owerSpecfzum .ofSDM~6utput ~ t=~45;l~O,ISOHz .

r

"

'Frequ~n~y V,.

^No.of

~ .'m·~u·~tions,.

^{R=50'K.Obm·s}

C=0.05Mirnfarad.s,t,=2000 Hz,Delt.a.=U.O . 115

.

^{' . .. ', : " .}

FrequencyVs.

N o.

orCom'm'utationS';\Ji"';'S()~-Ohms C=O.OSMicrolarads,r,'~,4000Hz,D~ll&= l.O 115,

•

.F~quenc~_V~~'·N~.-,~r Co~nl~tatioD~,: ~=50

^K-Ohms

,...., .~O.oS,Mlcrofuad s',.r,

=

6~OOHz,Oell&=1.0

J ' ..'.: .

5.3c Fig.No.

5.4 &

5.5c 5.S..

5.6c

5.7 ;, •

5,~..

"5.5b. ,5.4 b

'5.6&'

,5.15 InverterOutputVoltage and PowerSpeetru~

of.LDMror f~100Hz .

---=~ ...

Inverier'Output VoltagesndPowcqSpcct rum

0>....-,

^o(LDM(orr~^{120 Hz}

5.17 Inver te r OutputVoltageandPowerSpe~trum or LOMIort= 1,40Hz

5.18 Jnverte~OutputVqltageandPowerSpectrum orLOMforr= 160Hz

. ...

Fig.No.

5.10

5.11

5.12

5.13

•

5.14

s.rc 5.2Q

5.22

-xiii·'

.FigureTItle

Outpu tVoltageVs.Frcq~eneyCbaracte ristics oCLDM, EDM,'and'SD M

. /

.

Inverte r Output Voltage and PowerSpectrum~ oCLDMCor.C

=

^20Hz

Inver te r Ouipu t,VoltageandPowerSpe ctrum ofLDMrorC=40Hz

r«:

~--..

Inverter Outpu t.Voltage end PowerSpe~lrum orLDM ror.r= 60H z

InverterO~tputVoltagtlandPo~erSpcctrum otL~ ~ rorr=~OHz . - ,.t,

Inverte r OuiputVot\..li.ge and Po"werSI;edrum ofLDMC9rf

=

18bHz.

Inverte r Output'VoltageandPower Spectrum of LDMfor(= 200 Hz

In; erte r Outpu tVoltageand Power Spectrum oCEDM(or( =2.0-l'lz

Inverter Outpu tVoitageand,Pow~'rSpectrum

?CEOMforl= ~~'Hz'

inverterOutputVoltageand PeweeSpeetrum oCEDM CorC·~60Hz ' .

.~ ^/

Page

117

120

121

122

123

124

12G

126

128

120

130

"

,\

"

Figur~~~e .. xe - \

.."7

:

.. . .

InverterOutputV~1l4geandPowez Spectr um ofSOMCo:'r

=:

20~Hz . . ~ '

LDMI~ver~;OutPutvoltag"e,^Current,andp~wc;^Spectrum ro~ ~of?r^LcedCorr=;=.~Q Ih.~. ^{.. '" "}

LDM Inver terOutputVoltage;Curf~n~~dPower Spectrum'

r~rMotorLoad

rOt.r

⁼~OHz. . .~_~;: ;

.

DM ID~erter Ou~~ut Voltage~-C~r;e~~'

end Po.",

I,..

^etrum'

':10 olorLoadCo rr;'"60Ih . . Inve rterOu(putVol tage andPow~f"Spedrum

o(SDM tor(-= HSR z .

IDTcrter OutputVo lt&geendPow~;Spee~m

Q

_{~~ SD~}(or4=~60 HZ'.

Inver~r'OutputVoltageandPowerSpectrum ofSDMIcrr=180HI: ' .

05.4.2

5.44 L~I.

r~r Mo",?r

5.45 Ll) MtDY~;ter Obtput.Vol~,·C\l~,en·t.;andPo~'erSpcc:ir~m

"IcrMotOrLoad(o r

r

^{=100 Hz' . . -}

SA3 5.38 5.31

5.39

5.4 1 Fig.-tI!o.

SAO

'''' '~: ::'' ' > ":.]'; ' : " !' t\' ^{" ':;-" ":} "" (/,C""::'" 'i" "'l; "~~~,·~:¢;(;, ,,

" ' ' " ," , . ' ~, .r . ^'

_.»cee.inTtrt enliet~e~k~me;)rdevelopmentSinmtdu,latlonatntliie,s.·_v~.

'~l1!

real-time aai

oll'-~,PWM

.trdegies

havebHD.

Propated.·an c1 liri

plemtlllecl

..tb ,"

-~tb

^.digital'

an~~~~ ~e&M. '~:t~ p~~' ~ ;~&n' ~.~he~·:h~y~

, q .. :~ ^{P wM} ~d ;ub'~"lly d oli. _{,~ ;,~~m} ^{.. ro;} i~,;ri~. ~PP~;~

-tio~.·^Extensive~~chOQ_th~,^:Odul..tio~^acbe'mea sbowedi.mP~';ed^perlor- m&b.<:= of~~It.9:g^•...,urc~in'9'e~en

over

other~~?~n~tioD&l.•oltB.geiource'lD~;ri-o^,"

Sine PWM tethniqueh8.s"beenan~ea01 researchtor'theput.lllvera!yean• .i,his'

techni<l~e

^was'flrst

pr~poM~ ~d

implemented,

~ u~iQI-lLDl1lol' C~I;1~ae~tI.

: .

Mierop~essor:~~ed·· si~e PWM,aid oPt~b~c:LPWM.

^Inverters

wer~ I~i~~ 'p~

~ .~ed: Mic~p~r4a~r.b~,~ ~ ·~:u- ~ . ~al~l ~';ne p~ ·~v~rte~·~:v~<~.~~D

^.

< . :'

goOd··~erro~..a~~ Ho~eYer.· .^{lnY'ert en,employing} thismodul.iio~ I~beme^.

. "',. ~.;'. '. . . ' ! .." .,' . . .. '.'-

t . ' : :' " . . ,

^t.

.'requ6ereft.tively complexecnt roldrtuitryandheD~elnvolnUsoc:~~dco-~: -...

' ,

In-tb~-~'~i~r~~~~~~>de1ta.~~~I'tioD:·,e~~m~- .hU" ~~ei~ed· ~t~.~.;iO~l.

^{in.. "}

: .0. · of·

,, P~ in;"': ',pplleallo... Th< ~i.'''l ^b d"~

^to

~..;o .. '';h.~., P';'~ .rit" \l ^':. ' ; i ,', :::::u:;;:u::;t :~i::::::~~:.:~f~::~f~~l~:~.:::~::; :~'.;' ' , '" ^{' : 1}

-. An~r i.IDp!;menia!I~D o r ~elt,

^modu.'atioD.seheme

~Il~

^ita..

~uie rea~tI~ in

" r ,I, ;, ' ;O ll.;g. ,ou,,~i~';rl.';; h~~' b.~.'reporl.l(i.2J, How.~,,!

^itsdigi'.iimpl.m';'" "';;

; \ _{' ~:::Z~} :::u::'~:o:b::::::',.,:::mi:·:·p:~::~~.~;I;~:: ,:":

t~.\ . '~;,.ms'(1.3J'~'U "~UI~

mOlbi'e<!res

""he" ';; ~'~IiI~;"lh.~ibiJl'r ,~I:

^{',. 'f}

~. ..-J. ~

~ ~L~:i~~~;;;;;~;;L'-;\l :1;ZiL,;, .;:~;,~L;~~) ^{L-J.;; ',"} ,~';.i:;;,),::,,~G. " ij;:;~~ ;,J

implementing delta modulated PWM inverter with microprocessor control. • 'Software

'~ontr~l ~f

^delta

modu~a.tion

^offerseaseof

v~iation

in eontrolllng

pati¢ .

et(!rBandopti~izationofsystempertormance.

,~ ' -' ,

,The mainobiectives.ofthistheSm areto identify var iousswitc hingst rategies for delta

'~od~lated

_.

. .

^PWM

i~verte1s ~d . .

^develop"

~'suitable

method ology

to

gen- er~te.deiia modulatedsWit(!hi~gsignals undersoft ware.control. An~ther^cbjec- ,tiv~',is^f()examinet~~speCtraJ,clia.r;cter~ticsof existingmodulation syst ems in the..

con ti!~t '~t'P'W~(v:o.lta~e ~oil~:~'.inve.rt~rs.

Such a'syst em-can be

chara,c~eriz,ed

....sere

·1;Y" ';~i;.

b"g:bang

tYP. ~

^ontroll.".

:' ,.•.•" ',. '1""'~'''' ^{"" . ',' .. • ,, _}

T~e':~~~f~:V,.~~ctions:.of.t~i~.:c.~~p,te~alwi~h'&~rier descriptio~,or _I~teta- .t~~o.re~i~;"'r~I.low·ed

b y

_6bje~tiv~:of lbepres.ent~~rk ,and^thesisorganizat~?n.

• io.;",

and frequency co ntrol and minimumtoler able harmonic

. .

'T(~"'"''' ' , ": " '~" -, ~~ : ' : " ., ~.: ". , ',, " '," , ' " "«::~',?

\ . . c'l

perfOfjanCe inin v ertera.ppliea.t~on9~7Iil.The SP WMisa. variati on o.r i^~ultipl(l pu lserIJodu lation where thepulsedurat ion'andnum ber ofpulsesper half cycle are

det~r~i~

^{by-comparinga}

~odllJing

^{sineww eend}a triangularcarrier'

, \~

, ,

, i / .

Atfirs t sine pulse widthmodul ation

18-'3

incorporatedinesync hrc aous PWM mode and.la ter,the srncbrcncus modeo~this~WMtech nique wasin.tr~du ccdI

lnl. In asyncbronousmodethe sinewave

'i~

^{comparedwith aconstant}

rre~u(!ncy

carri.crwave._The

~isad·vantage-.or

suchoplJra tionis that

'~it~ con~tll.nt'·rreJ\1en~y

carrier,

..

the

;n~io

^,"or

si~e ^""

^..and

frian~Ular ^, 'wav~ ^{' \}

Irequcu ciee^"

Cll.~'!lot b~

^{, ',}

~lLintni'~ed

^{, ' , at'}

a~.^{Integer"Vll]UC..}TP.l~,~iVC~.

r1S:

to.sl~-,ha.tmo~~9s^{at the}mY'~,rte~, ,~,~tPllt!",,:h,ell',-, 'heIrcquen cy-r aticis

ri,e~ the,d~I"di~,e,g.)\

^{value. Th':,ohlemi,}o''''of,,: In, synchronizedsine PWMmode wbe rethe

_,

carrier

_I

wa.ve

~requen"y

^is

_{. '} ~ied

^.with

_.

the,m~d ll !ation' "...e Irequoncyt~ ~eep.t,h~,rf~qu~n:CYratio,t othedCs!~cdinteger

vpl~e.^{How ever,}'t1;~s',~ddilionnl'req~iretnen·t\lor, synch roni zedP~Moperat~on," ': .

. '.\ ' , ' '

complicatestheim,plen:entati~nofsu ch,a.,tec hnique. :The pri,cl p a! dis.o.dvantagli,

. . . \ , .,V •

of,synchronousSPWM technique Ist~ll.l thc,c&rr~crfrequen cy.must vary-ove rIi

. . . I . I

",'~.Wide.rl1~,geas.th~outputfr equt'ncy·chAn~es. ;Wi~e~n~iationi~carrierIrcquency

<-is·not very

pra~ikal '~pcc ially

^ininverters

rOt,~C

^mota;

dri~e

applica tions:Furt h-

.. , i' I' • :" ,

.erJ!l0~e!^{n.s the,}~~rrier~r.equeitcy^,isi~cre.o.s~d.^ithe~,umbcr^orco~.mutations.,.,per cycle·in:ireas es,·whic_" h in,turn_'. gives riseto

in~re~ed, ~oinmutatioD

_{i-" "} ^'losseshi'

th~

, <

. . \ .

'" Theanalogsine

PwM

^{techniqueisbeeed}

on'-~~~ural

^{samplingorthe refer-}

:

.' ''; .,

',.', '. '.'~'. .

.. .... . .

eD.ce.,sign~l. ~o!e~~r,'microprocesso~~~~~fsiDe.p~ tecbDiqu~[12-151require

widths prop:~rtion'altothe~p~iiudeorthe m~~i~in~

w ave.

Ai;~lhe;'PP~"'h,b"'ed ~nlh; minimi.li~d)r ,erl'~ ~errorm_"'; Vari:

.' ". : ,', ,' ,:'\" '.,. ' . . , .

ab!e,,:;usedoptimal,PWMswitchingstrat~e8 Il~18J:,~limin,at~onor.minimiza...

ti~~

^or

p~ti~iilar ha;'~~ni~;~ ~'~i~'iz~ti?D ~rr,~ar~6ni~' ·~u~e.~~,·,d~torti?ti, :pea~' CU~fe~'t;krqu~'rip~ili et~;, ~e ~~eh~a:m~l~>:~1D"'corit~t" to th~ 'n'~t~;~;~~d

^reg:

rier'frequen cy'maiDtainsa, c;nsta~,-=i~vel.duriDg'tl:i~ iiJ.ter·'~arriple^·perlod:.A3a

.:. ,; .'. ',.' .: L " .:\ . " ....'". , . ... ".. ,--'

result,o:,th'is operatioD,theoutput,sinePWM.s.witc-bing wevercrmehavepulse:;~

. " . ' ' . ' .,<; ' .

.high carrie r rreque.cythroughout.the operat.ing railge,.~her~~y .prod,~gonly high trequencyha.rmonics atthe output or theinverter."Thesehighrrequency.

~ . ' ' .f . .

harmonicsare~ilyli.lteredoutin..emotordrives,

',:;

Recently,del~amodula~i?ri::~ho.iques ^rorres~n8.n\link"inve rters havebeen - .. .reported

(2~231.

^Since

~~e

rre<l,uco.cy

of'switchi~g p~ttern

^isgcnero.lly

l imil~d

^by

- .-

/ - ,

.

T hemostrecentteehnlqueto"(eneratepulsewidthmodula.ted!witch inlli~- ow

~

^dult,"

~ul.tio."

^WUOtial;Y, delta modul.;io."eeh, ;qu"

~

^eve1>"" used

-- \t "' - , • '. .

in

di gital

eomlRunid Uonteconnti aulogsiVJ1als'intodigital~~before

" -

. ,

tr:~T.ission 131~~ed~lta.modula.t ionte~hniquerequites. a very!im~eCir~uit.

implemeDta,tio~.,~roYid~^asm~th^{trenstticubct_rWM}and single pulse

> . ...

modesof,opera t io n11,2J.Italsooffel"9.~onstan t .vOI~pe~ertzopl!rlltionwithou,l.

the need:ofa~~~tional~!rc~iteompl,xity.Theinherentcharacteristicsofdel~n.

--modulation

p~c;~ '

^arethe

~iri~ar ~.aria.tion·

^of

rlln~lL;entnrVOI.tn.r

^{wIth Ire-.}

.quencyup,10bpsefrequency and

con~'nt vol~age

^beyond

_t~e

^hase

rr~qllcnc~

^.

.Thes~

.

in

..

turn

.

provideconst~;'_torque' ... chraeteri. . . .stieup

. 0

bMe,hcqucney·. ^'

. .

and

COll,.'lta~t po~~r_.Characteristie 1?ey~nd t~e b~

^{frequency,The}

"lU"mo~ie CO~lent

in delta -mod ulat ionis.l!9;"a nd thedominan~h~rmonicsare'at or neilrhighc~r- \'.

rierrre~ueney. ·

^{". ' .}

l ·". .

" Annlyt;' t and experimental resultsbave

p"'''1

that lb. dull.mod

'I'~

technique:.1a1la5uperi? rperrcrmeeeeoveroth ercoml nlJ esed PWM tec hniques

' " "

.

^{;. .}

11,2).Subsequen tresear chershavemade anatt~mpttoimplementdeltamodul",·

)ion.technique

usi~g dise~te

^{digita land"}an"aiog:ircu itcompo nents 110,20).

• _ " - . " • l

switchinglosses orthe device'used-inthe inve rter:,Therercre,byusin g zero

sWi~chin~

loss inve rter

top~logi~

^i22--Z3),'

-~ueb high~~

^Iwitching

irequ"c;~i~s ar~ . .

aChiera~;~: ' AI~hough

thedigitaJ'

d~lta .~'oduiator, ^{in ,. j 't;} Y&r~"u ~5-~o~ms, h~' 6"~~

^{.r ».}

- ',

repo~teci\J "vario~s ~ege&lebers_i~

^{thepast1;4-35);}

n o at~m~t.bu

^been;

~&de

^to

" " , " J \ /

outlined'-'.

d~Y~.IOP

^:

lo.rtw~e .~mpl~~entatiOD O~'

" "mOdula,,"(OM)

""?"

^for

inverter.app.UcaijOll!.~e'm~~1aandm:aplem~ntatioDof delta~Odulatioil.teCri-.

nlqu~^.descrlbedbrva.!'io~,^-researehera(20.351 aremainlyforcommunication

appU~'atio~I 'anci

^hence

..:re ~ot e~UY

^applied,to'

~vertef!.

•

"

.

.Preaent Work- .1 .2

. . " .

.'

>.,Thep~for~a~ce"ordelta mcduleticntech?iCl:ueininv~r,t~r.-applicatioD8 hIlS been

'~tabu.,h~ .. ·:A1t.h~ugh,' an.alog,'.i~PI~~~nt~~i~n, 'a~~ys~ lLD~igit,aI ~,ple-

^\

me~tati~n:or'deli'a'~~<i~lation 't'echni~ue h~~,

beenreporled(i s.2D],.s0

~ar\n';

.: 'i , .:. '. ':" ':~,",;. ~.,· 'i ':':';' - .,,~. ,', .' " " :.:,

8i~ifl.cant',~_~rk90softwarecontro~~ delta.~od~lation.8trategi~eshIlSbee~ear- ried~!lt>.'·The.preSent..w~rkexpi~res-th~~pteme~tation'ord~lta:mo?-ulation .

ie~biii'lu~.

_. ^un'der_.,~.

·~rt~are

_~.

:~on~~i.:; _. ~: dei'aile _' 'd'

arid

co~prehensite _. 'anal~s~" ~r

. . "

~

.Three types

, ot

deltamodulatioD".techniques.are~t~died:,nDeaideltamodu- .la1l00,

~~?Deil~ia.l.:~l!lta .~~~Ulaiio~'

^..

and Sig~~la 'deita,·m~~u,ia~i~n.

^,Fint,a

Iin~r delt~· mOduJ&r,'(IDM) ,

is'

impleme~t~d·

^and'its·

p~erf~u:'takce: ~bar~terisk~

^..

ar:

c'...' ..

' :' ,,"' «' . , " ,. , ," :',

C'~"

"l1I ob,t~ed•..Tbf!"e:fI'~ta-o~.v~a~iollinv.'arioul~Oc:l1;1,latorparamete,lSontheb'a,.

. ";0.1; 00.1" 1an d

'power 'p"lraollh, invDt',eroutpul

v'61b~are ,tudied.

.. .

" Th'e'-~r~" is~the~'

^ext;nded.

to'

exponen;ial

deli~'

rii"odulatloD,

'and~igma:'~elta

^.

. . ."'::'.,'" ".;.', " '",d,. ' , .. .'::~:" " '••;:', ' ••" , , :'. " •,,'.':

"",

modulator.andt~e.1liglp a'd elt a modulator'ere comparedwiththoseof linear'deli..

m~~ulatO~~"

-

'~'~~/~e~ental

, .-..

verification_

',.

~r·

t

theOreti~~

..··, · ^resulh,a.

~h;ide

^phaSe'

(1~) ~r&nsistor .

^{" invertereadassociat'ed}

'b~e d~i~e ' ~ircuit;Y

^{'werebum: The}

9wit,ehing.sipats'.generatedby'various types:or,'delt a.mo~ulators^•were'then applied to_the"in~erter.•.~xperimentaJresu lts thus obtolned",show8,',elcee

eorr~D~~nce Wit~ ~he theo~e~iCal

^;esults.

1.3 Thesis

O,ganl••

t1on '

p" " C

( -.

- .<--~ ':: '\....-....-:"~'

^{.\ ......- ..}

~" . :>, ^.'

Inth~Iollowiag~bapterlvarious eehemeeor Delta.Modula~ioD:a.r~~:dl!!lc~b~d~.:

T~!·:,:~~;;i'~~~ . _.,'. ' .

^of

'op~rat'ion

^"

_{;.' ,} '·alld;th~reti.cal

_{," . '~}^-'

_.'.<

^'-

· ~n~I;"siS

^.

o r .diff~r~~t

^{" '}

' ; ;P 8

^."

or

^delte

modulation.teehn}ques·a~e.d~.s~u8Sed:

'r ' '--

J. •"

Cb'~pter',3eO:n:ta.i~ ~he'descrip tionorsoftwsreimplernentatio~·of

\. he'

_t~'ri~'

mai~ ty~es?(delta. modulato,ts,Theimplemen.tation~\itena.o,and st,ep'by,ShoP

~ , " . , I "

procedurefor sortware,'generation or deltamodulated switching,sign~bare dis-

~U~·:h.;~L

⁴

~i'in' :h~'~~I~ Qb;~"d;,om'imUl" iOOO~di~m.i~OdUl~

.

)ion'~

strategies,,"

.~~I ' stn~Soidal, 'InPU~

^{'respcneeand-}

,!a.ri~us outPutchar~ct~~.tic~,

'due,£0'dill'erent.pa.r&Jnet~r.Yariitions,are obt a ined, Harmonic:analysis9fva rioui.

~

. .

..-: ", '

",.delt a. modulator

out~ut ~oit·agefis .perfor~d,

^and

tbe'ollt~ul"~ltag~

^harmcnle

' .pectr.'.r~

^{ob tained. I ' " .,}

.,' , " ,;

Cha~ter

^;

,'pie:s,eD,~, the..

experim:ntal_reSults'_

o!'

software

contrOl~ed':

^de.ta:

" ~~~;~t?~: . ~~ie~4~:~,:~i';'ab: ~en~t~" bY ':d;lf:r_e~t"mo~~i~to~ 'are"US~d t~

.).

,.

..,Sontrol at-~.bridgeinverter. Invert er output v.oltageharmoniccontents aie

•obtained by

uS~l lpedr:um

_{' ..} ^analYler.·_.^Theresults

~; _.

the soU.ware

₎ .controll~

^delta

_.

modulated-inverter ror~csistive a~ddynamie loadcondition~are obtained.The pcrro~maneeorvario~sdeltamodulato~.based oli theoreticalandeiperiment al

. .

:esUlb.,is~mpared .nd·r~ults:abulat~. ( . '

.Cbapter6

pr~ents

^the'summary •. eond.!slon: 'and

··reeommeD~ons

^for'

furt bC!rresearch.

. , I·....

.. ~.

"

.. .

~

..

t. :'~;'..

.;

/. . .

caAPTER2

TUE DELTA MODULATION

[0this chapter theprincip~e

o r

^operationandde~ll.i1edanalysisoffOUftypes ofdeltamodulat ion syste msare describ ed.Analyt icol"expr essions ere developed to describe the eberecte rtetlee

.

ofeach syste m. A

.

brier com parison between veri-^.

"ous forms~f^DeltAModulat ionismade,("and thecharacteristic featu res ofench

\'re cOlI'!p nred")

'For~.nductioDmotors , the general requirementis toop~ratethomotors

n:t

.desir~dslip a~d^keep.th~.^voltageto'fr~ueDcy('V/£) rati o consta nt to,maint ain

tlie'nuxdensityat apa'rticular value."For ptrmancnt magne t'synchronous

- ^'" . ,"

-,

meters,thest:Jt ingcharacte risticsrequir e the'same V/1'char acteri at ieauptothe..

ble.:

2.1- Llllear De.lta,"Modulator,

.)'be

'sch~m~tic

blockdlegramof-a line"ar.delta

~oduiato:

^{.is"shown'in Fig.}

H2.1. The

m~d~ lator

enco.des""a

ba.n~~li~ited anal~g s~gn~l

^x(t),intOa.

t~~lev~1

·'11 ·

ou' , : ,r(t).'The

~u" u(

bi", ,,: w\oro, m".,,,,boo'

~h'OUgh

an ;nl ,.,alo, a: d ccmperedwl~bthereference signal..The-errorsignal.isquant ized ioto~o eortwo. pPsslble

!E!.ve~.~ep~Ddlitg,IJPon~'s p~lar.itY.

^Thequantizer

ieompara.t~r). ~~~p~t

^is

rqg~III.~Y~a:Pledby aeem plero.pera.tingat1I..d~C:kr~eqUeDey.(r.)topr~clueethe .___outp~tbinarypulses. Thecr~s~.,J~p~~ra:ge~ent

0:

^tbem~dulatoren!ur~.that t~ eintegr atedoutputfa.ithrullj'trac ks~be.in putreference Signal.~ .'','

y(tl·

' - - - - -., ~; 1---.0--.,---'--'

Integra tor

Fig.2.1LinearDeltaModulat or

2~1.1 PrincIpleor Operatlon,_

themagnit ude.

. .

^'Theoutput'oCthe^'quan,tit er^. jssampled^' at·every T seconds to

.

dir~c'~IYproportionaltothe insta;taneo u.s slopeor.referenc~signal x(t)13J.Itthe slo peor theinputsignalx(t)illpositive, then while this condit ion'exists,~heout- .putwaveformy(t)has morepositive pul.!esthannegative o.nes.Thissit uationis

reversed 1'Ihenx(£)has anegat ive slope:

in the magnitudeoCthe' errorsip al occurs.ITthe erl'()rhas notbecomeoega:tive, ....

bythe next c1ocr,i'nst ant""theoutput

o~h~ modula~r

^will

~gain

^be

~. pos;ti~e ,

pulse. M.loogas e(t)~O-atsuccessiveeloeklosta ob,'asequenceor ppsitive puIses

_~

^produced.

~nntually,

^{y(t) will}

beco~e g~'el.ter

^th\nxft).,At

th~t

^clock

. '. " . .-1 '. . " ., ....

inlIt.a.nt e(t).

<

0,therebyp~oducinganegativepulse.atthe outp utor the:m.odul~

tor,reslUting~ina dimlnui ion In'tb'eY{t)wavel ormbraD amouotl.•6'.,ThUi whenaninput is presen"t,,.them04u,lator.attempts~ finimi%~ ^{the error} w&v~form,^byvaryingthe~polari~r^{of the}pu'ls~^att~~ o.~tput^oft~e^rrWduJator ateuceeefveclock inst ants.

. >

When these. outputpulsesBoreintegrated by an int egra tor inthe feedback path,theresultingwaveformritl consistsoC8~eps havi~magnitude±6vol~s .anddurati onT~econds,whichoscillate aboutthe analoginputsignalx(t).The .difl'ere.nc~between x(t).and.ft t) istheer~r si~ale(tJ..Thi.-'errorsignalisquan~

tized to limits±V volts.Here, the sign oftheerrorsignalisquantizedandnot

produce y(t) pulses. ' "

)

" -~t

aD.iD,taDt,the errcr elguel

oIt)~

^{0, '}·p.,itiv. pub.

Will.be trod~;'d·

at the outputorth~mcdulstcr.:When this'pulse'is ihtegra ted,Y(trisieereeeed bya'positive step

+

~.This'increase'in:Y(t)is8ub'tract~ rro~x(t)a~IIchange

.

, .

,Vis the. levelor

q,~

^an

\~O" : ".: " ' .. '.

Sgn(t) is the signfun~tion:+ve fort,

>

0and -ve for t

<

0 x(kT)isth,:

.rCfcr~~ce Sign~ arri"Plit~de~at

^ktb

doc~ ;~~·ta:n..L

r J1kT )is-thepredict edsigna lat

k't.

~I~~k i~stant ^.,<'/ A

~rac;ieal

^{deltamodulator}

cn~od'er

^{has a zero}

.orde~

^{hold(Zoit )}

ci~cuit lol~_

. ' .

- '

^{/ " . ' .}

lo,: iogthe sampler.This circuit~ausesitsin~~tvalue

to

be'h~eld at:~~oDsta:nt 8.:mpl~tude^{for 6ne}cleck per iod.Asaresult,theoutp ut~~vero-r~ y(~)^{now co.n-.} sists'ofbinary leve'ls which m_~ ay.or,.may_{• '}nllt

~hange

_{- '}^at-_.

~Icx:k inst~nts.

_{•: 1_.}

·

^The

.outp~i

_•

ofalineardelta

mbd~lator.can

^{thus be}'described by:'

.' .-; . ' < : " ,, ' ' "

It ebculdb~noted'that when the slope fillthesinusoidislarge :nd negative, morenegat ivepulses

~e geD~rated th~n

^positive,

·p~ISes.

^The

si~ua~ion

^is"

reversedwbe~^{the slopeis}Ia~ge^andpositive.At maxima and minima ofthe' referencesignal, wherethe slopeisclose to zero, th ere'ar~ap proximat elyequ.al

~umbersof pps}tive and nega ti v\! output-pulses.Thusthemodul ato r'atte mptsto generateay(t)patternwhosemeanvalu:approximates the rr:e'an'v~lue^{of the}

.-

slope~r!~e.sinusojdoverashortperi od~ftime.

"..

~",:

andTis,'thesam~ling^interval where,

:y(<)- E VS,_I'(kT)-Y(kT )I~"kTi

,

. ^...,

( , .

2.1.2....'..Idlin gCharaetert.s,tle.

- -....

^J.

)

". / IS.. n.1 H' TS(USl C.j-- -__

DClnpul=.0Voll .Slimp.Frleq ;=2000.~HZ Coer AO

=

0.100 Della'"t.Q

':,. ,I

Fig.'2;~.,fd lingChar!~teristicottOM.''

(

'·'.5

f:'L,

t.

_~

· , {

0•• • •

Idlingiharacterjst icorlineardelta~dulo.tor(LDM)isshownin Fig.2.2.

WhenLDMisturned

o n

^andnoinput is applied ,artcr sufficien.t

~etUing'

^timri,tho

~tput~rthe'LDM has asequence0(',..010101:...Thissequen ce represents~.

square wave.outpl!,i,However,sinceno

in~ut ~.

^:his

stat~

^{oft ho}

modu!~.

tor~calledtbeidlingstate.

• • =

INPUTSIGNAL ~x.

=

ERRORSIGNAL , A"..ESTI~TEDSIGNAL' -L.=OUTPUTSICNAL

~.

.

~~. or~'~

^{to ensure}

.th~

^the

(eed~ack si~al.Y·

^(t)

t~acks

^the

~re~~D~el

^a

sIO~~

. ' - ..

. ' ": . . ^.

overioad~DditioDmust be'aatis6~.^Thisrequires,t hat"1tx(i.).~bo~~d~e.ver·

' ." .

. ..

^'.

^.

^,.;.

; exeeedthe~a,ximu~'rate01tha.nge~ry(t). Let. 2.1.3.

.then,

'*).../'.iD(2dt)'.

:\

(2.2)

ExponentialDelta Modulator·

-",' ' .""

(2.8)

<->: .\

AR . _ . Af.' .'

vr,

~(('rl)fJ

'AR,~' maX~!Led

^t;,

~nS~rin~

that the highest

rr~u6ney tOb~e~'eo~e_diS ~~

\.

-" SiP~I~~17:~~i~~c:~:~ ::::::~~~~~C:ttcrn

,-he

'YalU~ or' ~he inp~t, ~j~~l

^which

j~~ "~listurb~··

^theidling pattern,is',.f(3] .

. .' '. . ": , .... J . ' •

· .t~~e.r~te;" , ( . ,

. ,. , '."' , ',."',.' ", .,".

Ie a pertectintegtator r"ther than an'nccircuitisus'ed..intheencOder,'the

"

'·.pr~~~t~ w;~~ror~'"~t>'i~',compoS~·~t '9~:~~h~,'~';" 'W~~Ch ~~~e

^either

~'~i~~v~

.

^{. . ~}

.,,',T heexpone~.~ialdel~~,mo~u.l.ation system_(~M)'was,8rst'described'by'

,.

Job~OJl 12~1.·~~ pe~ee't'~tegr~tor

shown-inFig.'2.1;'canbe

r~~laced

^by

~ {to

.'-,':''.', -,., ^" ,. ' .'' ", " " ','...'., ',." '-'~','-: ' ,, " :"' "

e~mbinationso~bathitegration oraconstanfinput,~ultsinan output which

-. ' ;~It~~~':'an ~p~~~~tia1 :curv~·.i~s~e~d' ~r:~:si~a.ight'line~" 'H_e~~e;'·thiS co~~~'~~tion

. . '

Thet~ansrertu,ncti.on,of theRCintegra tor in the,feed back path.of Fig'-,2.4,is

~hange. Thisis becausethecapacitor Chas a voltage'differencewhich isi~1I whcn'y(t )isalogic1 hut largewheny(t)is alogic0..The changeiny(t)is a'

.tu'n·ctio~.of.thediff~rence'between,the 'voltage to which-t he capacitor is being

, '

chargedandt~eact ualvoltage-enthecap,acitor.

It is, therefore,

~pp'~rent,

^thatby

r~placing

^a

perf~~

^{integratorwithanRC}

circuit inthofeedback.loop, thevalues

pr

y(t)aremore dimdultto"estimat e,

.

',,".

.

Further, theamplitude'~angeandoverload characte ristic.sare alsom?~!fied116].

,(2.11)

,

....;-. \

" (~

. .

⁾

~_1__-!...

~Il'RC. 2fll HUo) ";' -,-' -

(l+j.t )

, r• .

-...~(rb+jr)

Forinp~t-,tr~q~enCi'C3r,v:.hen

f »

r~,equa tion.(2.11) becomes,

H(j~) -:-']f' '

~,~n~e .~r'~nsfer.(unc~.~~

^oraper!lretintegrate:r

is _gi~eD,

by:,

. . .

smallerthanthelowestinputfrequency to be encoded,thenthoRC circuit per- formsL'Ian integrator andpredict edsignal Y(L)iscomposed01straightIinesell;~

\

".:.."

.

.

i.Dstan ty(t )will main tain.i.vol~ageor+~. Eventually;ytt) will goposi~iVl!ata Idll!,B Characte ristic

. /

Inordertl?understandtheidling'behaviororEDM, consider the8it~ntio.n

. ', '.' . ' '-~

. . . ". .

~h~n'power toEDMi~~v.:.i~hedODandthe~cisnoinputsign~.Theout~ut.yot-

tage~r:tbe encode r.'wil~

b e .

±V volts, ~uPPo8e,theiniti~lout putvolln.ge of

ED~is:V~.th~'e'ap~citorwill charge.t~~m

"0

to •V~.an~theerr~~.signll.l(x(l)-

ntil

^{wiil be}

~itiveBinee

^{inputsigiial.xl!)}

i~

^{;ero.P09itiveerror'signal}willclh;'sr.

.

.

-

', ' .

. ',

.y'(t)toS~ikb^to~y'ndy(t)tostalt'tocbr.rg~to'this posit ive voltage.

Ir

nI l b:"'m~ ^{pooili ;.} b~ ^th. ';"'I·.amPIi~~·li~"

^lb.

,~or·wm ^.; ';"'li'~

~ndy(t l'willswit.eh.to-.Y.Ho~ever,iry{t)is~til1nC!f;a~iveat thenl!X~sf\mptin~

, .

jc 2.2.2

.J

5a~plingins tant·and y{t) willbave~negaiivele~eJ-Y.Thusen era.ecrtain!Iet-

. ~. ' .

. "

-

, .

tJingtime, y(t)willshowa...1010.•.Le.squarewave idl.ingpattern.This OCCUI'1. '.

irrespeCti~tor.~be i~iiial .~J~itY

^or;he

outPu~~i'gna~

^Ylt)..

~ ~

^'..

~

Theidlint ~atterDotEDM ~thesame85LDM.'.T he

nc

time.~nst~ntor'

' . '., ;.:

. . . .. , . .

" ,

. .

, ~DMis.muchgrea\er'~h~othesampling~eriodth~reb~ens.uri.e.lthatRCeircui~

.. (~'h"" Iiko'_~ ~"l"t \nt.~;to'

^and

h'.~" ~ainlai

^..

^Yl'1 d",~ t~ ^"'0

^durin.

_id.Ji~';.p~riOd. Idling·~h..racteris~ie o~,EDMis'ho~riin.Fi&".2.5.. - .•....

, .

It ' iS observedthat duringtheidRngperiod,.due

~ ~r~eDce ~r ~'~am~le

^"and

~Old

circuit, the

_.

output wave(orrvy(t)

~.

^a.;qu";ewaveandY(LJ

~

^a

'sm~ll'

^tri-'.

.

.. :.. . . .

angub r wave.Thesewave(ortn.!laresh~wtl.ipFig. 2.6. .

•lNPUT SIGNAL '"~"IlATED SIG~AL

•

'~?R SI~N~'~

--l.-'=OUTPUTSiG~AL

\'

.

. ,

.:

--

.'

" ,J ".r n.' n.1

H"TS(IlSrc..J--- .

.DCInput=.0Volt' samp\Freq. '"200 0.0 liZ

Cod AO=0.091 Coer81'" -

.

:8t8 Delt..

^. =

1.0

•Time e6nstaDt-T,is"found by'd!A~ingatangentattheoriginoffit)'curve

.

",

"' : .

\ ..

". ' .

- .,' -'".:

.~~'in~~~eet.they~tJwa~.ero~at

.y: -,

~u.s.TI.~.theti~eb~~ween

r

^originand

thePoint orintersection.Oy applyingthepropertiesofsimilarlriu r;le':. ."

." , .

.

^.

^. '..

~: ' -

.

(2.13)

-T

\

.

Exponl "lio

,v

+

I ^{~ ~}

^{:: ~j j ;;:'}

--..

^I ~ ~~

I '.

I ^{~ /}

'0 ^I -; ~

-0 I

,

I

,

I

,

;Ul

I

,

I

,

V. b>! + ^'-;-

^'----T

^{- '}

^'-::-

^-

_0

o

J?.. ;;'J.;

f-

T,

Fro~

^{equation(210j,}

r, - '2~ Ther~.r0r~;

~ • • b

w~e~

^.

" . 'b

i~.the.',cba~ach!ristje.(r~que~~r:'9(ibeRGco~binati~n':..

- 23-

2.2.3

Inexpoaentlal delt a modulator(EDM),themaximumrat.eor increase in predictedsigDaJy(tlisexponential. Suppose,theinput signalx(t ) isasitewave

- ,

or amplitude A:Overload condition.is.defined -asthe situation where the

-

slope or

•the signalisequal totheslopeortheexponentialatsomeplU't,icul.ar a;mpli(ude,

b':

^at

, II

o'b~:^{amplitudesthe-}'~'

0 '

theei...)is

I" .

,'hon th.,

o f 'b e

exponenti~Let . _:-- ' • ..".

x(t)_A sin(wt(

x~t)""'.Awcos{wt.)

:=.w(A

^cos(wt.)!

_~"';A2""X2(t)_ (2:15)

.-Assumingt1;at the

~DM

istt:l.cktngcorrectly,thenthe

i~stanta.ne~lls

value

~ry(tJ i.c.the voltngeacrosst~recapacitorCcloselyapproxi~~estox~t). When x(t.J isin~re:LSingmonoton ically wit htim~,y(t)cha ngesexponentiallyand its .,s,lope..is'the-voltage dtflcrencc .!'etween theaimin.g'potenti~1Yand the.voltage~(t)

-

-

~ontheca~ac!tordividcd,bythe RCtimeconstant T.< •

Thcr!ror~. th~

slope or the

~poncPli~l '":Jv _;.~(t)

^"

_!~~

slope,or the

~ine

wave at-a"oy

.

a1~plit;de^{=w.jA2 _})x~t) ^...^"\..

·Thediffe:~enceinslope~betweenthe signa,ly(tfand.x(l).is:

h (,) , , - , ,, h 10' -'" . wenxtts.decre&:llDgmOD?lonltlLlly,t

e,

peOf(,t)b:

__ V- :dl.) T,

udthe sloae01x(\)will beDe~.tive. Eo,tiatio n(2.18)iJtherefore ,.&lid torall

TheslopedilfereDceD.is •(unction of~(t).A!JIo~~as theslopeofy{t}-\

, "- .

remaiD.llgrea.terthlllt~eslopeofx(t).tbe overloadc~!?,~i~toDisavoided. In Q{der tofindtbe v8Jueof x(t),whi.cbjustcausesslopeoverload,we calculatetb~value

" of x(tner .which0iiamini~um[i.e.thevalueofthe'instan t an eousinput for

whichthetWO "IOP~^arene~rl~ ~qll-a1).^Iti5determinedtrom equat ion 2.16.

<ttl·

,(2.17)c.

\ .(2.18)

.

~I

~ - ~~

'",, A_ _ '

. .~

Dilrerentiatin.gequation(2.1&)wit hre~pectto x{t):

dO " ' l-·+.,~

'dxlt )-- ~. ' .~

•:-equa t ing~uation^(2".17)tozero,a'.od solving(o~^x(t)P;t:!I:

' . '

.

.D wi.ll be_.

~Di~um

_. ^it_.^d:?_~^{; O.}[)i(l'erentiating(2.17)

~Dce

^{agaill:Yi,,{ds:}

'. . '

. ~ _ w;~2 ";'x~(tJrI/'

^+wx'(t,}(A3_ x'(t)I.4/3 .

. . dx~'J . ~. " . •

__lA'-

X~'I~' I~' [I+~ .' ] . '

^{JUO)- I}

. " A'_x²(t) .' ~..'.

SUb9iitut~~g th~ ~a1\1e'

^{01 x(t):}

m "equat~u

^(2:18)iato

~~a"tio~

^(2.10)

gi~es: .~:

^I

_d2 D . '[ :2'."A ' ]-1 / , ["l+~{A2_ ~ .rl]

.'dx' (l )-wA-,I~I" l+WJT,'..

twT.'

.

^{. .}

"

(2.23)

J .

._ ~^I[I+w2T12

]* . . .

(220) • .

A~., ...,....,J .

SInceall constantsInequation(2.20)are positive,

thereror~

~~»o . . .

Equation(2.18) tbus gives the value or x(t}torwhich D!.is a I urn. Hence substitutingx(t) Cromequatl on(2.18)in equation(2.16)gives.

D·;·-i-* V .l+tT12 _ W'[A2_'I+~TI2 ]~/ ^. '""

V -A~

^{' . " .(2.21).}

- ~I^{•. ' '. . . .}

The overload conditioniscl\araeterized by,Dlll i G= 0,therefore'e!lua.ii?D (2.21)r~roverloadconditionyields: 'y.

.. 'H(j(jl) l_ '-. .. '.". .... . .' '.

~ ,

. .

The

overlo~d charaet~ristic '

^oCEDM,'described byequatfon^{(2.22)isshown}

i~

"",.

" ⁽

where'

,1

..

.

^'

^.

AmplitudeRaJ:ise(AR)_

The~plituderange(AR) torEDM isdejlnedas:

(AIIIUlrdecreases withIrequeue)'. eo

,2.2.'"

.oble~edthat theoverloadchata.eterist ie

or

EDM haathe same !Iop,as the tra ercbaraderistic(outputYoltagfl"VI.Irequeuey).olRCnet.

\ , , , '

he eu"!falll011'at6dh per octave withincreasing frequen cy,whicb

<O~"'PODa.

^to

'h'·.~p, limi~iDg

":DditioD(i.•.•

h i

^'EDM

W~Fh. omlo~~~

.whenevertheslope01the input signal becomestoot£r;h). \

. , t' ~

•Tlt'eoverloadcharacteristic givestb'l!valuesof IUI1plitude A... toreach fre- quency

10

avoid overloadcondition. For qperatin g

rreq~encies,

^r

<~P1i

^•.

tude A can beas lafl;t' as Vbeldre over load occurs.At higherrrequenei~1f

> >

f

l".the'RO.circuitbehaveslike perfectiotegrato~and^tbejnedmumv~lue^or

A

/.

,. ;:."

A' AR- ; ;

Where,A. ..aDdDareginnbye4uations(2.22)~nd^(2.14)respectively.

- .

.:';

AR

V I [lI'vr~1

.'- V(I+1JT121 .

T

.

~u bstituting

^T1

~' 2~~ ~iel,~1o:

Wh~re.

.to

-27- _~

,/' .

. .

\ \.

\.,

' \.

>\

.

\ '.i5thec1pckfrequency

'~.i~ ~he chl.fa~terilltic

^{"frequencyofthe}

R C n~twork

fisthesignalfrequency

. · 5 .

In theslopelimiting~henf

> >

,f~,theARofEDMasgiven by~a-

. -

tion(2.24)isthesame&.'IARofLDM given by equati on(2.8).In EDM thevalue'

A...isi~dependent^{ofsa.mplingra tewhereas}for lineal: delt'll.modulator,the'

va!:c~f^{Amy.'canbeincreasedby}increasing.samplingra te f.Jsince~me^ispro- portionnltof•.forLDM). ",

2.3 .sIgma.Delt~Modulator

Linear.della~odulator,precededby a singleintegratOr

!s

^{calledDelt aSigma:}

Modul$ r or~orep~isclySigm:..Delt a'Moduiator(SOM)(31.Theschematic blockdiagram

o r

LOMwith anint cgra:to rat theinp·ut

i s

sbo~in.Fig.2.7.

Hard Limiter - 28-

(

'-'----I~. t----,---..J

Integr at or.

jill

Clock

,

Fig.2 .7 LinearDeltaModulatorwith Integrato rattheinput

The twointegra~rsin Fig.2.7can·berepl acedbyoneinte gratofene rthe

{'(I)d'-f, l t)dl-{o(tjdl

TheequivalentCo rm~r^{figure2.7call}thcrero~cbe represented byFig.2.8.

~... errordetector.Since,_

- ....

.."""IIlJlC.l:---- J.._OI1TPITl'·S1CHAL

,....p."••. •iOOQ.OH2 lIolla.l,O

• • '.lHPUTIIGMA:L

,',liIHnlilUTlDIRAal

Il~IDp~t••0 Volt eo. 'AO ,..O.lOO

Fig.-2.9 IdlingChar aderisticof SDM

f : r:

tt.

2.3.2 IdUngCharaeterlatlc

propertle9,harmonic content or the outputvolt age'or SDM are,lowerthan that'or. LDMand EDM.

' The~ior~, barm~niC"

contents or:

theout~ut' ,volt&ge ~i

^all.

inverter employingSDMsche~eare aboiow.

,

Idlingcha~acteristicorSDM is~imUartothose orLDM andEDM.When

.. '

^{\" "} ~ .

.SDMisinitiallyturned on, artersufficientsettlingtime,the modulator produces

. ,

. "" ' .

.

a...10lD...J?attei nAti.t9o~tput. F~g2.9 shows,tbe'idling~haracteristi~^orSDM•