Sandu, D. D. - Probleme moderne de tehnica impulsurilor

41 CTOrtlh.rl.roGJilmiIt,.si,ossiPeoornnnr,'tx-rJCobr.n,SeshFPna-pou,sLri,o,t1rltRs,l,-,er.2norAo,ef,s.1bpE4Riopt9nurcrslrocl(eeL1sr9ra'c6tnsr9ea,)mlr'gWliascoil'sinsoWdaf.Ltc'ticooCtmonorprtvldlee:ermsuaiesMc'enOsNta, SarsgmocMleoidrmoi-csspctFallimtEmeTeenItfhtliodendutce'etfosrror'tenRtrh"ebevg1su6toel'rlcu2TIt3rieyo9pcneh(1ronb9fioq7tlu3hice)e'

4t.

.L3

41. f\tlL:.ncWtio.rn.raslodNe,sDceriupetitoopnm, ePnrtos ci.nIEthEeEd,e5siSgn' 1967 (1970)' lingineering' 50' 615' 4l
of tltgristors,Illectronic

(1e78). chopper on oulput uoltage control, Eiectronic

45. H. lI. Rlsrrro, Ccmrnutationlimits of DC
Engineeting, 5l' 620, 103 (1979)'
40. ,\.\'. Brnnrx, I. G. K.tr'q'ev, I' I' RoZrov' Genetator impttl' s ou tll ia mo dul i a|i i mdg netr o not)

o sut'Ltimetroottm d"ictpazone ooln, Prib' i Tech' Elisp' 5, 117 (1978).

102

s0r

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rurtrslra1 u1 ri runcard ctruuutpoTrrral prqlllqca uI luiqo g.rnFrJ nlp K?InzaJ
lr(rulrcn5aarlgsacarlun.nr6u1'r;e['tffrfnJteuau.urraaa\la€ppnelorosysrai+pruulrnls,urnlrca'flslull_rrrroIa*+pcanr'tpiiouurolJaurlauucrraaus{ocoe lpuorll3aa,lJt\srtusf€r"r(|uI(rvlfr.{:1Z_v'Vcor'.j"tt1rfJI)3Cogd.-

'9Srz.ralur

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rolm 91110l€61 'clm oU€oJ olso or€lounq. op lndmr? rEI r,rts+Irofeur r.rolpgmd
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saltmur;reg gnop nc Jolcnpuocluros al+izodstp un elsa (96-) Iotrn+ €porq

lO !lrtouered 13 egirnlrsuo3'1,'1,'y

1g rulaue.red ri

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o

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unslndul ap ol!n)r!) 'lo ear€lnruo)

o

r ]n]olldvf

zilor, atlicvaWuplff"p (la polarizflri inverse suplapunerea benzilor poate
avea loc qi Ia d.iod.eie obiqnuite, constituite din semicond.uctori nedegene-.
ra1,i). r\fai5, d.e suprapuneiea belzilor,.in semiconductorii puternic d.opali

(clegenela!,i) mai iu loc qi alte efecte_importante cu.m3lfi : irnprd,qttgry*
iffi"'lt"r donoare qi acceptoare in tranda interzisH, 9i BCt respectiv^-Bll :
diiuimpin"uoa""r"e.atatbde,nqziiiHin;tteirmZis;ere[2g]i.unDiaicd5.,e suprapunerea benzilor este suficient

tr|ceie este mic5, (lo:50-1004) in
strrictura hin flgutf 4.1 poate avea loc tunelarea cuanticS,; tranziliile

\

Fig. 4.1

posibile pe care le pob efectua electronii prin banila interzisd, sint ,4-+B
il C--nA. Procesele-c1e tunelare sint caracterizate prin probabilitatea de
tunelare D,; in cazul ef ectului tunel interbenzi se aproximeuzd' cd' trariera
ormx, triunghiularfl (fig. 4.2 a),
energotici, are f iat D, are expresia [3'4]

4ltlz@*)trzwTrz (4.1)
3qhE
l'A,:utn {-

1.t,

o

.a

rb

c

f,

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Fig. 4.2

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rnea

104

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ry *e€J--Iolr4rurrI8r*arrra)Iooo-;Ad1auvIl1uotlsr=;{t&ns(Ufq''Vor4l.rr.)tl.ss'3\rrt{+p9tfo)eaeulbrpaa8l*d..erraiglue,ra{pc-onopnt*gN;oAurrvnrt{lsrl.*srrUpuuburtallo*-lc"/lAl("fgco,,ulM):snaISy)c"eA$uruu".1r,rzcb.lt'lglffegzieXlu=uoaudq(6rsAxoI?on.,rIr).cro"ard{r{prezo,aI+tcltymr"lrrov+u1uolrldI(.urn*rra1ru"rotris8rnlra,,rBrf-q$sr
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(6.)06 Cg rol

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lirct[lsr.]5iuliil'zrrta]rrlaeronr(rirreftrriiiJiiricg\nrrr(",r1e.iir)i,iaraec(e\ctavs.ucizatvrte5rab);ce,,vc)oe";ts,uer"ci"enrto*itt'p,+nsitim"p"st"it"c",a"iala*.J"n.""";itiidat,ahr&Iio,t^;i.i[lo"*tc,"afio"^im;uin;ac;nGpis5;iJcet"'*rtf;;p1u"ii;otlcer'ic;n*ebntda;ip'vt.rrossietuletlabaaatniturV,wiii'sDz*cptid:SuixlV?",V,,ncrAii;Ncil,cnfoituanostrrmvLerdee*crr'vrleeLrstilzcneeeVpunzpo"lrqsiryulaoiiiaaubilpcratvneierlzeeolsteamraeceire.nlaeieesnfspxe'id:lpufdi0icidrenegeae'riacittmxdtudrH,eane.'i'fenpDur4ltoeazae'l3liraaleeleai--'

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tlexiune; fd,cind T:rrt(Z) reactivd' (sau

frecverila de rezonan!5, ProPrie)

r{r --_ZnllL,C 1t --drLF' (+'8)
v1

rdr care are o valoareminirnir/ro in punctul
tinlcfleinrfileu-nrjeundpi.ocFlaixirnailuo-snceilai.n' punctul de
numai dac*

.f ,,a(f,ot deoa,r'tce Ia ft'ecvtnle ,f 4,0 avem
il,c1Z1>o qi sistenrul nu lna,i oscila.
poate

,$intl in vedere cir l, are r.alori foart'e
mroti"bca:!:'1iriniaOe(rl-u.e,.fir,nrn=dirfd-i4tIef:Gl,et,)IrIef<z)t)n,,.1p"t0lou. ttlveCaal:ou1rni0lae culente

Pf'se

in prac-

{bl

4,1.2. Metode de aproximare a caracteristicilor
statice ale Df

inproblernele ttre anaiizd, a circuite-
lol cu DT este necesar sd, se gd,seasc5' o
expresie analiticX adecvati, pentru de-
sciierea, cu suficientS, precizier€, carac-
tlL-ti tceormisptilceixi iqtv'idoil,letfaiincprlipifouezcriieecs,eeIaslotjarotnidcceel.iuDntuaentaeolraPitrdNe'
"couucitoi"ndc,entralii mari de dopare, precum
si formei cseltial neliniare a caracte-
ii=-"i.ii statice'globale, este extrem de
Fig' 4'5
d.ificili, reprezenlarea analit'ic5' exact5' qi
gpa-ip'ptd^,i*eorru;;-o.cinu;;nnr-aicde5ll-ierl;,r.fi"^aaps["c"cnIle)oi!in,tt"lcmeroIaiirlplrqqpiiisii"eoarr^pti.onenci(zc'r4eeleti*eiic"is)rnntmea"t*tsetelteuo,ftdi.,aunetorci.t;tJiii"aIam.iicct;f6irui'r:laipe-T^a'cfi,pf-iii-ItAii."ee"uot;piiDu;rnrf)p*iai;isic"oi*f"tqoap*iIia"c-sia*tl"i1eixtt".",:,.t"i.ip"Dtc"ie".rbtra.*rtAiio"apnbfrzploaVind,eunac'caaeesect;1ztne'eein;2dr"nar;a1v['fiiiimu;.safsaudipe+ttli;e,^aizeopecLliiilb)ielBirinicme,sasso(gpa-aetuuumquaruzplplf]tiitddoiapnoecre,,sloe-r5^xdttpl'rm,a)pe,npce'osre(eorn3cotosaaorep)rt,ipdrenuedleriesrfonoieddainixnaead'laiemereItpaiaexzprnaapl^ieneanrrpreaelceriup(tatsoii4unpcoixap.roSeaeriae--ri)l'

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a0I ' l,Z0t9IZ?'0 rr -
r0I ' 9I0€E6?'0 * ?ua-rcrJoo) (
r0I '91?t0ZI'0 lu0IJliaoS
r
erBolE,\
it

a

J

-l

o

-
Ii

I

o

-

a

z'7 YTASVJ,

A gt6 : ort tA ltg : dri '6'T vlaqn\ ux a+€p luis n'0Jlu2a+d t{r'r: .xluf I*

pu1,l.€ sv€.e laun+ pporp o ,lolliuaic

t-rJooc olrrolts^ : (E 9'? '.31J) olts+ualulradxa olalts+Inzar n) '(roleln)ltsr atI E]nr

-r+qo) acr+a.Ioa+ roqJnc piuaplcuioc tsunq olJBoJ o aulitlo IIJHTJnI Tllrirllr8

Qrr) '",Lou3:orlr: n
OI

'0I:1/ Flrsocau aot.lrl1IBErrurrfrirxptouurndoc€caKJpduunroqscKor1al+tos+E+Jrs€luTorJJurooruorulsrKKJrJoCca'lIF+o++Ecpe"+eoJSr€sBcU{acorlsI+€rS[l+oIoJucta]iallDlJlcu"aerlcrJ_EtlsoJ'J'.l+pra]rr;tplrl.nlu,liucTn_t

o,rrlcnJlsuoc alup
o+rJeJip u,r F+iLuII

(rr'r) 'rl'nK - (l)a: I

'-eoa1pneq,eromo.1regFlndro{eurcrprJo+uCEuo?rllsonvrdrczcrr,\r+uvosa,rlaa.Jraee?+zrvctn1tsc.rJ1fJtnrscc'K[3gp€uf(-eoJOsinrrrpcofa]cu.arrdptlF1aoangsrtrrue(rtioso[u;BetJtylJeootoust[oLmFnuIaxrtuteo'tnJ-SuduaB"n€r)rrooaectltrd{€neyxiut.ca(r..,o1-6ot]+:1rqsnnauJs
'o?uapuoDs{re,r1 rr{enca Joun lzoJtsaloza.r ap o1e.3e1 aseorroqul oltl'lp:,1
+nuurrqplsugozndtsocp(Z+p)su'uorsIco:tlsouJII'rE:iOelu.:n(u-l"prer/tflepnp;)ru+IJuro+ado,dr(fed) 'lAtSp:a+1Arur{rnunraqlutcerqrciarlpo(ucgo)alutilqa"rl+: I
ahr7es:aca/u
alar
-uo+Krurn

Practica arafrd, c5" o aproxima,re satisfd,cd,toare se poate obiine qi

prrn utilizarea unui polinom de gradul 3

I:at\I+azvz+a3VB i4.13)

":IV:.pt0CIqo:ief(iIdcr-ie,f/nd(lF2ii))p:Voli:0no;Vmsoue,ludoibllsldienved:e0termqini5(,3d) ipnencotrnnilVilii:le l13l : (1) I. :

Vo se consider::'i,

9I^ -" 3I^'P s l^P ,
4vi
4Vo' e
2vi "A',,:-(l'e: et- (1.14)

Notlnil n: YfVo, A : IlIp reialia (4.13) devine

,:(+-+.*+). {4"15)

a ed,rei reprezenta,re graficH, este ard,tat5, in figura 4.6b. Din relalie si figu-

ra:54i,teseVmode,etpdoeudncetun.drseoIr:aepgrIoaoxliit-mS,a0lirleea:vppeoemlinntoVrmu:iIa:lIXVe,,,a-pvrien3mdV.eVos.c:Ionmplu1Pn3e,rle$aseiluVpir:Iol:rpOsu:(nIIs)i

intr-o funclie pard, gi 11i1s, impar5,, gi prin utilizarea polinoamelor de cli-
ferite grade.

reqti 3a"p)roLxinimiaraiztidvree,ainpesppeocri!a,ilupnei n1t1r1u-1de?tleermstienaforelo&situ5n, oinr calcule ingire-
m5,rimi referi -
toare la stdrile statice. De reguld, se folosesc 3+5 segmente de drer,ptii
(fig. 4.7); Iuind de exemplu o aproximare cu 3 segmente, ecualiile clrepte-
lor pot fi uqor determinate utilizind coordonatele punctelor speciale (extre-
1mnsa5le, p).eEntvriudednett,erpmteinciazrieaaaepcrouxaimliildo,rriidrcerepqteteloor crlaets5p, eccutinvuer,naSf,raurli,sed.gempeunntecttreolreI

Fig.4.7

speaiale (extrernale) singurele oare reprezintX, o inforrralie exparinr.ant,a-
15 garantatd, asupra caracteristiaii statice, intervin qi alte puncte ale cilroi
coorclonate sint greu cle deterininat. VerificS,riie experimentale au ari,r,at
cd, in studiul proceselor dinamice de cornutare qi stabilitate, aproximitnle
prin segmente de dreapt5, introduc erori foarte rirari cantitative Ei ciiiar

de naturti, calitativH, L27-23).
tla

l,Lt

ftz'v) xl(A-8l)l(1"-ill-rl("1-- ofl + or : r

ee.rerugxo;de

aztp+n oleod os f-tr eunr{.rod e8ue"rqul nlluad Icun+€ (a1t,t ep lnlcunc{ op
g{e; cr"rleurls al?€mrxo.rde asndsrp +uls f-a 13 A-L Kcllsrrolc€r€c op opu
€--noor.+r{€d.r+eo-d€rurgrcacal€eaOoud'rpp(cOr+Kfcc'fer)+;rstdSlJuo(1S+cfR€'fJ+)€Iuc.rnoa+ppqrfugeloap.uroni1prn{."orroco1rdnro[surrcune+crud'a7d+op'a61+:tuaa. )l"eclppJunrlsnnpT€l+oEutnudlx

Pl,zlo,l) q+ "(oa - "a)
'w:i)(ra'r)

erse"rdxe oJ€ ,? In+uolcllaoc apun

(oz't) 'oAlLor + gA zl,L)q+ "(a-oa)n : r

'[SZ 'g] gcqoq;radrq
uoo-srrpr{zJclo?uc++necuy,€roJdop€+-uc;ro€1rcrugusrzo.{ruqpdonus€srranrcxauvo.nr.dlrrgd{ov;Zrpoe'd1+cu6f(oJ6'rJgc'IqyATn)fselp3l1ruo(rq+nSon1lnf.eq'llc)eIu{l.eirnnomdgurrr[x€eoI1o"Ea+rd.€rIe+I€E'qruf;+lceyEol'ucatrlopudvrIrmlo?oFucprnqi}gl+?"ur+q1,Ioqu-aps'uo+.rcounlp+1"
-uoze.rdo.r olse rr{nz1a;r ro+sac€ ue.rucqdt ut"rd plelinzal €cllsrJo+ctsJt33

(olr) *,4.<A '.(F+),"r- uil + or = r

arznJrp op +uomc op gluapuacst eaunr{.rod -

(sm) t*11)A>u,r ' {#)(r-'fl*or: r

* aun

-rxolJur ap lnlcund ar,+m laun+ +usrnc "n uro"no3#ln"#""tlli"r:tu

:ir,t \
(zrr) ).4 )u,{ ld t b t - or)- or r
)*,
'.("r.1- =+

-o$q op lngcund u; puld loun+ +uamc op Eluopuocsop €oun,lrod -no*F

(srr) :d,1).r=o'[.(+-r)-r]"r:r

-Ioun+ +uoJnc op g+uopuocsu €ounr'i"rod
€oq'1d6ouro,y1,'rrc€r6un+nlfnsdreunoc1oJuc+K'vrauczpvnoq'i.p;rrouoeg1didtq'orrozucucrr+'r+usen€+.aosrqJeo€Fprucull1?ru,qsl;Jur#o{au++foofosip€e#J+€*rciu."lsatfs"cooJnsl-tuas"tcau"o;reJ5pdpfrorrrSl#"sr1ep;cltJr1to.ltld$Kaucp:rIoY$"cIr+lTEvilJTrzrT"{-aItu&"truglx(YaIt

'ifZ - Sf] r,ungitortr ad (pmr,u'qan) pyatwout'yod natntutnotdy ("7

4.2. Probleme de stabilitate a circuitelor cu DT

4.2.1. Stiri de echilibru

utitirevmXloarrtOnecueraigcDpeaa,trlr.q,oe.insLnt)neem*ec"se"cts*ae,irt--earciidoacaoppnr,atqy]:ittn1oeeirtdo_cdbl^i,sirfcipoieoumi,znisitotieverecpoccnroousnbiddrleee"rizm!d,iis,ei tuescndn1,.etsaisi'sutdttaeoifbmeoislrieatcauniltteteoizaneloat;imcnd.ierrfcgeouapr---t

TlD

ML t
ln

Rf

IJuoo

Fig. 4.8

mi;en;i""ia;;Jc'f*",";panttr#n"aiti;p-v^";c;-d""a;tl"E"iu"t;ift*enea'tonpdngttpD"u:e;;t.otiXiainvTinii"ei-ild,trjee.lio"eeeor"nSmcC"scczelie,alel'ite1"cgsin,mau.ottosoann,Fntnmr.asiaiu,sieitprnllaueilPl4midi-nrntRs.uN"at8ai,erhcal,rceilarveibqn.dteiosgin(eSzebiSfcsii[lJg,a,atncfetip.liarsanigmmea4elute*cau.leqeBaricltaunls5ebli.eiltns-,)4ealac,tdai'lrlh5euucouenicatvnr)oopctz,,ada-)ntala'pLnereorrt!neatm5tdt:zn,ds.riRte,et-srLetp1uciinmr:ot(.EutpmDapine(Rupsr!gIn'nupl.r'e.ts"rhr+:tscudeia{oi,]arOsdali"adar(iemotriCles)oai)piislrsilntmsriieet(encarmreh",'nirteuneettnrrrsctinliaLcufl5siee---ie'

Ldi :VoD-iR-a, (4.23)

11,

i':C9 * io.
d,

iicomportarea sistemului autonom poalg fi -strld]atH, prin re_prezen-
ta,.e* *ceTior ecualii planutTssttltaad'nrriewlo-lrr.f(a^oz(;''tes,el-'oir)re.LpFrzea:z-miVnitl5?ia,.li-,nntrtura-miuenicttoasirCsiietleosmeradd'1eei

caoxoerldeodnaetecooorrtodg.oonnaatele,aclearcearcaocitnercisidbicciui
statice a DT. Din sistemul de ecualii (4.23)
se obline relalia

di:CVoo-i_R_3. (4.24)
do L tl -O(o)

Fig. 4.9 Traiectoria punctului figurativ d('u)
lenrezentatd, in figura 4.9 leag5, valorile
ioit*ot"o"" aie curenlilor qi tensiunilor d'in

ll2

tll zoe.c-8

ui €uoricunJ eleod tC ztsc +soc€ uI '11q€]slq +u€Incs€q +mcilc ap un8e"r
I yulrzod- eler{ue.re;rp g{uolsrze.r ep

alrunl,iJod od Knop oll€Ialac J€r glrluFou gler{ua.reyp p{uelsrzel ap €aun
'elcund roJl ul
-r{rod od pun €cr+€+s €cr+srJoloeJ€c ?ztsolcasJa+ur guror€s op

ot'r '8lc

(ql

ulclua"rp (c) uIlruqdelsr,opautolrzuodlupE1n'ucrsiuuaq;rolprpncgJ{lucelasrpzeu;nr 8aap.r u1 tuor'icun; oluod
tounr{;Iod ed lcuncl
J(f o.ruruJn
I"r(nl5tpurrossunnu-rJBluJro?l€c1r+rrc3s1os tsclqslJo,lc€Jnc vztso+DosJalur fulcJtss ep eldte"rp (q)
n€s IrqE+sE ?uEncs€q lrncnc) ]utsFcsoo+n€ ur18a,r
ug uuor{'auny eluod IC zvc trsact; ur l p,rrleFau pler{uolagrp p{:ualstze.r ap
'luaunrj."rod od lcundln8urs nu.nr-qJr+puqrcfacol+pts?asta€ucrn+dsrJgo+ectJ€J1€1caryEZoEuar+{qcoasJloa+duIersuucll??tJ1E+Ss
'3r;)
ap uldea"ip (e) I (Of
T 1* oc-,t Jola+uoruola olrJolua ep
lnrur5al TurruJalop alao er{cuny u1
-alo0,}ooru, gntu{ rucrltsalEanp+IrSlrf+uualsrpnJnqcIIIIqIca
'?Il(0 1-as1) : of re ocr+€ls rrcr+srJ
-a+czlal e or{ces"ralur ap op oIIrEls gcrpu

Gz'r) g :0o1 - o7

to:o-,1. -?ro"'!-ooA

T+1nzar (ga't) tr{e1a;r u1 rr{rpuoc o+sacts pulcnporlul

(sz'r) '0 : (oI 'ra) !;V '0: (01 'or)?ip

rrroa€ nJq{Irqoo
aoppurnJifs+usa+rouonJueclou+r€€uoopJ€rolsocrg(luorIzo'o.rAde).rpum1l1noruual+r'siersqrvurnqtcqsxaTu,lpualr0upfJnzn.m{u?eS.rnc rS

'lqllqI-7s:o'-v!-ooA
F-:eullsqai,os! q-a" 1o!ed:eleuouen!l.irsaouldeorl+urcrourpduelErcgorruorurpdgpcn1ongp1xuuoarz.urenr{;cqdaotl;mtlozNetl.drodseInJ(l(t1sIt,^r{rdlonllIucnruI€nm^dJa)t +tP1uupr llac: prm€Islnor:up
ueludede;trap.realds rS (7g plcund) aEdcr+o€p+sdEcIrnlsllcr'(auglncedgJuuqarcroatauds--n.ropopuplrJr{nocleJnsrJo.or.r+'d1sel€zpoorsJtsynts+ocJorJaool
op t?IJo+core.r1

-tsr a.r]!c op E+€ururJo+ap a+sa gluuil rarrpc € (gcr1"eq.s KurcJES ep eldee"rp
?crlts+s €crlslrolc€r€c
IS JO ,B E+€+uoza;rder elsa gJn8g rSeoece ad) urelsts

4.2.2, Stabilitatea circuitelor cu Df

Stlrliul stabilitillii sistemelor neliniare constituie o problemii, irripor-
tanti, tratatd, in mai multe rnonografii de sqecialit'ai9-L!!-Zpl p"999q]
csCseiooainlnumfoluiairn)mieprleiao,scalupitsceintreddfi,iirtmiciirleeestfcoeelcubrlisaetoiz,,a'edsratienazdblas'ipltietucaidl,t',ecimuualeitueteolnceduuacai uafsiiidsDlotoeTrumad1.n(i3fcee0llir-iren3eni2caf1triia-,.)l(eMas.tellaiuntboiiatilll-iart,eaia,atpencuaaanlriouteivnc"esir.oi'
ob'tiir iriur.ma considerd,rii unor mici varia!ii alc variabilelor.
]trliminincl variatriala r. din (4-23) rezuitf,,
ud',r'*lt'|c-4.-:D'(tiloul' I jL-C'r, 1 -Ro(r)l :
Vno (4.2'iJ

LC '

care este o ecualie cliferen!,ial5, neliniari, de ord.inul al doilea (o ec-ualie
avencailnoXgit,asteeaobs!i,Xin"eitonsii pheenetrcuhril.i)b. rPue,nstreuparocsetuddeaiazds,talabiiliitnaitaeraizasirsetaemuultilmuiieni

eA*ic"ciolii"unn"-aAaidl-iieei,lfzieinlnvosvvclteteduac,crlrreeeiilnroaneirttacuTddtlaeeuAyaielooicanrh(cietaljieusbtmrrouulqriilr-spAaitmoXic<srei1iiib.s0iCOtleono(roneq')vsirpiapdualeronteredrusmi,mu,mpe3luicmnd=eit{maVt'soml,a-+/icspi)L.ri?vrme,api.rir!iead=zloi.iiIni.t0taiei1're*mctoeeAonndr--i:

O(70 * Au) : O(I/0) f Ao @'(I/6), t4.28)

uncle tD'(I/o; :(tli/do) lo:vo:l ilnrotro: dugcDirnedpteazcienst5te, ceoxnpdr"euscilia1inla DT in punc-
tul de ecnitibrir 6on'siaet"at. relalia (e.zi)

{P .l+.*] # orezultd, ecualia diferenl;iald, liniarX,
e'# *
[' . +)Au : (42s)

Ecualia caracteristicd, a acestei ecualii diferenliale poate fi pusi,

sub forma adimensiona'l5, (4.30)

trz+r ('*#).#( r+$) :o

ale clrei rdd5,cini sint

it\LZ ---Q+Llr,RQ)+lt .(+.31)

z

fs) Dup5, I.,japunov stabilitatea stlrii de echilibru de coordonTte.(v.gt
)'z : (1)dac5, p5,r!ile
este determinatd, de proprietd,lile rdd;cinilo_r.,\ qi
rptei"-'acatte;ioa1ezi'ey"udrdtae,ccil,Sinm,csitina,cibloairlrdsu,.innEativedid$ineantridvtdedd,a-csci5nta,irrae5radedpdiaeinrteielecahairleuibarpldua, rlpteeosapzeirtceivtaivildSs,'taeergseat'ael5,rs.e.tcasu--
iEAfno(e'tirf*"rr;ce*oie;*"o,b"cu""iro"ri,ae"id2rtseteioltieriAevanisureartiuleutrfetaoni*llsui(uiiuepssna-det-^maor1"aaaadnpi<ii-acl,nisct{pudrtiorXr,rr.uoxiloBnLlqauble<idc"gigOaii5naLpc,iglttrauairpecrulasaeRX.mtveCadaaa.risirngInuidatupremplremiaaeosrpedntadaalttirroqabra5-ubl-igg,lmtilrita,rgga,ept,adtlme'rlrtf5iogi."in,>ird,tliZiuQd*If^int,lgc"Jppruionpdyfrziri"ailreniittml"!i4vl1tferu.di15g,l,q))2ru'i.errsripaS5ali-dl'neede4n-dt,p.t'ac11do!li1unee-t

r14

Et l, eI

qqo--r-nJJ1Kpaa€ur)r+rrpTroiournq?rc;rurreduualaioeoltpJecppprsapglEaJn.to€osl;doal;Eogru;lrrJses*rreuynrira5+r+reaanailJaolear?ulrpur++eaornruc.K.;Tule[oz?rosQournl1rcr"rtJazssna(uuos]pelr\lJlurnanreandrcclrwalsrrlau$;surnloior"psul6?rcolIn.rie.{rldua}.c;lprln{uereogq.rolraurn€dlect?uso;sryvupqo-unIrcr'creJ)afJnqropsoJ!(il.l1l+ttr'ls1q:.rrgrirucronrlrJaF..po.rrr(nlTpaeecKpurrouunairlTeor,pTrslr+ue.KurrJcoolnoosli+cn+l3eoJra.rnprprircel€ulq-ueoiualeds.f+Ferecup:c,ueroacJlr..?rtlnsrtugq.dc.sr"r n

luaJnr ap aiEuuras ulrd es.ietnuro) 'L't', op

lo P aJelnLuo) aP asalord 't't uI

r'-p.rrr{"uourrr1'{{uirr{glrgar1anl?1Jpca,luugrodc€poocppooIooIurl+sEr,qBu+ouJsrqornrqruJcra€.+lpId_orporriuuu+nrauorI"sScmuIc(aI*q+oa€p+a,spI*n?n+l)n.ard'qGstorTeraserluqr'{recxczau?our.)nazrddyspe.rroa.dar11ore(rf;{c!rnou1(,lseno. +u;s. ol.oaitrz{r(lu"n.x.+tp.rotsxu+lt;rrs-ao,c1ll*aosr;?rl s:eaopulooun,1upnder +o

krt) ll t-^s J/. s+/<rl :(*n,*!)d TI

'rio.z".r 3 *nJpn.z \ K -I

;n€uprr.qord?rlalgqn1cJrou'l1fyogepp'O.J(,0qrI!lTJr'*oE1s+,o)SJ4J€ar1i+r,etus1o+{uqEo:u(1eJcc.drogaoapupoIglxosnrJmc€loru;rrordlro{BucpuoJn+o;olarreuu"aur+ur"szrrdqsrglnuleo,r+Upun?Urlsy"q.q€J+Hos;lte3o'cJl nc
(c)_ i* cul o"tt>r n;1uorr n,,onr*''rfi1"'"ln-'fr. "tgi'Lril;g:TlfJH"r"Jli.x,-;
l>T'lo,t, roluT r.tolpl ep g- .ro1e{uo+srza.r Inz€c uI ,rrcrlsr"ralcu.ruC ,rz garl,uSd,u -l!(

!l€r{TisroJlp g{uolsrzo.r ep teunrd.rccl ed elunlrs nrqrlrqco op oFrK+s mluad (p;) -v,

nn! oJIroq+rtflfllrq<a?+tacl ueFr€puoroclrtl€Js!T?^sarp?(,6urn)Flonlruraotg+nisae1ql{zcuosaJ.JrooolsplrpJo++pe€{uucmlaF;lIsrJdrzror.rromairFplqrnus.eo4udunear{dr.{reooud1rqcbl€ud?rosouclreaa?nurlJiIsSo o

II.? .FIJ a0

(r

(

N

(

(

(

'

-
-

zpn''tC'{.r_nryalg-u,r)1oeopsdllrilgzuIaolac.rlrrn?.qotlp€nlp7?grlsrsoryo?Fuuul"ontlrsr€uo{1.pJdr'ro:Aaodu.r,eree.€rrc1lrrl{o5€"orpce+grt€ut"drn€aq:g1prrrus.i rl+srnnurxzcorqrtJi?cq;asrJg'rqrfJnpc-oouo<lcrp€aoJupAlurrceqeU1Bro1oFu.I.retrlpsrlu1T*gglplau1(1rfircls-)l€z.ozpr>l'zdraTt{tt^1oglrnc+pIIu.rrrtza{4uogcreOLK;rrlpua1Kaupc1JpsJ ,

si cea inversx, elenrr.:rr.tr"le circuil,ului se aleg astfel incit, din punct de Ye-
r1e echilibru stabil'
O.* ,tt^t., -Pf n,i aibl cloufl stfiri

a) ConttttarecL 1trin, cttrenli lentr turiabili 6n limp

TD -t

+ A' tc

tn fr Ill

u

I

tol IUJ

Iiig' 4.12

Considerilm schema din figura 4'12a, untle -u81n'DgieTn/en,rasetoiar udesucfiucrieenntt
cle mari astfel lncit ale-s"toe reiolem"*-ente sil constituie se p-oate scrie egalitatea
""^tt""i ti;g. +.rzbi; ultirnei scherne

i*r*Io:ir,]-i" *io (4.33)

nut*'gtiluijiePsaeizun[gtrcuuururael nodtetuecll,upnc6reionel-xsrpa"rurec.siiniitidle'tl(it'?li'm-ci:prciloouori.r)cqleeis,ctienomdcuaupctataarcenitlaa,,tienpatrainjroasnzg'c:r=tliitru"' nLii"'it'

T J
I J

I

rL

I

b

I

t

Fig.4.13

presupunem cii, semnalul c1e comand5, ii,,(r) este,lent valiabil in ttml (de
ia;s;fcend;ei"n;t.io, iddealcdu,)ie, niat rtusntaerel a(fdige' echilibru stabild, se afl5, pe porliunea

4'13n)'

116

LIJ

'vtT', ErnSrJ u"r p+€+KJ€ elso o?coJrp rrJog+nruoc €ltsJnp od n, rrun

uqr-IiSt:golAooIJllCCg.e'r0{-=.e=,r'l;lruul1lT!--'iiel-Arl(I TiIE:":p+Inrou9,uAlrt.-(er*tpArtrrors*;}rVc1vuee*o}bdluln:un%occr0'n;f,7?Ti6rt+'c-(srsuannosrcrp+ludu eIoop"IdACnrteuwqanrrdoror'Irr.lrg^Oornurgco1t.',rAung;rca=uoeI"t8stl
(se'l) (l-ut)l(,t-etl)c:'1

-r;rldurrs elso.rdxa K+InzoJ .1 = (L)ut uroats ,U+6:,t rulued *,"orroJ Uto"

0,t'v)

vnir;-{i1o1r Qt)rtr,:

"*#i:ffoa?ps+slpleer€rcqrpqtsdsrJooudoplrs'xere[goooriluaedp;]luraaeu:luutrIqnlpuxl'ouro"olz,roiJddolt,dsre1cre.rugJo'oocrprcx]v,erony3l3reirdluJuaeronMsJeJronyolr+rroFuyrIunSarqlre,ox1oo,rn,d+rrdlnueursad:eucr:oc'll'Ju:,aB3r'6Zlrnd:r:Iuitr#j+uryingq)ilown"1r;;uTobrrdyfFir6is'eqea:u.;r,r"ur{c,cq@tltxro,1,;gu-n;rrt;orla+Ta+u€oU6pds

(ge'l) :-(a)o! ur u.l'o+4 A? 'l

apc *,ru'o+arl

:(;ror.roluu rnln+uoJJ e1e:rnp) a;ra1io;rc ap prdrml .uL1l oA-rrl pul?o-t[ 01so

(ge'r) (a)o !-u r d -1f tl - tl

apc ,,!:

olo+$rll q du4l amp pInl€B+,Itnroz+aau.+r1suo.r(8rou/)1OKlSd: nd1o113 o.Ta.Sr,1rduu7grFuoaz.lrlu3lurrJrJ'pEp,'teao{uleaE,;arracu;amrppsrupaelu?+rrzuEir.rrrrtdruannl,Dcr 't
"! 'egI'T rrn8r;
is
(ru'r) "! (
a.'s
nlrc ):'
(
Cl,!:oJtslnluoc ap "rogdurrl Inlncluc n.r uecl .1a;1su ! eriela,r tszqrln u.! as
P
?i!/(.,p,]lipllcr:cl,gc,r3 ortsc ?
1

rJu€nr-o--S.JniC1JrpKun+)o.2-cracu.?(gou3roouacc1Id<aonleloonn1lu-..uarp'lr,1e2nc11lrauuFuo1Io1nraI,qqni'pr*1ll,ldu_deutpg'g1_a'g.Il.o:1uu:crJuaJqr1nucl-u+gouJcnKnuTpltSalls?sduo(sluIooTeJip_Jd:osarooturgs+pr€1cnu+g+€s,lneutpsenqaslulaupe.uldIc,aol+_uIui+cuorrngnrorrczncJs,arrarlrdp:pp:yr+pauamd1onia'ln,apeuc1icra1trroosrf1oelrl,Jiuu+.arrIu1.aersunO.loJ-ilidlcrac:updcrslapunret,julnp1oslmugncclasraTa"Fulrsc,plru'l(ruistSco1pocrulcJti{+p;nt1r;cpsur1dnp.piltenurFolcrip{[caicrp,isyreirlrluc"ni(ulequlr.nBrrlodre"€dglr6ppup+r,Bzari1urni(riS;aul,.rirrnv"u1urlauotufopdt4€prv.cryro+ee,utE5cc+Eiruont€zagsJn.]aaau,rnCr,r'+LupeTgdlirr-nJlrrlu7\1nr1u{o]Jdrsn.3opu,.zuoJrr(ouurnreor3A:ontccar+lrt
rl li---€aoourlptos-[o^luaoruo;rJedou-rqlI€n€l"uIoo€!*ma0ucrnporsrutuslcourl'uronJl EqEJdqIe.ow-J_pfop,TI+enu+pauTea1oJn*-rac{lrcgn.Fcrerlqu.oouJaacrurn€rcsCq€;+c1tisd,irgrJu1€11a1cu11dq1e141c1eaulnar{p.

cotnut*ren inuet"sd,. Affrplitudinea sa,ltului de tensiune este T/"--[/o =

fIim/"i;i"te.tifmu{-.hp"i,u"golV1d,irierip.crl0ee,sc1cisr1.e2i;,,re1liruneiitli,,tlsinecotolncbili}neimrei _iintperlliienmsiintpeteelecgirfaticleraetiaentreiemglzrpra,llrineeei i("4c.:a34p;t,Dein(n'-uttr)rue-

vj

4.9 v;

0

Fig. 4.14

rctrif-ieof,rmufi:dnIef^gi.tunirmio<-tlVupdt(^ipuo1e;o,)dcil,an.aseelst,liee,rdef-diceraef.fesoiedcrcucaSeitotpu,iirvmmlercihozaa1uxrasi::,tiiectvmrae,,airarneitrnrla,ieca[intn,laratpv-e,p,uepli,iarirnttilsnrlticem5eii,rnnt.(ici4tttsPeliea.ii1oiunleair6:na,ilt)treiifluil(e(o4+nco.ieil.1nne1av8tt8ltae)eid)mgle.overxaaapItcrinrlna:eenrrsiae[llrp2,ecego4tplelati]ejrIai';f1st'iibi9rtnviqicltlaurSireraii,an0cgtte,ll:i1arcii,naiaTrctpcletrtanfieriri,,reiverrcfat"fiOinlrrcu=dlc,ue9l,l
dintre F, qi I'n ; se Poate sclie

t,": c\nYp (Iu - t\a

Jo,9v o I,)l{V,- r)l$:E-*- lrp}f'{

:: .(i,--vI,r--I'rp l1o(1 -tr/ pf v )f't -1 -tr (4"3e)

Y-1

Luincl valolile tipice YolV,: U5 li T : 2+4 rezult5,

tr: (7 +170)C(tr:,-Vp)l!r-1,) i.i.4o)

'

atvdeaelfrlteocrlratifrrrou-eitua,ittll'itltts:tferia;mii:lncri:cv'aafei.r4lsr1.ri1iri:4cllrib,",ii,risre',cc!nilaiee,uxtulepnilr"idcs.iceiru,:rrntpeeilziminltrirletf:pai;oicp5dtd,uepuirarocascietieamlsaeucnlreiraearlcnezeucllp'rtel:urtoaitiuurialtnatvprire,eor_Ciscneee's,c'uce:''1lessuqti.e-li,

este fori'rte ient in sgleci"'rL ln, inceput, unde ri" cste inic.

b) Cowtv,ts'rea Etrin saliut'i de cwt'cn,t
:,\:raliza pt'oceselor dle colnutare a DT sr1b a'c!iu.nea semnalelor i're:tp-
ti, esie impori.anbri pr,rn fapt,ril cri prine in er-iclen!,i, tirnpu.! cle inti,i'ziere a,

irnpulsrilui tie ieryird q; erfllciteazl, influenla ampiitur,trinii irnpu,isu.lui r-[e

I tg

6\L

€Joplsuoc pu;ero.raFe(;+reudeuqrouo?rtlsJp+ueogrd'iu'1aoe.reomll;ordquqleouprrcxlotc"r_duJor;unoluIiJoFdlI,(roo),alnt daopcuen op
e'
u7-'6'T'?
.T
ftr'v) '(o)o!- lr *'r : c3. nr *':^\, : nI-*!
TS
,&t'V) p1e.reuefi ur{u1o.r tsI op gceold os (nqoru?gul^lo'ati[p'S'p?IlJc{)zr.Jurl'plo*pnzrIznnu?lzn*?€ucortCTxrI- oJ€D o ?rq
or€+niuoc op lts+ol rnlndutq Inpclt?c r!e} -Sa
p+cs4p
Ini
.FSTZ (o

e-nprredeou.rndr{?iosdJoeadurg€.roluJr€+,trnguur.orna8gr;zglnogrrcruJnndrriopdelrlie(Scagut p'llu'r5{uii)a...r,?aynrpl giu_o1s1zo.r iar

prild optscD* lnl

gt'r '3lg ofI

o) (q) (e) 11J

L!t1-/I+1'] p
6'
-lt-- In
€,I
l ?A
I I
9.
-,
=
q

-1

.oerrg€p:.r-'roorfiIop1rsarrils7c11courrouipaanla*uuu)u(oT.u€rlsnru'8ls"la1ls1fdutZltpeiifo+u7TilZf'fro+e.ggrqnr-dp+Cgc.ioEo+Si:f1lp1erpanlrdo).1urgTpdlri3qbtetK"guurseu-udjJol€;flodnutoceo-uso,dnuurrtzrl1une-1forr;'uo|ap"<e1ga+r'alrp1recprerlep1Tselnu.rrx+ulorglocudrnfrorncln{llrey+cSuuoeuosoraeIe8€1lo1cluqnrlpsuI€scccolotdJ'arlTrirlrlzoslg*.estppuuroe.,polirOc(upplI;+€groIot7s.RuolJooderiaJlI€IaJgd,Jup:op+cEdtfa+sfl+u€eat''oc(orInooa.uqo'urdrluusIrdn'4ufa)lnrscCI.onau9nrprFsolurf1+rsadt'{ulsrp1;cep.uzuostra-.u3lo+(nrI,e'41fo9rndo1tt+p1ro+1.F$lu€rtuoirsde)l11Eluoyx_p3inut11rcolooJ1nJplr,.?rrfu'!ulrtrld:'r-Irgulrolp+lIe1Idilcnelun'adrm{uutIe?un.rmInlrnu.rIrJqer?ooulrdX,xeorcrIue+ua9qul.g1rFntsroIirasn1Jlludcn]dgrdE,urnurore8olo1u6qopo''lrcar1orgocus.uo13rpurTcd1.,uL-op(notont'tnpqp1'T';(liol'odl4rluLuuren;suzllIuca"ec.Jso'rrgtlru.n{laeroarrurro5ru1n;ntr(rrutrlTddn3edod;lir:
uo?-rnf-rfgu..pIuiururqolo^eIlJ€to€r.e1nIulb,€c.rci3uc€r+eo;o8oKrppJuJolo"josdlr"ugnrr'olozeluurn+l4u"olnr+sr+psuuoIuor;?r€rcloEpsl+oc+usew.IoJrr€optnzoplpouaJpuo,uodrdllJaoc.umrlupae*rr+n.-rirrJrulp-p;o€oq,tltlnf.cores'ncloallulll1icnnno'1etu?cp?;Itu.l!oIroz:r€6odoJu)ep.qJtrllgutJstIu+s+nn(I+nuicauutr"ksgrriuJaDioorrnrcplolnIopoIqpsorodg.lasrspoel8au+rloao.oJ)pr.uEo'pCrcntloorollozdJg.sl'roTlnPo€{oe+s'e?s++puo€.os;rI.oJo;norelocdnla.c{orIrpcmn4.reru-u*tcBsge,atqcJr*.i;p+1r'ccuuu_pms1-efeqrnpo1upcpqsu1eet6?ul.€tnr14.1ourrt:pepuJonrcEoousre1dJr€q"1pour+cueduruqdsrerrI-

aDroximarea lui f, lrlin 5 segmente tle tlreapt'il. (fig'"4'7 a, culba 3). Ca
.r.-ut" rellt,irl (4.4 t) poritc l'i irrtegrati pe porftunl (1 lg'
4.16). Avr:nl srle-

ces. lv ao.r I1

L.r,l

l-
l

Ftg. 4.16 (4.42\

: ,t dc (CV pll p) ln i/i,l E/$,1

tcn : C(Yn--Irc)/81# :' C(Irn-Ir;l8Ik, (4'43)

t,e: (' llo6In[(f, + I,*-/,)181#]' (4'44)

tt. : Cgrr-Iio)l{e + It''-I,) * C(tr'o-J'u)llr-I'+ 810+")' (4'15)

tp6,!tp5 +=)|r,"|*ffi"f, ({{6)

uuAlrzlntei;icl;iizlvi;elrna'il;l.i;li,xH-ic"apriar"tlr6iiee"a:si.pb(Iit1i.'.tarotift<i2xooir)a"rturi:r,(rr<tt"aye'r*r^,i1pil-oud'rr-,rerirV.icdii'c"seo,te.l){i.*n'l"[a"irea'"l-etsriIteiet,iir)m^lpauep;l,aiilp:ioi'r3raJttatpi,,ua"t:,nn**tifi,-m,ztae;an-ilcef'i'alI"r'.'a,*tc(wrs4t'e''-1eI:6.prpis)o:tt'"itccrio8ui*1bi;dl":itnor-:m"o' e8p<yrprti'i'i'pn'l;i

,r, : ,I'p dt,

C Io * -I-.k Iolr- (1 - tlv;')

\uo

*v$#*,,,.tsfP1*, (4.4i)

uanpdroex8in1t,:ll-eaIe(4.1?)Io.In mod similar, pentru calculul lui 1", se utilizeazi,

trr:c\ v1 dtr (v^ _ vr)n
Itp :##\*"rV1*'

(4.48)

-v Er{"\re r4

(rg'r) )zt

loL (a'T + 8'r) : t{ 'ur (8'o + tr'o) : uI

egrftleloc on+EtsnJ1?I"oqp'"€n3+"uiISgJ-nfl-tumrlol leaFp.rgo+fuutrsu+sruuo1cueoc'pl 1Tmczoo'rsd-etptu-urlulrrlcl lCns:oord'

o+EIncI€c lsoJ

It'l'Ft.q

{q) tDl

(^tiil/'JP * c'U^+
,c0t/ +tJ2
z9'1 190 0 z t
za tDsffi

-t1-*\
I
LI

-l- I
I

opun (or,/rl oJorzJl+ul op .l.r+tsIsJ durrq un ?EJoprsuo.c v-s ;z'l * r"'l: n'l
"*i'i'l"aift''rr'lOl;"rqb.,rt1"n'"t,5tn'iSr'Ael piriin+irp'n.al4pcuudrtn'e"n+idf1tisg''e'sVnlpdo'pnnprsf{gtbrurr"rloi1EsgSr{ol7ri-zr.groS1deu71r3g"1rJdu+"4rEao.rcpl?eruou.rrprl.nsrEpnuucllrrowIeJs{Ia€+uolualqaIn.t€?*orrrun{tsusl,oelF.gn+1I'Ii?'Idu+eOt!'lr-p'oE.Iqteusoo+'lr$'tItcass

sxJqtssr+uflrcoop.Ilrpnlonrluuolnrrnuror"nl-n".pllu1s1dutarrul+rpTlDyld+utsrIEmloqJn+sPoc pop+ur'itu?'{+u.reondu1nJuerlcsrgn;re1nd

TlI- * *(os'l)
"r)l?zs rflr'z r 51c"ru 1C,4rl .u

,.@/ (ru=-t 'fXliX-+ r/ tt,
-=---
' (nr -ot)lttsll I
"IrJ

-it'(l,t'y) '.t?nul r*ll1l*n'JuKI oFIIcJ€E{tr'(gg't)
'[95] olsa e'1 InI e R+JExa r:rse,rdxa
0 <- f-fg glelFoqut
ogtsa,rdxa ur'iqo es ruacer

(orr) - -rr (or ur)/Trs + r o1 oI-dI

*,0)or-1il:

- - - -* *o)z ut) .tL &/71'o+dA

"t
t c:",{,i(t -'t)l(t rl(r Tr

op eA6'o+d,l

IA -,1 I'0 + u1 -'A ola+Irurl oJ+uI tizuar'lcoJo E+InzoJ '.*A 6'0 * uI
nc gi'rraztyln os e'? o.rolSe.rc ap Jtsr 8:
GZ';) en"stttt*t "ae os uelelfiolur J"

rnlndun? Inz€c uI

I

I

I

i

Este evident cd, pentr-u arnplitutlini mari ale saltului de curent Ifi .re olilin
timpi cle intirziere mici. Din <liagrama 4.77 b, rezultS, c5, amplitud.inea,
saltului de curent Ifr influenlear'Fa in mod substanlial timpul de crerytere
l"r. I)iagrama din figura 4.77a aratd, va,rialia timpului total de comutare
directd, tu5, in funclie de 81#. Se observii cd, chiar pentru ril1.roarte
cct}i5urIfn,r"repliQnfoct?e-ea-rvIteaeIlr,[mi),ai:lrcieiili8aamt,lieprl.'oBlmurltViaieentiot-seie,la1oc0lebu. lrirnbaeeploeortad,uuimlufiinou}sIat,'rlceQae,sIcu-ublsaIita,,e)'nplipaerlo[ndtaruulouviranl*Lo,-,dr,rifiilinc-
Creofmeuritnarliei ac'inuureernstdu,l.-IPortn: ctIutl, figurativ se aflX in B (fig. 4.15 a) ; Iuind.
drept eurenl;
amplitudinea saltului negativ de
trebuie s5, satisfacri conclilia I;28Iu:7"-f,. Presupunintl cI ca,pacii:,r,t,o:t
de barierS, rdmine aproximativ constzlnt5,, timpul total de cornutzire in-
versi, fuo, se calculeaztl, pornind d.e ia relalia generail (4.34), astfel :

(.4.52)

Expresii aproximative pentru trt 6i trt se pot obline prin utilizarea

aproximd,rilor liniare pe porliuni (fig. a.16). Aici vom prezenta ins5, expre-

qsr,iiil8es1ed;eu-dt6iuli-zs8ee1aizn.Sulu,. caTrpairrrnoepxauiml12ta01le]cacoar(er4es.p1pu9un)rzri:niitnocreaev,rtiedaepTenil:Xpri3en)gfi5u,etitnolaareraeds,rteim{ilpoer li3trIu.,

f,rr: rVu I"-I*,-{r,*(Iu- rJa

C\ 1,)l (u-V)ltvu-V,)Jij

Jvn

c(va - I".) '6/5'1 + l/5r;t8-I;
TC
l/86GfiP [*'"
-l------I

v 1 * 81;/8rr

o.TF1arc's 3l/57;nn-11 (4.53)

--T-_j'

Timpul f' corespunziltor comutfrii invorse propriuzise, cind tensi-
unea variaz5, intre ilnirtnrietgeleinYteonryai Tlurolesdtien(tpleenIt;nor;fi, Vse,,uhtiiliiznedaz"S1 ,:3ap; roximrllia

(4.18), extinsd, la

,rr: ,\'), Iz - Iun- {f, + Qo - do - r)l(tr', - lL)lt)

I,)L(tr',

c(\r, - vp) 1 -i-1l81t"l1; -T)

(Iu - I,)(81;")z [*' Vr + 8T*/(T;- L)

-F_vL3arcro" zJrt7"rry,t3/gla_ r l. (4.5-1)

J

't22

tzL

JOIIJnIIES €oJ€JoicFlr col oJY 'oJ€.i+I4 Op In+IncJlC l}J+uod oJ€O+otrIOJ+coIo

€---cotrstrsJ{ar.+tc"surec€occpI€soouuJprnnuiAllsslcuuepoopd++po'o}lcrpouruInnnI+dlI9€+IuJsru*Eugroodacssefper:cK"er?evnuc,roogarJ.r{Iuvcpa+irdnn€uJa?rJuoouocp+rcnollnrJprnlrcoIsnucltnneosdudonocileoscluJiq1deulro€IoorIprrrqvJ.+en1Iq€rzssr'lrplucorrtJ+l.srsan+rzJ5*oo?rquu;.

uI : 'tolts'lJi€lsBnru+i uVlzsreEtrr+tscLoJ(lr)p*taoJy€c+neuunroccTnosop.rdoleaSso'"cgo.Jlli'{g.'opa.e2.1T-'po,PnTanlntl(nqu,Oofc '3ll)

gpu€uioc op +uolts^rqco +IncJIc un-J+ul asnlcq +uIS €rncJus 1i e"r'u*uqcop aIJ
guolu.roue5 'rnlmpnqs e{ur.rn*n n.rluocl | (e Ot'l '3r;)r.ro11aedtc u.rcT unur}uoc

orp 'Flg

lql FI

eluauoduroc pdnp oqeredos l(urnISpt-oro?1Inec.r.nacuaa5+)satncepy'gnpc8poc"r oO 't?ulcJ't3s op InI

-nlrncrrc e ri e,re*uulcap ap o1a{uepeckm o;r1gc
alosoJoJcl '(o;e;r1ur ri
ep elu uonlJur cruJalnd Xqs oJelnuroc op en*ar o.rqul
arfcue"r nc) 1euc,r{aariplq lr'lrzodstp un o+so [(I Xc +€p
Flts+o+ putl.{

rnlsusl ap al€uuras ulrd earetnruo) 'Z't',

o€1,grIur€,"0rrro<ro1cJcrf€rIuJo-€rorJ+r'Too+fal)rl€"?layaorqlp1alrqrp:nlrruslrruonca€l,pndEoln!^clatounruo-lnlrsoaldnesdot3scE1lorou+iilt{€?Iru+rer(Eonfsuignuooqa't^a|1)^n(J.c1;lLSo1l,,4rt''(rVp?gtp(ug?t'fl'rrtl1n)g€(r;fgrz-ooqoocptur)rt+';{t)e€ual+d1g?sorJnl;lircollcgIocrts+pssr,rrneu.rrri?ranc,E+lrlarr?oropeudrJauerul?rueo;clrrl

ourlJ/Frrr op ulpJo un nJ a+so rsJarlur oJB+nuroc op 1rldrnrl lrodt.r rn+sotts

8t't '31,{
t 'ar\-4t tu't o <

e r'c c0'0 L0'0

'

po:friI1t€;i;1roo("dIo're0"1rdpq1unolcsi )lnorddaurarrlan+uTtl+rrIoy.rLlotIsJeaIp.rndprnolsurreor gdu{;u: opunzlegetuo'iurfuo^os€nqa€llIguS{iouioiel"gnrulplsir7sgo7lgaorrootsgumo(r"8:rtp*uf4uI1l)'(i8YIl'g}'

tle tensiune falii,clecazul generatorului de curent (-R -u oo). Datorilii fap-
tului cX, o fraotiune insemnatii cle cruent este absorbit[ de c5,tre ,8. are loe
curentului t", a r itezei de comutare ; dac:i :i,ro o valoare
mic;orarea deci f{)a,rte J?
micit', il'nume I r-o,oin ], ltl
ll{
r lnai poate a,vea loc procesul de cr-;lnu-
iI tr. tru'e. Da,cii, sc oorrsi{leli, r'allooll'i rela,tiv
' R>a mali :lle lni 11, prccesul de r-'tunttttlre
I I
or<
\l |I rezultat, in urma aptriotirii sa,ltlilui de
ltA'zI ,.-.^.r'\-" ot.....
I tcnsiune dtl airnrplitudinntt'',, Eil)or, egte siilltr:irilalr'
I ',' ', tc'rut cceetr! ohbl{inut iirr t..':;ir}.zzuLl sarllbtuulluilij dtlre'6ern1rlte'nn1t,,
i\, l/, i tnn'', \ / tc'oonnl(irnrindrl to-r eettalpli pr'er'ggii'ltitoatr'e \scii r.Jr re'!t;*1p151,[
\ / rapicii,. Trebuie su'oliniat,e cloul, palti-
ll
L\l/ , //1. ' t(s':tautlallattu'rilrlitrill;'rtilerfaac!la,u[redunet tc'iilizzLtLlil cuoort]tnuuLt,iirli'Jriri I[,)rr'rinrl
et'apa pregati
-- ----r 1- - -- *ll : in
toare acfioneaz5 un curent irulrortant
il" it cltia"e a capacit[lii de iiarieri,,
t rII iI dtlurirt:i, ei rsae pmiidcrlytotreapzaitrIteinimep1'oa,r1tr:ar,'nctle[
I i. iI
comttta,te
,r-Fr.. (1in cirrent eite absoibit[ de PJ iapt ce
i / ir duce la micryorarea vitezei de eotnutare.
| i- Proeescledccornllttresinlglr\'('r-
V :\ \VI::ff/\ \i \ \\, nrtetlecilrelegeadevarialieftc'lr.]'en-
,, // :\ 5
[l\ ,
r\ lrrlui plin crpaeitatca DT, a t'ittrti ex-
\i-{ p-r-e, ^s:,i-e- e--sr^te (zp*-u--^n+c--trul ff:i^g,.*u^r+a:--tiv e.,,v.,,o-1lr,-t-
v,\\y t/ l/ ''> eaz[ pe dreapt'a cle pantti -1ilf).
tl trrr \/ \/ 'n'

i, ,"n-TEll'o-R--iItptT(a):1'!t

* Iu -ioo(I)) : I{- * Io - it olrtt),

iJ...i5)

untle ioo@) : ip(al I alH ce;nstituie
caracit er istica vol tamp ericd, echi'r.atr en ti,

a, sisl,emului constituit din D? ;i rezis-
ttrdoarcirt'eiuutl'cui.Ju,r,?u'rr,*pbncuefoti.lgnielterarcrcdtrclteaaaatlevi4Daa.i2nTr(i0+aPbi.tna4iersta)cil)aneal;zt.ic'trrteulirlrs)re]a'le<rlzlt'uurezllIuuu]-iil
Fig. .1.20

saltului dceomteuntsSi,urnii ep(iiroelas.tuiattu(4ti.5d5e)')t.enSsimiunilietupdrinineaacaeceeasrty,oi.mr ceutordbtei permite
tratar,ea timpilor
plincipal ;ic-:lt' in
cazul salturilor cle crirelt. Dinamica ploces0lor ;i valorile conr'u-
tare in cazul salturiior de tensiune, sint deterrninate in tl_e extre-

ctre

rmeelaleliecurrebzeuilti5"o, @E),: care se oblin din relalia di,"^ldu:a. Din aceastil ultim[,
de rninirn ,1i maxirn rezisten!:l
irri, adicd, in punctele
clifeienlial:i a DT e,sttl egali cu rezistenla generatorului de tleclirn;are;
este evident
ci,pentru -R4lr;*1oi avem icrrmax(O, deci nu ma'i ale loc

comutarea directi a DT.
Comtrtarea 'int,ersd,. Considerd,m c\ punctul fipprrativ se a,firl, initial
negativ de tensiune I)T r:otrtuti,
in B (fig. 4.20 c); pr.in aplicarea saltului
cle joasii,-tensilne -8" grmind dreap&r, cle paltil, -i/.R. t,le;i
in starea

124

9ZL

o--crc,uiJcnEuccol'uu[I'gurrs(,r*d*T*na')cupar.luru1ro)o].);rrcBoclS-oY?, a1I:plcaepldc.eerJort:;lirurp-rraeI.€crrlnrtar I5aol1lns)alIuancllrolu:Jr+nqo6lfpr-;Itn1l{+nuu1eo'crJaun;ncrpda'pil'uJua6nl'n-z'atfal t1ernnp1

tz'r 'Flg

{o)

rru

tt;.

L-J./

r1e1oll-n,lroInci1lnJnrni-o;rIpraiFJ-pnraIjSrnnrlcpsuqCaeoln1Jrgl1rEnoaos1n1qdIulrr-g.etar(a%aq,>irsr'imraglal'prrfdr.eq,1rlrraregcnuparor8u;"rIrrl*Jylu"p"ucpfrnurir+3s-'gr(+":*p'ltroc"rou|,"hi'V€grrqAu1.ni1red'rl.qcswll+l5esoosr1:;rn?t'1appul1prulr7pult::nc3".-lie?coTuudtJ1uesn"uFeepnt+C0frJnoi.nUlruoprtpOrlaoa-o-lteo'aila'oi'(prl.Il'rrltIQ?otaIrfg,nIos-t]'Iaul:alnsoqAp-"sr-v.rI+l?)s7nlrularednt-ltJsucurv-arru-rnrlI,sroalrIlrIucggars'au.-lsnnll+.oncTupuI€'drnutrooJuJlltIsJepIr-CrYorCoKJogvo+aJ]g!Is)tYgt?rsprcr:oirrdorIpn+-IrI+unurEuIolaJrnltcupJill
.ttltlrn5r;'qrnIZln'tl.cuu.nrndFre; rrrinl l?o?lr3a+K,:rtu? al6+s'fo alcertp Irrglnuroc Inz€c IrJ
osJol{rr r"& 'Bruaqts rtrgJaprsuoC

t,rnfr; ulp

?ua.ntc ap u,ns1ni[,ul,r' ttttil namTnur,og (.ra

'dlr,rop lolairreurlol.ratl tuqztlua,r BaJapo-l" u-3 (ppeol,red 'g1u'rnp 'aurp

a--+-'6n"u,urq6-reoro"1lJ,dqtilrcrarrrtr'Irr*,Ira,arai)luetlJanluo+3lrnuietissrrslusolpAro,uorrr+clorBkn-u,{urean'r1Jsr".Rir1+ior?1iu1'ugagr'r+,';Jtntsnpl1e.,etraoptop"l ppm;rr+irirl,llgri-tnlTt1trslu:,oluanI"rnd,'crl.uoriirIiulnlio,rssr1+??laoru'?luDu.ar'ptJto.nsurJod++l']rrniB-1urIJ+ufttslnoguI.cJue.ura1oasprcopupJ"oEg'anpondliocui'uoDptilsllos+aJtulseoenoouuc,++.r,ludou'o'lrarldsplsieor;ntorJa€ecousrIll

",::;:-:l:",:"::.,;":rd

'.rorJa?I1r nBI)
eau.s"rlj?ol'+r"uoiirJlJirlr*tlrO"i.D)fleuedalcruillureirl,e'gxoo:*r,o| nu(,.i,tip,jir,nr'rru.p*'[a{ruc.ireJaqo,r"+uii-lrlrrr:ro1r-.;rsacj€pl 'g{o'zInptaapnpr+rooclafpulo,iiieouaSar5{4ceOeqpaupr:nco.p'perc[9erp1lcodt3nuu,r)ll
u1 gc ,rrriu,r,iosqo f+nl?I arrqaJl 'rnln}l?.t5er,t]d uoletaqcul utr

'(o
IieloFni,irt *,t

oqo+Ji.sltue,ql?ct*n.a,IrrrnJicoI ^raiprousgr19r'dErauIlu1"raoIJctosluuIr\riira+olEunnaniI{E..ar'r5zqr,lerrrJd_'{oa,oortu,or;u,5ruuou,gorurorpu3rTp;.riglarrrlrla.rrlutl3rrruurrllIr).JIoeoIlel'^el,pov,KIaB+tIIq'nrlvonst;"oqll+}:
oel.ore+)€rgrcn-poetp+uoaprnInc?ouporrlnl2lno?JirpsoxlrrLl!z5e3c'rud1 tldele uI : FcIJIpotu es atluia
-io*'oe" ou. e1 5;rncop alasocold
ri ua 1e;
.roTo+r,leilp

capacitatea tle barierzi,, astfel tcnsirinea tra bornele Df creqte, cleci prcesrrl
de cornutare direct5 continud in sensul dorit pind, clncl punctul figurativ
faaigjsntrnfregrilertciiuvnreaAjn'u.tnuDglaelc"Speiiqnidssriecrairrp{imttra"bordi*eIsaesnatesrurcmli,niciniaaipnre:rapcuitimantcpetuaulslduQelu,biuadnreideecrdu,Iroesne:t punctul

I, {ip,

descarcl
si DT se intoarce in starea inilialX.4. Condilia de cornutare clirect[ este (se
presupune cd condilia tle amplitucline I6)E17 estc satisf[cuti).

'rr)>tr"o,o: rv,to ft i[,u t (+.,roJ
C .\rlA
-i- lfo- tn

aceestii conclitie poate fi oxprim:rt:i qi cu" ajutcirul s:llcinii minime trans-

polt:rte de ci,tlc scmnalul dc clcclanqare

)Q u Q uo- : \:;'"* i h{t)dt : trf,otuo,,. (4.o7)

Arincl in verlerc c[ pentrri milirea sensibilitS,{ii schcmei se alege
Io cit, mai aproape d.e Io(Inj0,8 fp), caractelistica voltarnpericra a DT
:rpl'opierea punctu-Iui de virf prrate
in fi aploximatii prin doui segmente
cle parabolS, (4.16) ;i (a.i7) ; pentru tr"o* se obline expresia

(1.58)

unde SIrr: V81nq#-/8Tf:jr.eYstaeriaa!r,iiiatamt[riri:nimfiiigtur"roa*l "40.,2u2nad,ec"u0rbCa3t1r/./lDInI,t in functie

de ra,lrortul cazul cind

impulsui de declangale este de forrnri, trfulnghirrlar[ (foarte ri,spindite in
practici, sint impulsurile de curent care constau dintr-un curent iiniar
crescitor pe intelvaiul ctlre/rc-otmr'"ut.asri euninutllelinniiaverledleesc7le,sc;i:itlo-.rnapeestient[e2r0v]alul
Vr-I.no), tirnpul total

c(v Aa-v,.)
E/,
l('*g)(*#)-1'tc,on_-rLc(l'pE-lr'A, ) -' (45e)

, r'i

t
!
I

j

I

fa'

t

t. ^o\ 0,02 0,05 0.1 0,2 a.s 0,05 0.1 0,2 0,5
0,0
tol : -> d\/dh +dln/dh
Fig. 4.22
ibl

iar leprezentarca gre"ficit a timpului nolmat tl"o*lro este tlatX de curba 3
rlin figura 4.22a.

,?6

LZL

o!-n I:r,.t In?IIoJnc apun z@ lnlcunil uI KuIDJ€s op 'tlldeo.rp ed a8unfe ,u1e,r
-n8r; p1cund rnlnspclurl €oJ"euyrrJalEl{uorty2r't €c't?61'€r €oJts?s uJ P+nruot
1;noL/n.I(q-1,c<Iu:p"'if.rat7,llprrrna4ul(iourrsplotpsnJndlrnuuldtci1rrouuuuopocuJo€nupuirIf+rlrulrJJopooJ4+nlcJceutz1onqpd(rorsFfppiIpdFutusuonaI.cl+Ju€ol3?1nsslcoua€cprtdgsuecucltdllud-p'auyc-;o.r'reT'prc+1ouJ-c1ool^JverIqS8p{u?o.ntJ:'{r-€elr+lttzl1nuoer.ud.rronncepSlsto;rapit
rilo-fnsrdsoab.ocrodti:dI"'@iuttfltjarTu:cvr;rru'nfotyuri)n1dnrn.rpsqoql.gurqdlsconroqcprgllI6qrE'c7a?stlo.lrpanr8+rrzSafrq'r€r?ll?ps uI KIJ€ es Inr11o?qs 'pc uronnd

qF€SurIonqmcas+srsur1I1JcouJ1oJ1ea11l{se tre1u

gz'P 'Elg (Dl

{3} (c}

'g6"? u;rn5iJ uI o+t?+uoze"rde.r o?uolts rqca oloruoqcs urp tsun l:I snpaJ_iJ
aluod a,!nc;r1c elsectz ulp oJticlJo ulua^?q; ri rropolq JolouloJoo+
repal.rruucrt;ldeu,r
ur,rcI 'H,1tsrporu pnrle8eu plerfuero;rp e{ualsrzar rrc.ggqu;ruduroc
(a.ruquowll't? op rosJns In+InDJTJ ulp)_tU lrYS "P7- "Tg+-sugo.cro'ulsurzIo.t
t-r3ol'Er o alu u11i
C nc olo+Incric o+l3o+ sslllcul ]J +od er.ro8alec
Inun oJ"ec EI aunxsual apr t"tttt1ntknt ttttd natngnwog (q

'€r ?IBliIui

l,ql--:arruIc3a+leoou"uJrcng,iuronru?duunJlos'r,ofTabpiuurrp.up1ryrIJulrocgasnrr+cnunpa;lrl?Ernun^up1Oqolsc(d.JaspucofeolAuiidapitpn+zuoe€dgO"raolr"ls;Ianr?>EirpdrJ{aKa'.€eo;nJ?utcclo'uo1tl-rasllJ-tagelup€anJ5J'uqu;Biautr,:prSo?cnolpfiaa'qt'tvucsp,BloBut3puL1eu-+rorept'llsB'1'uu*uzo+uol1oyurnDlctn'2'6i(nrhrlstqr-s:tccayouIu;Torflscipoclna!'nlt.?l'og'1Jot(2;d'Inq!euludr'Jn,o.guur18)qt_-nzuT-q1uon:p+1nfou?+uorap_{7IJec5,-.rrrrorSu1oan€p1+nvcpce€i1uouel"oTJrnlpnecla301,5ljru3arrSl:Jnd1lu-eolIl.nEalpn-Jntsl5IluqllIconoI-rc;u;Jsdruae+nr1nlln{sunrcduoIr-rl
'tren"ailn-unsrpltnn:dlruldrutrlEgv+I€qgJnlcpuo1plcKt{asJ.plr?uuoIslslIutIsqnuixu.ioqAIJI+lnKtatScJuoarnnpcqolouoJ1+sJu+o1uaorcfJol nlIIcJaEeIB+pm,FrurSlouJDo5aeIunuIzearc3nolnnJseI?lnlnculnlorCt
.nn;.1tRu0,rt-l-lro6cq-';,errepnluJnnrq:,5qou0Znlr(*;.r-:1:,OsTliHn-rdnor5uerry)fnu-,rrl(lu) .orodi+r,;rAl?BrrrrqJEloqulJunTlocsI'I:urt'uI1DlSnTlE/q'?SFlguonparlc{pelor.arrprei.i1lsultnLc5ltuirlr

(rs'r) ,,-(+*),(ffi *')+u,4 sc :*'"th

(og'r) l,irs ^rr,>re *'.fjrrs]n{ls6/n.1 sc - uorr()

r n-rg

€Joqsoc€ o+purISseJ.rtdsxIailql5a'uon,lunrtul osclndopura*lur1lcc.ar'cl3lssoe"rr{e,r.urepprrqs5uoucnlculIanrptsIsoinsc?hcutrsOru1uad

einstief'ianelUig,naAtri.av{,Sioi ndaemscearnctS,ancaaploagcitsaetepaoadtee barier5, astfel DT revine in starea

face ;i p-ent1q cornutarea inversit'.

Referindu-ne la comuta,re.a directl, pentru calculul ItLi t,"o* considerlm
schema din figura 4.23a in ca,re subsist5, reJalia

io * i" : Ioq;{Em-a)iIf :10 * I; -uiR, (1.62J

\,

A uo upn uo

tbl

Fig. 4.2"1

pinq;t:rari'o:itcIc;i/cle,ees(IcfIfailrgeI.:)Iso4Te..E,2dDr4edobseulRfl"iiciim;,ueorssaitbet[reamilcapionamuncnsvpeceaiiidttscauetiintc,ri,:llipi)ntoaopetraeelDialutiinm'"pfue'upinecuuacclisnthrueudivllusuaceililerpddeneopetiatir,tdl-gefierofcfserlcmaarrinlinaeqcltdadaurrepda:.eicnltIaneoDrt-irs:Ju?-t'ic'!cqagiiti,i
rezistorul Il conectate in paralel, atunci se ob{,ine calacteristica

i,.(u) : i 'f u'lR - iD Io I ulH (4.63)

care in interva,lul o-uq se poate aproxima, printr-o paraboli, (fig. 4.24b,

cnriJa plinzi). Timpul 'tr"o* se cleterrnind, din relalia

trro* : C^ r"o t!'rL
\Jo
ts

u.ntle ic, : If,-i"(tt').

4,4. Circuite cu Df gi bobine de inductanld

4.4.1. Circuite rnonostabile

i1 marea majolitate a schemelor rrtilizate in tehnica im_pulsuriltx,
circuitele asociate riiodei tunel (de alirnentare, de cleclarrgare qi cle sarcini,)
au calacteristici diferite irr legim cont'inuu qi in regim cle inaltS frecvenlil
alimentare (tig. 4.25a) saq
(comutare). irr mo4 curent, irr circuitul de
irr cel t1e sarcin[, (fig. 4.25 l-r) se conccteazri bobina cie inductan!fi (uneori
incluctan![ pot fi qi conectate concromitent in ambele circuite)
bobinele de in func!,ie de valorile rezistolilor R, Rr,si a sursei cle alimen-
(fig. a.2i c).

9I-A99c-6

!;6-1iqo eungsuol op .ro1-r.rnslndtul €uIJoJ rrcrlqJotctsr€c e p,Lrq,rzod 91uud
ep egunr{lod od e1uo1 yfnloaa fnop r* eplde.r lr??nrnoc pnop 3e1cut';s1p
aitu+e'rurlud em{uoc rnlnuralsrs .e erfnloae op nI?Ic un 'uoll€ptupJunldua1c.ru4l 'a.lu$
-utspop ep spdurr nou un qeclldur;oluodlueruour+socts

9ts't '3r.{

Q 7"V d,l'l *.

u'p-frrlapcEleugIpnqpdre{dI+qeslooltJsrEolnsoJl€n€r€rlBu+'Fanuu+tI.usrrqolnsoclnq€EruzouatJ1s+to.srsrndrlsurJrl1€n1up?o'54?c1uuluoerlrIrlsncroJuc{lnrnu(d1uooeaq.,roregr.+ro'ougrtoncltpluuplrzlc)eru$eenqsr-d{eeeledu1ret4€sp+afse(osuIpIlIrCIqcEeI€+t;ion€{IJFqrtarrllsy}r l
a--'rccrgntlsep(r;€u7rc1ny5€orI;ontstrloznrJpnltcls$smupunoo^cd!p+ot+(Tso€ItouuoJnodgpTesuJsuooIpoctsplsartfsd+retI.€erre?Juurn€lalr+drotnsp'm.?r€coeoncJdu€e€+epus8rlpnuuinnItsslKeuel+cc,oqJlrt".s1rndstu.err€onp+c3€urrt;lnd(ppuI olac"d'reup(lnu7padurroycrrruimlunJepsnl
!au-'?Vu+.rwqsrlrat-cnFaTp-rlprur(Fa*rpppelguuqs€erpuupdmdfnsuelq)rrlcpdrKsrrIruqneE€u{cI1nroIultperrIIrl.s'rrepepa.Jc€rereru€Jlpdr}cstouqJuFF€srqus(utpn"sezrq?nepsdooueuru1rerpo.lr'dr(nueonuo-e9rscpp6gou'r?.lnor{e+ul'n8puaIutoJqsr,)8rrroe8JupCalnurrrs-r.ur€I+aonocprzF+esru?rrru"J+roo+tus+JumcoItedsurp'rt€Jsqcoe.lArant-p'&c} il

9A'? 'Fld

{q}

'1,iHl7T-l'Y,',,5E-,If-r]*Y". IUi-,J+_-g'

liYl-'? T-' ;fi

'e.re*uulcep sp
lrnqndurr Joun rrrgclldt eurn u; ?lnruoc epq€lslq 16 ouour olotuoqcs I gq'a1su
nms llqrlsouour'1-rqe1s1q nnFer u1 euol{cur-r; 1od eatlcodrc.r eleureqcr 'ol'tl1

nute la ieryire este arS,tat[ in fip3rra 1.26 b, unde sint marcate qi punc't,ele
ce delimileazi etapele speeifit'ale.
imTpimulpsiui rdileorc,omauutaforestdidleectetirr,nsiiinnar-lei rsin5, care definesc fronturile abnrpt,e
ale paragrafirl precetlent; tretruic
subliniat taptul cra t,(/, deoarece curentul de clesciircare a capaciti,{ii e}e
barierd, Ia comutarea inverszi este mult mai mic clecit curentul de inc[rc:rre
la comutarea direct5,.
I)urata impulsului de ieqire 11 se detelmini, din legea de r-aria'fie a
nteengsiiiujanici uIarebnoturnl eplerinbocbainpeaici(tiantterrarcjiot nnceliurenfeiiriimc:la procese lente,
Cd.aldf, a,stfel se porr,te
---'[D\.
iL

Ldipldt : r", lut : "\+ (1.$i)

iri circuitul din figura 4.2ita, subsistf lelalia genelalir

t1 : Jrro-Q j- irRt), (4.66)

deci

', : ,tc <t-t: L\,I,u,r"":; cl/, ,,H): r-\(,r,p dto (4. riT)
\,u
+ a{ipB,-\'oo

Oonsiderind R:. : 0 qi iuind aproximarea liniard, a porliunii cle ca,-

racteristicd, cuprinsd; intre }r, si I/r, sc poate ob,tine o expresie aproxirnatir':l
pentnr 11 anume

t, : -g- :Ls","o" l)on',. e,- V oo Ls,or" 1l'oi-*11,'o'"o , (r.6s)

uztited.ae,gc2a2ra- ctQerois-tiIc,\iil(Vstra-ticel-,()veaslotcarceotmtrlueedtiaant[ta). I)? pe poltiltrrer de tlifrt-

Daoi, pentru portiunei] tle
caracteristicd, cuprinsd, intre Ir, ,i l.'r, se ia aproximarea parabt-ilicii (re,-
Ialia (a.19) cu y ': 2), se obline
('-'rt:
2 L(Ie-r,) -:i:"?#.) (.1. ait) )
Vr- l-,

(influenfa lui -8, va fi considerati mai jos).
Timprrl de revenire 'r, reprezintS, intervalul de tirnp in limitele ciim ia,
punctul figrrrrativ evolueazS, pe porliunea ascenclentri tunel a calactelis-
ticii, intre puncte D qi -4 de revenire este determinat
; procesul de icgea,
de varialie a tensiunii a", canzatil de cre;terea lentd, a curentului
prin rrlnrare iy: io,

:'":\i,,idt L\,,: dio ioBr) (1. ?0)

vor-Q {

Considerind qi in acest caapzroRxirr:na0tiv$5i,opaephrotluximtiamrepulirliidaeriir' eavccnaiil'aette-

risticii, se obline o expresie

- Lgr,-\v:b \rnn
.1' Ad,u Lgpr, t (1.71)

:L t,o\.,
-3L-JI D Voo o V oo - I'o'
V nn-1)

!30

rst

.1epsu t (s or-0T * e-OJ Inulpro op +u1s rt IS 'l) optder oull-oJ luls JtT 't?

orts+n.ooc op aleseco.."cfgi leZlco,rO.olnqor+ IIIgI Itsi['eralco.rd'u op ar+Jatqo

Frd,u ? iD) l-'oiirxuiie'i)x-p+fu#e^*c#olriJ?g+"lIT€uff;#e;fpfi,rirf{ru;lJrc,#soH(fAld) 'r"i"r"'"rni:s1l't"t?ltr;rr

4L{q) 3F i#i-1":#";",":r',tfii,.$iri"li**"ft,Tllilifi
+' peduri as ELZ'7 e.rn8r; ulp tnuoqcs oJ+gc op o+l?zlu
g-;rrrniurq"riil{e*l{UirarlssrOze,'r(1ii'7roTu:r.qrno8crlytsrz?actr)ul6qo67me{ua1l;srarpz"are.r1c'lt.riuo,tpr
"A^L--1rc
u-ooqpir:uur1npLprert.a,6rrsue.grae'oV4url(sd{alogecJtsrfnr''ui('oncsf'rqru-pli)8elInanqrurla+;o'rVrrqr1siqnusnJrc.'ppdn.r;J3orucsrrolns1cegyuo1),r.Luogi'uPIr1I1oa:IupnJJurJ'rc+auualossurig++Eoton^ucplrtItrpssqq0uueecuIlJois:pacuolrl+ac€l{rttsrarls*gpsIuzz..lurotOlzl;nlqtocaJslc1cono;soiptll.Kpur'lueetl3sca€:rpolrpuore+pnJJnl€otooucospla.al?rplFi+pIt)nI?o;IrrrIiltllltIfl(rrluot)?uiJlJ{tl
1tb r rB

t .).'uli

:tj*tL

'ir-rxl?ur 'es.rncxe ap rs

Jola+uolualo oIrJoI€

Gt'r) alSoo i1)d !'Cglot,i< T'lo.tl >tt

epritpuoc olncPJSr]rri

o+,t.1eqnl"up,1ra*,.Iur"{Sc'oql"*ruJnl*rTetr*ls'ucrqicioluse*€c+oofpFou'rizcib"Icsnar'ipsor-+JpJJcbmDu?eanrs.uo.rpitlaeIptisapJ.ls+p"reuFlasnmpruc{egrlqltesueps,oru5dinl-evoia5luzmu3ouuivjqdr1'osa-oug'o4-1ce{olaletuledr1Aoi'a.pur9,r,lpoie"cCpua?o;gors,t;'r?osroeoJoz;ld1rpIrooep1oscpp+lceurnqgruu.9lrciruIu,5Drl.J'lrreollrsotItJl+?scsyu1{IorroI'zIPandoICaqIg1+pE'q6'rs€'[email protected]+rtlo?q;csl'1'm€Z(.g+cor+'Iuu€flonsunJtlf'ges€FJ,rrso]5crrlrcu;o)rotooas'Jo}o+-luspal'rr+aoetasprupl,uplu1pcnule1elurllo'srIuurtac.+"rrI{p*rsrul''lrlrllasl'rlrliTlu"mulIoioIluI'li}pJop!r

{ I',nyfin1lc s o t aut'to n t c[n sn t 3'in.tept's tr'o n

ollq?ls€ alln)r!) 'z v'lF

(o.ruiuuluep) oltrcose olollncJrt u1 (t,rolsrza'r I"r JO op'(Prurirucq;uq"r-rt'oa'ctB1(ua'st't"trrt-r\tlttrr

"ooT;_;-q-"piocpntn,;{c",u1.oilpiEron,*rn1l1J1cJulpJus.hr1o.;opJt,z'u;Jpebol€e(Jl-dripclo,;)To6a)i'.cllrfzepres+EJol*ofdJeqaflfncrlSc+pbin^reerl.utu*r€,6"1.ru,,fsty?opurgr".la"9r'.C'e"o1l1tsn*prpe*i*rdapooo1pi.r+1tlri1"llurl'pl.alg.rrlfcrislc1rpu"lutoia*rioaelpr'p:+luf.rrlairn+ncturuopl;ailsrrl'uildu!,dltlrd;rznol11llauertednauruuz.rr,r1tl1rrsfmlt+'?u1caPorseili+4,ueuorB;rau.q.orrluor{pDu'l.}rouluusEa,rqrt1rrlsop.oreei!unuatl)1oeIoIaouducdu'"spstsrIotoeter:pprI;'IosprUot.uorI+iU)Bo''rrlrrrlru1aoIIJnnlr1nl';narpuu'"qrqsJrzoul1lloon,rquJo:pjrqd.r-ju{iJ13e:ur:ll,'ntqrr:)sro:r*'c.o.ldt)($]i.dg1Elu"ur,t;]Rpao)tltst(lu'oulein6n-3ollll!€);perr.te'l€ltl.tI.uotlrtt.p,r1l,o7dl,rI](atc'I;'l1rsltlItsrr{Ur>1r}ttsl.JLtulr"rslort.tl'trI:)'r;p(trtr''ipiirl

(at'.r) '\(n"in-o-o'"A, o.1-''l - oA-n-|

"l nl - u, - --t\) l,I vrWZ - 2,

our'iqo os (Sf 't) gcrlocle.r'tzcl
lililltl
?euoa.r.ernrutrxoop.rrd?u+uoaapuno;"rslueemtt.tpnutip.rrol-O'(flerl&?r,p6o6t'utj.uual.crunopluu-or)allJalllssla'radtc1tsfdJ'7l?:cor'uf
eipun

pelioada oscilaliilor de relaxa,re este determinatd, in principal de e5,tre
inductanla do ,,cronism" J.

Ecualiile care descriu evolulia sistemului sint (fig. a.2ih. se eonsi-
der5, C constant)

LdiLldt:Vnp*itR-a, (4.74)
Cduldt : it-in, (4.75)

iar ecuafia ce descrie evolulia punctului figurativ in planul fazelor (st5,ri-
lor) este

ldir c vor-i7E*a (1. ?6)

do L i"-i"

tiri Ciclul completaluneioscilaliicuprinde 4 etape distincte : doui comu-
rapide (directd, qi inversd,) lnso{ite tle valialii rapide ale tensiunii la
bornele capacitd,lii C qi doutr, evolulii lente pe porliunile ascend.ente atre
caracteristicii statice insolite de varialii relativ iente ale curentului prin
bd7 oitnb:insc[i.hneIlm{l^od"t,ir,n, dlinp:urilntoim/lV*e**le,rS,ittrO1e-:io,elticfmru7ia,t,elitlices:edeptvloractriuainnlitedroeadluer,cceu: rmeLnfltIru^imlu*iillVeqintnaeoxn,rsmriucitnt:eii
: CV*^,\I^"" se obline :

,li" Vep *tir"Rt-*- o (4.i7) t

dt" -' -F
I
ddat": ir,-io (4. i8) U
/-", ,
I
,li :!t (V DD-i LR-a)lV^ ' (4.ie)
tlu" t
(iL-id lI^"'
b
unde
t'.
V: rclct: QIL) (7-"'/1-*)2 (4.80)

constituie un parametru obiectiv de apreciere a formei si frecvenlei osci-
Ialiilor : (1') daci, tr.->0 se oblin oscilalii de relaxare, in general de joasft
firoecraednegdc,o, mpeuntatrrue care existi,o disproporlieesenlial5, intre duratoleprocese-
(rapidd,) qi
afolporsoirceeasetlieorDdI ecu,,ccraopnaicsimtat"e(ldeenbtea)rie;rda,cemaisctifi,i
disproporlie se realizeaz5, prin

cqri oaniinsdmucsteanaljeulnogredleavsailtourai lmiaaprir.+; 1(2c')inpde m5,sura micqord,rii inductanlei dc
duratele proceselor de comutare

qi a celor de cronsim sint ctoomt pmaarai bmileul;t se oblin aorsmcoilnaicliiir,.d.eI-ninaplatdr,afgrercaafueni ldde,
de cea
forma lor apropiind.u-se
fa!5 ne oprim asupra oscilaliilor de relaxare.

b. Paramotri,'i princiytali ai, maltiaibrutorulu,i cu DT

I') Eaolulia punctulai Jiguratio 6n plaruul std,rilor. Pentru disculie

se considorfi un plan al std,rilor normat (2, 6) conlinind caracterist,ica

staticd, normat5 ioli:) : iD(rlI*, (fig. a.2Sa).

132

88t

:-rtirlasJu'lrstselosseJ(npolorlpu8€eouJ€euleorl{huuen"Jrag'+prnpc{useopdrze'€rIlaetpooe+anunEr{€"raod_Iandulpo1'lesnls11ias JplusrerJ'FruIIqq ,B;)
ee.,rrnn3F1u;rsayl r'ntlCnurengc.s?tsnlineeo,rvr'r1qul"arxn?8rIn; wrnpnlacnuunodf_icne'rn{.rn{1(ool6a
-Igq./a op oJ€l.s g1u1 at

-g.ru o+sa qgz,', o

gz'? 'Eld 'P

::lt oJ
op
pplde.r u1{n1o,ro nou u}p edecutr a'r1unft;
tD
i*irli6rlnrd{gn'pc1lube,nraed"np'dtlolou'io1eop'paniucyueultcrunnsdr5aefulpys1'l1€ipnouu1c1pa6olruirpnnctrrn€'mi+1u1t*oo-"c?p01"ur1*€os-oc1bJs.tdrsde.'r'co*rvuptivluaucrueund{orlIot*Jsdu'o0Tp+q=.u}r-eoKdp"ceul rsoguccrosedaeeoretctgs',ouI,oarltuqJs{u1"oor1o1a8.rdqa'
FX
(re'p) d clp ?.1 slp -as
orl - gp 'od ,!p ?s

:efgn+o'1dl'nodlsusglrir?ofors+a+s'pceTutssserI'ceeIJscpFtT+eldosep(€irnleofgn.r1ricu{onr1od.irgi-erqq.lee{o.rrynepa"dr€prlzuu-ooe+ucdT1Ae[gq{lcz€uuu1qness4ptl(sGppadr'0te1o'r1uipll)m'ao'5-(s1nt1tep;('.leVp9-r-u1u)tc1"ceus!opn)a"rdgfPeEczlgrt+espc€J.eruIop'qoepoPcwrprI1ur{outlPssI -I
o"seolullelrpou+eccovlea.rpf'e,6gluuen'p1u{iaocdsts6Eegeu+n.g$n.+rolsd'eegdqbe+qusnu+llsol'eolgaquenlds u3 | gzwazll
-c'"ler+ elelcund u3 (o
-Tqqs
::--'toLcia{icJLesurr"loi(r"eunl-LrA+ospeo$rp1ocilooog6lcls.uroenlcldcouttun""rArn+l1reuu1)sel'oipr3fenFpiSxmeildmsorlopi uuoec€rlale.ls+plssolrda1r+1nocol€l3sruIrc'o,,+ancpo€1'r'dge€sclr(o€( aco+IT€T+{gz}r1zr (o
er{cas.re+url-ur o'*pqoploo'l"ctl1ttndAy'r,o.p?uqbnccltscrocdoap.rwp+pumozrlsrooplrrro*+ecloelgen.4oue4dl
;t -:aopldorpe1u (e

*d,(n 0
gi"g-l.uaii"ifo*tnpa1"zqo;Ie+un1".ilndror"crf;(i+n""rOn1c*aoifa-1''ptoq'1)osuupeiq.irlur"n{grnufytcl1yisgre'cpuglolaaTcpieuP€penro'doegpp'<pl(sl-eruArupotuarcrtdlucu1o?larrlrurno'1fosepr1dyies"4ruolesnroS.euc€o'r++cIrt*l)€ru'rBi(nlonolppssluzJorvoldyllzpltz-prlt)uacp1g1urqxprneoutdmrl'ddOrpeo'Im--Eulqqo+Fp€culrI'lolluu-pSpp1ssll
o11

II

UIJ

oI
€I

-11

(gr

(r

-I

3J

la irrciridelea, circri.itului tle a'limentare ia narstere tensiunea, cle induclie
r{u-talo,rcarreepfroeazritnetir'ndiciifre, rlean,btaorndeinletrDe 1te',nassiutfneclapduencatluiml feigntuarraetirvyi tensiunea
,tJL, lentl a curentului se gd,seryte
<fu: punctui de virf al prin bobinS,
vcciniiiatea lui -4 ; apoi are loc creqterea caracteristi-
in prLrLctul figurativ se deplaseazralent spre

qi
aii D1'. Ajlrngind in punctul 3 are loc o cornutare clirecti, rapidil pinf,, in
pnnr'1u1C.In timpul comutiirii tensiunea o1 iqi schimbX sensul (cind punctul
figllntiv so afli, pe porliu.nea ascendenti, tunel, neglijirrd termenul frR,
it\1,'Jn rr,: Von-o)0r cincl punctul figrrrativ se afl[' pe porliunea ascen-
tlcntri de difuzie avenl rr,: lrto-o(0), astfel evolu,tia urmi'toare a sis-
temtlui este deiterminatti de micqorarea curentului ?:r; punctul fipprrativ
sc tlepla,seazdlent pind in D, unde incepe comtttarea, inversi, rapid5, pini,
in ,puni3c")tuI)lu,,r4a-tae,tcp. i perioad,a i'mpu,lsurilor. Procesele de comutare directS,
;siinitull,errseiliasliiant(4tl.e3s8c),risreesipnecptaivralygrraeflualli4a.(43..101);iadr utrra)tte,.leAaicceisntoer
procese
referim
Iir duratele evoluliilor lente a punctului figurativ pe porliunile ascendente
alc caracteristicii 1)?; notincl cu rr dnrata evoluliei pe porliunea -4-B qi
cu 12 durata evoluliei pe porliunea CD, irr cazul oscilaliilor de relaxare
:lYtrtrl tr, tt4iy l'2.
Eaolrt!'i,u pe porliunea AB (durat5, de revenite). lieglijind cure rtul
fs oblinem
siste'mul este descris de ecua!,ia (+.i+) in care 'tz: int de unde

-,\ ,nr o tlin (4.82)
JI, Vno -@ -f i,oB)
":\it,uoat DavTerrrlyitererrzsiiusnteeanlaUD]R?:foramIeaizofiB' o;

relatie simiialri cu (4.67). Considerflm cd'
dioiti tunel echir.alentS,, la bornele cS,reia
cat'acteristica diotlei echivalente este reprezentatl in figura 4.29' curba
plinri (dreapta cle sarcini, staticii reprezintd, o linie verticalS,).Coordonatele
prrnrtelor de r,-irf qi dc vale ale caracteristicii echivalentc sint (V1,at
Ir). \ l',n, 1,) li (I'sR, Ie)
rtirrlt
Tpn : \'e -l InR, \'rn:Vo * IrR, I'ro:lrB + IpE (4.83)
Portiunea ascendent5 de curent tunel
se aproxirneazd, prin rela!,ia (4.16), care in
cazul nostru cler,'ine

io^ : fzll-(1 -aapil:nr)t'1, (4.81)
unde 11:1 +
2. .;, : 1 rezultX
I)ac5, se
ia

.vpE tlooa :

att:L$r"\n. V pp-Ltpn

Fig. 4.29 :Lspt"(ffi)' (4'85)

uprnrrr-lteirtgnrepa:,4RQi,soi -VI,)ol\:Vol-or--I-o\)'ruclsutfelr.coDnacclu[csteanialay,d:io2tler'iezeuclthdi,valente pe
:'9+F+[' fi__f'" (ffi")]-'" -
(4 E6)

t34

9gl

qoAtutz * r- l' t'

( ao'r') t"w,G, - -

auriqo as rliule.r gnoP
url] rs ry : zr1,: rr:, €Joptsuoo oluocl aS srrcrlsua+cB,rEc €IuJoJ
ara{,{rrirn
n1oi"""11,"T qrIS 1u1s drr. rt-ir:. purc rurldo urr3o"r un e5alu as 'gc€p
;:;il';p

l\/dfofril Alur aI oo! ttu - \ - zrL

T)tut,'z

(ro'r) qo I Tutr uT Il{{7r - rr-:'

ooJ'*+ L

aur,fqo es (pzned) o.rIuJ-\Jr ,ap InIB^Jo+m &r+uod

f (o*-l - utA)l\udA -*'-l)-ztu
"l ,', - *uA)l(u,l - ur^1) - rirt'
(oe 'r) I

[(oo,t - '*A)lFoA -oo-l\ :. ouL

- - '. [qrrla"ppr"e"roi+(lu.rdoaziOtulr"*roOre^'ltAuii.)ircnl(tpIi:au"rodudnrisl)duTO2-af:sI*i''a-(iotttbyl"' *-r*o*"lrllqrTrolr:qrg$urulrl,ff n"3llu*e.,d:8';r"o-ig-,trtn"Jslfnfit:lu:Sn
o

ra{uan1;ut €or€nl€ag

(oe'r)

! I,*aoaArl--"uaott 6f go,t _utA. E6L
rJ
-(r ur)Tt,

ourfqo es t - z)u nilued Fo1'euu Poru uI

(ss'r) 'ff \lo'"o,A--nao7a)\urasaaoA--ea|.a,o* _l eaA - utA -

L JTi -zil 16

ooL-udT all aa(L'-o!PooAoor/\l z-_:?D'' ct(
*o?p oil'7:
q\l:azr

ur'iqo es (, - zL PuInT '8 + 6 : zJ' oPun

{rs'r) q*ltruo1 - ss;)le.t.L - *oa)f(*I - uI) + "I :2!a!

Inz{?c trJ e;rrc,( itl61'p:f)tne1'iiet1sap:cr *urr'"urgdtpinzpue) 'rt(xroc.rcnlauu'nosxi.t'rocrlt+r na.l:dq "fiit:|""fr[H:
I€aJc,}fiI
1*""* nt'in2oag

Atunci cind, lErr.vroafli,azpda,rianmliemt{iJterllemp,eiarmvisaeloproilnetrwu te:xListe+n.la'Ta; udtoeoasscei-- d

1aliilor 0 < -R { ia
rnene&, limita de varialii a hi 7o2 in d,omeniul de dt
f-i:g0ura+ 1. fnfluenfra acestor paiametri asupra lui autooscilalie este
Tinar lJ
4.30a. c, oste iiustratd, tI

Pentru durata impulsului se obline ll'

i t Iltzz: Zr"*rft - mz(\ - VooT In 1 + m, tr'oo t (4.e3)
TN "(
v oo)

r:r - J 'r"-r.[][--2 "m'rzr(-r - /t oDD)I *--- tnt,tZzJ\ - Toil"tu f-l rnrft - Troo\ 1-

rnr(T=T;* ];

(4.e4)

d.itcf, intr-un regim optim se poate consid,era rzz : rzs: rzr d.in gltimele

clou[ relalii rezultd,

az: tL I,5m, (4.e5)

L { 7,5mr(7 -Too)

imlu,stvraafttnidaf,zludine, nifnliagluimmra5it,e4ri.lm3o0imlbo2r(c:YinaOdp,,b$R+i ?n2 asupra duratei im0p<uAls{ulrriolo-rroeslt,o
limitele
variazil in

1,S).

Perioacla impulsurilor este

rrltffip;T: rt* rz: * Lr\rn,

L { I,5mr{1 -Vor) ] (4.e6)

?

I

1

0.5

Fig. 4.30

tr'unclia T(fr") are valoarea minimf, pentnr o anumitl, tensiune
T'nn: Vonoi conclilia r1e minim este

I d_T \l (4.e7)

( at,, Jio, o:vooo: o'

It6

Lg,l'

< o!: * ,I :olnqorl

olneo."4
lurlrr,zeo1dg.rrnnpps"lrnndSrrsnarp€I+*€0rnp ed I ,r 5.regcnzrireord{r'ep!upoese?c+bn"aigi"JesLrltqssl

gg.cenp
ylyj^ "d-Jt/< ?"l*r€E:-r1lndyu.RI.r{mIo"*T9rpilrqr!pn€1a+uosyep9uf+9fnq'd.=Ionilrgsn"aci.radr.i.eaelszBer!ueo'L.tudrspro>nrorta+s?+s?i-ir1sd€K)uousrJzrrepa7o-aregtu*su)rrr.urLelao*psqlnebrcf+1ssilaeqd_o.euar+r[.trenpslpaoreceptspilezb,anrilrenrp.lrurpsuzrlphoot,drdren,qaupsspl,enad.*?pr,ou',.1pn.rt'aa'r"''usr1l€an{e,slr-8ro.aro"o1rupdi

rg'? '3rd

l3l FI pl

-wX) puI+suo" ,qlt.? Frr**-lJ uJ F+€+-€rts_tsrr,roJ ne a.rutuelcop op elrrnspdun
i y ggqels rar*ls ui
e.rnfir; urp rouaqcs IFtIsJ€o.orstsuuuoor{qccusnylE-eIipIu'prrr'd,ii',,rrr:6,Ig,d'p_.rng*.rduL.*rtap$p1-'1;ni """ u1g.p
q q .tCaT-?:partd4r{,as?rualu'alq('suotrrtl?rs)rxJraoiJ€e:qoaacJ(l"aasrarp.eurs,oioensup.qoedr.eJlc;caurauarn+tnnpufduuun€omruesprrpotou,slrnlno'a'-cp?l,lrsErarm+roloauqusOlanolooqod+d_crrp+rrsusssIrJeinguresdpaoaacl"+iarpraEeu+1ac+-niipnrr,xlOruprr",trtrurio,o,tnJa"ilIrppdr.amaislp"Sasap^l4rppon.rl1dnu,arusu,"1,nrirnrnsde1ypueenn,r;tr1nroiowe1pc"a.qd7ille"dlui(ndl"ew1q+r'€c,(;mi5++i)sl"f*lr"1qd,s;

:ffjin tl?i:fi|i,?ff

.roF.rn1uo.rl rs'iirurrol
dlqffi ;"j:# T;a T,B a

IJrls
luop uo Ds € o ru..,f d"ro cI o o rtsnq rs 'rolrrnslndurr L
rar']. aJ€
tsulaqcs cllts?s. urrFa.r uI

nrt1ui*urv1,irpllyd,z,TtrolFug(.aDIdrdl*_cn-nKctnulrr1ad{€,lgrrrcclqirpueBu1rot+.prr,lsrudc,rnle"qquc,ruaJacrlolllo.ll(,lappurnlcleoic1qsJeoar'caacael-usaaurpprc€?,elelnindu_clsIruouasor,qirqci€e€aol,aterts'rplo.smr1ararJ"ulr?nr,rrpuaouou"prlotoqaqios"zulqpar""llrcrrpo'anpup8-gneuJ+lrerBeJiloruar+;iaputsalOr?rnze.pa1urodrqqrdcroEmrqi; (

allqPtsrq allnrr!) .e.r.i

l"*f lr:1 u. lunpro dur r. s unr ua xu'.'ru.nr rrr n lr+s uoc ar B lnr un r" prufngx,u;u*r'uJiulJa,lriclSa.rT; io*Jl€tu' rJfnr

t4ie1,rur oq.se JolrJnspdrur
(.oeapoer1o)rr:r"adrroeaut1s{qooaaarls-igoao.irli;uoirg,s(usoO1.f'a)'qei;ra4de,lpaql itp;bI;+;opl
u-or.,rrdlu'ol !'!P7qa_A?)r?u'Llul:ru

,wv ztut z,
(sa'r) -. I 9
r'TtJ- _-oQQ t a

€llnza"I opun op -

-l

sd, satisfacd, o condilie d.e forma relaliei (4.56). Parbea negativ5 a impulsu-

lni-qneai,gipoacoatii)rv,ei,n0u.esrvmPtoauleruenaeazca5tziundli,imliflaieegldndu,itraacstltepidvoruaepare5sjrc,treancregieaneapiinnsottzaeDitbrivvil,6dasi,,i,udBnluu.pt,dS,p, ooatesaYirtnmeedmicnaoaimlcredu:aotailIiemttarpis-ui,tmalIszbpu-iullu-ulsil

\.---

\ \..-o

_\\\=* ':

Fig. 4.32

pozitir., punctul figurativ evolueaz5, P!,ilo$ignea ascend,entd, qi la ieqire
ieeiemsrz-t6pneluiutsdlesa,at'izcsddofi,mv,clauuerttind5a,,tl'icsesocpnhi,dreoinltreiaasntsaiini"ruen:saitiaIilrnufeiigal-ia.4l4.I5.,.(,3u2-."4.b,)pi.,l'ine1ssd0u,_pspucnaheretemtraaz nu com-utd, ; dacd,

negativd' a acestui

) lr,r,o), do und,e

l.unctionarea corectS, a fuistabilului impune ca cluratel€ ra12 f1.2 $i
faAimxneppalliittzuuiddl i,ininniliulefu1fnr,,c,qlIi,iesfd,d, .steraetiDbsfuaTicei, aasntfueml 1itet*co,o;nn{clil'ici4resttrnictivtze"o.^ Duratele se

sd satisfacd, cond'ili-i1le 1 T ry 1t1.

11 7 I n^u, - I n^ro _l-''i pcmtxs (4.ee)

IB.u* - fr.ro *foc-u*{ fr/-In^ro- 1^u* iiocmitt (4'100

r1r.rtle i.o qi fos reprezint5 curenlii capacitivi in punctul de virf, respectiv
deechvialiblJr"ua'gciapiir,occteesiie*ltercdiiesctoamtiucteariteoplioctuarveenaliivacreiac,taiirastcatteisritziceeaziai rsut6ltriimleedlee
dou5, inegitiLS,li trebuiesc satisfd'cute pentnr condiliile cele mai d'efavo-

rabile. in relalia (4.99) nu se pqu conalitii restrictive cu,privire la limita
Deqi
dfcsttldc,iuee,iuaeoiptnnnisprn-dsaseeiddcceiicurauue"caitno-dcnellaudeeatriranaeriaisidncnqcnt,ei!aftuiIra5acTargcln,leaasaufqlpemlatuiisfioatvetbia(lrae,afelriiit&srae,giiVpctz;,.atdoei<fuin4bl,eara.0enizal3rlaurdba.2azvd,lubOceuapiDe)ioailei,es.nzdIst{nddPeeseii,tnemiuprcDunboivuppnntaiInuuvritenuleelcnopcsinrtatcrasuiesinatteailuplujaSzucfio-.(ddinp,nfgdtr,,igruiglueaoi.orup.crnadnaoiaprnaJieoe.tzebnu3idaiaviml1tldlaeitcav,duand)ce,iedoclntecaadiv-b_nsortueY'etcoiinusrlao>.spittDpndiaYnonpo,?dbezerotu,(i.ialz:Dtcudceiji?uvotltafIiuDieenuv)vidzcsidit,(a,mtaosfui.rieatnudgaieenaear.igdcaoi^rf4-iliilPparudpic.,crn3u-ionooeuiq1lmnidslfaibtituur,udut)r/ufc-i-oll;

138

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ftotv) i n;v : ,ur_o (oIV-onI) -

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sosind. impulsul urmd,tor, pe intervalul f,r cul_entu.| i" *dTBu aproximativ
constant, apoi creqte exponenlial pinX la valoarea IA-LIA,
adicd,

A/u * gAa_ LI) [1-s-(r-"t)t'of : IAB-LIA. (4.103)

Gama de varialie efectivd, a curentului ri, in timpul procesului de

nuntir,rare, cind punciul figurativ evolueazd, pe porliunea ascendentS, do
difuzie a c:lracteristicii -D?' este

Ioo^rn: (I.{u-ll.r) *--t 'r'-l1r I (.r.104)

tinirrrl seama de relatiile precedente se poate scrie

-L[-1 r,-(r-';)'r.'..1I [Le( r-"]/; "- L) . (4.105)

IAnnit T 'l:, !-e -(f-:,):, / -

-- ''AB e

clec Anfrnsarsec, otpounlsidceleteri,rrmninpie,rniitrp:uer1io,aodeviarlnoianriernerneacclhienirseezualtaimtSp,udlsiunririeolra,tdiae

(4.100), anume

rTz-med - /r-1o -j- 1o*"* - -T* Dmln *'ioc^rn , (4.106)

2

iar abaterea maximfi, a amplitudinii r, fa!5, de valoarea medie este

A"m&:x I or*ro_ (I o^r*-1.,-ro) - (?iuc-u* - itcnin) (4.107)

lz^ea

Presupunind c5, totdeanna abaterea este mai mic5, decit cea maximdr
conclilia de-funclionare corectbi a bistabitului
in regim de numS,rale este

Ino^in)I"^u* - tromin * drcmax - irc^io * 8fz-.4' (4'108)

Introd.ucind ultima relalie in (4.105) tezrTlld'

(4.10e)

unde

l: [f^r*-I"uo * irc^o"- ?]oc.ro * 8fz."d]/f,48

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loc o,cre$tere rapid5' a
Au-i*f* Io, mai lentd,.

*l*p"frii"i
p-;;;; o p6ednnstrtuan.tcd7t 1rl,6:'pEra7oiep$t;t"epreeantrlyui-1?t1ers..t^epmtaurelt
ioi f iar
ln multecanJri practice semna-
lete b) Irnputsur,i d,e aceeagi potaritate. de impulsuri do
unei succesiuni
d.e'declinqare se prezini5,-sub forma

ttD

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a

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q

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3
o

i

ziea caracteristicii DT. tn final bistabilut ajunge in starea stabilS, B cincl
tensiunile in punctele a qi /c sint * VulL, respectiv-Vol2; dioclele inverse
sint ppoolazritizivatdeiolndapuDnIc,tualjaXng, eaIpetapraocrtlieurnisetaioidi esteaotincdeu. cStaosnilndd, al doilea irn-
puls mare directX

(cadranul f),1i impulsul este ghidat spre catodul DT, fapt ce echivaleazfi
cu aplicarea unui impuls negativ pe anod (in acest timp dioda
polafizatd, in porliunea de concluctanld, micd,; este iniliat astfel -D1, este
procesul
de comutare invers5,, la care distingem acelea;i particularitd,li ca qi in cazill
comutd,rii directe.

F5,cinc1 o scurtd, paraleld, cu metoda de declanqare prin impulsuri de
polaritate opus5,, trebuiesc subliniate o serie cle particularitd,li; (1) aurpti-
tudinea impulsurilor de declanqare trebuie sd, fie limitatS, atit inferiol cit

qi superior (relalie similard, cu (4.100)) ; (2) sensibilitatea bistabilului falir,

impulsurile de cleclangare este aproximatil' rle doud ori mai mic5,; (3)
bornele de ieqire nu au punct de masd nemijlooit, fapt ce lngreunea,zf,,
conectarea circuiteior in aval. Datoritd, acestor particulariiiti in practicd,
se preferd, de reguld, bistabili cu declan;are prin impulsuri de pol*ritate

opus5,.

4,5. Circuite cu DT si linie de intirziere

4.5.1, Monostahil cu Df $i linie de intirziere

Circuitele monostabile se folosesc de regul5, pentru formarea de im-
pulsuri cu parametrii (duratd,, formd,, amplitudine) bine determinafi.
Monostabilul cu DT qi bobind de ind.uctanlX, are doud, neajunsuri impor-
tante : (1) impulsul de ieqire nu are palierul plat, in special cind. starea
stabiid, se afld, pe porliunea ascendent5, tunel a caracteristicii staticel (Z)
timpul de revenire este fcoa, r:te mare in raport cu durata impulsului, in schema
ajungindu-se la
clasicd (10 + 20) r, (vezi fig. 4.26 b). Dacd, impulsurile
de declanq&re au frecvenla ridicat6 sintem nevoili s5, micqord,m valo&rea
inductanlei -t, ins5, in acest caz apar alte neajunsuri : slnt necesare arnpli-
tudini mari ale impulsului de declangare se micryoreazd, amplitudinea ,1i se
altereazd' forps, impulsului de ieqire. Diminuarea tirnpului cle revenire a
monostatrilului cu inductanld, se poate realiza prin conectarea unei sarcini
neliniare in locul rezistorului -R; ins5, prin aceasta se complicd, schema
qi are loc deteriorarea formei semnalului de iegire.

O lmbuna,tS,lire ratlical5, a formei impulsurilor de ieqire si, in anumite
conclifii de adaptare, diminuarea timpului de revenire se obline prin uti-
Iizarca liniilor de intirziere (transmisiei) ; intrucit se lucreazd in domeniul
impulsurilor de durath, foarte scurtd, liniile sint constituite de reguld, din
cable coaxiale. Schema 4d.e3p5rain: cliapiuboarnmeolenodsetainbtirlualruei cu linie
segmente do a, liniei
este ar6"tatd' in figura
de intirziere
rsYeeocoso,innpeotcbitnefaizsdoc,buDirqtcnTiur,citrueeiztd.isifitenorriutfeul nJr?ec,gli;eiimsduuerrisvadaeldofeauranelciamlioreennzatiarserteol riluanlrucibaoRzrun,leqmlei oadnessutiaersbgeli.-i
lului -Rt Ei Voo se aleg astfel incit dreapta d.e sarcin5, staticd, sd, intersecteze
caracteristica staticS, a DT intr-un singur punct situat pe porliunile ascen-
dente. In majoritatea eazarilor starea stabild, iniliald se fixeazd, pe porli-
unea ase€nclentd, tunel (fig. a.35b); dacd, .8, : 0 avem YoolVo, ins[,

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de reve-
nire- este minim5, adicd, egal5, eu.2t,
cind se realizeazd, condilia de adap-
tare la intra,re a liniei de intirziere.

Z": Rt * rot, (4.110)

uanDdeI 14 este rezistenla diferenfiald,
porliunea ascendentS, tunel.
pe
. Se pot reaiiza de a$emenea condilii
cind durata impulsuiui de ieqire esto
r,_Lr' 4c san chiar
6r; in acest caa 2 L.Irq
{Io-Io qi comutarea DT de pe ra-
mura, de.difuzie pe ramura, aaccen-
+ 50ns/d'
d.entf,, tunel se efectueazI dupd, citeva
Fig. 4.36
reflexii succesive din linie.
Detalii suplimentare asupra funclionflrii monostabilului cu linii de

intirziere precum qi asupra diferitelor variante d.e scheme pot fi gdsitein
ldtceldin,rtiilrezielJre{r 26, 36, 42f. O schemd, concretd, d.e monostabil cu ,D?-qi linie
oblinute ta
este afi,tatd, ln figura 4.36a l4?l; impulsurile
ieryire au forma ar5,tatd, in figura 4.30b, de unde se observd, c[, durata de
revenire este aproximativ de trei ori mai mare decit durata impulsului
(orizontal 50 ns/div vertical 0,2 Y/div, pmriicndutrimmapriedZe rco=m?u4tarnes'd).ireDcatcH.f,,,
lungimea liniei de intirziere este reiativ
gi inversS, devin enmparatlili cu 2r qi
mai are form5, d,reptunghiulard,; dIre: pt1urrnmiamrpeuiimsupruillesualudfeorienqiairearn{,u-
luind
tat5, in frgura 4.36c. Alte scheme practice sint date in capitolul urm5,tor.
O construclie grafic5, diferitd, de cea expusX aici este datd, in lucrarea

[39] ea,re se descrie in paragraful urrnd,tor.

4.5,2, Hultivibrator cu DI gi tinie de intirziere. Procese fizice

Particularitatea principald, a multivibratorului cu linie de intirziere
este forma a,proape id.eal dreptunghiulard a impulsurilor generate qi in
anumite condilii, stabilitatea ridicatS, a frecven{ei; o stabilitate deosebit
d.e bund, a frocvenf.ei se obline in cazul circuitelsr ea DT qi doud, linii d.e
intirziere eu constante de timp fduinfeclriiotenal2reO,q4iIlc. oCnhdeilsiitiudneileosdceilablaiezdp, roetfef-i

ritoa,re, ia tipurile de scheme,
gdsite ln ilnucrddo,mrileenUiu {ne26o, p3r5im-45pe1
; asupra luerS,rii [35] eonsideratd, funda-
mentald,
larg in paragraful uimd,tor.

Stt u99'o - oI

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Ioon ?g gprol;ad IF*u,rtpZ€cllu€grrn{ep"laoprpsuru.rJns(olnq dAr,ul"Zur,pt(nfz+spBuInocdI+n){urJp€c.sr?orqoJt+ss!slJr+€

aat;u.rts rarfcrulsuoa

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>ooAldl e.4u1 esuudnc a.rts+uaurq€

op ruilBua? nr+uad €Fcsoo+n€ €a In+r
-ncfio 'eleuop.ro nc
g1a1e"red sl.so ?crl

-€+s Kurores ap'Tec1rldnr€crrppqllcunIr1grr?l€zqrln
uola5lag turulSurp no €J€Irtuts also
{D} -0eaar8ttrfgTuolursnn,lI?rlnsguudoqncdp?uI:+ILislfr€f7no'l'9nag9u€gro['9flsf66]r's'VfTuITtsJlf a?(?rrolre('t0osl)n)rr8r.Jrooorr11;I
rnlnq.cund er{n1oaa ed, yzwazwq ss o.r'aJ
1ruo1nfe nc g aluod Inlruol
-'qELrq6r^,r+eI.nrnm-Btrl;eu.rrepueocrr|ycuurn$,rilar'0{cn: qttugocl$ n!4cu?(rrulgJn'f
gfeepl aTmI '8ry) gldurrs retu

sac tsuroqcs urfJaplsuoo acrzrJ Jolassoo.rd e gAI+BlIIBc tr{ncrrp n,r+uad

turi atunci cind valiaz:i tensiunea de alimentare (uneori varialia in salturi
datoritii general
poate avea 1oc varialiei parametrilot DT1. In perioada

impul,rurilor cle ie;ile este dat5 c1e relalia l35l

7 : (m, f- n)2t : (nt, -. n)Tn; (4.111)

unde rn si rr, sint intregi ale cziror valori, Edeenstarrucinod,linstieati(c2e":) tlaIra depind
rie tr:nsiuneaYnns adicX cle pozi{ia dreptei za reprezint'ii

naumca,)r,ar:cutledriestiinciiieipsiencdliiinaImdoiernpetenitudlincainmdicDe ?cucp,oomrliuutrirepae ascendent{, tunel
porliunea ascen-

ctleunptzoir{'feiundeiaflzaiseclern'idreenptrriecz1ienttliifunuzmiedp,minlXdeininmteornsteecnlitiual cdinredptDei-7clincoammuictefi
pe por{iunca ascendent[ tunel. in cazul construcliei clin figura 'L'37b,

ill'eln 'nt:2, m:I.

Un stldiu sisternatic al varialiei perioaclei impulsurilor in funci,ie
t1e tensiunea de alimentare este efectuat in lucrarea [26] ; tot aici sint puse

rAinn((:-nh,rzH):l-:rEe73iTav,0i1zi/EcrIi10,lrLet,l-('5inn0n:fD)f1,mdVi:s,;uL1oe)qntotir3(issdsp\ue:,)err(iogoVrh0opmnb,o)pr2:eilVunei7Inns,t:otei0'\,to,,.oc1LtlsiCe:l1:ecno18ci0lln,oad;'1s:g(b\eii4'idrllr)au,ehYmrryci,nnseortdf'l:Vteafe,ui:rxn-e1:slidotazet;i:ilns07Jau1tLavnf(h6i1gig:n1eml):u)d1cr\ulratiz;rirn(tc"i14evpu:.i(n7)3ibct\Su:5)r'rI0alV,(uo,t(3onia:Q7orna), ct::mV0.us2u2ino102:D1c2o,c7iYf:t5:c0o,diYr'nmn1ie1zd,13mo:t:0iLn:Ip1'tYnr;u:aas,'ll
(a)-(d) 200 ns/ctiv, (e)-(i) 100ns/div;vertical 0,6 Vldiv)1 se observi'

cil rrz poate lua valori cuprinse intre 1-8 iar n intre 1-2; limitele de varia-
in special de
lie a1e lui rr, qi ra clepind de tipul DT si mare cu atit irnpedanla caracteris-
ticra a liniei, Z" este mai
anume cu clt qi limitele lui rz qi ra

vor fi rnai mari. Fenomenul de hysterezis al acestui circuit este ilustrat
pril graficul tlin figura 4.39 : pentru o valoare datd, a tensiuniir valoare,a
iai ti clepinrle c1e sensul de varialie (n
: 1 exceptincl cazuI cind trr oo a

- 0,6 v).
o construclie graficd, relativ simpl5, pentm studiul proceselor tran-
lzuicLcralrtriedain[3m9u].ltSivcihberamtaormulucltaiviDbrTatroyri uolutiinieestc'eleairndt,itrazti5e,reinesftieguprroapu4s.54,0ian;
linia consi5, dintr-un segment de cablu coaxial cu impedanla caracteristicS,

Z" : b0 O. intrucit D? este conectatS, la hornele de ieqire ale liniei, in
Ia bornele de intrare AA' se fotmeazd'
mornentul inchiclel'ii contactuiui -K1
Er) : 0712 Y' Acest salt se propagd'
ssparlteulddreeatepntasiuqni eIaVm,ot:meVnDtDulZ"tI(:Z" r*
ajunge la bornele de ieqire BB'; prin

aplicarea teoremei lui Thdvenin putem inlocui releaua din s&tinregatebmorIn/oelo:r
EI3' ca un generator echivalent
care,in intervalui c{t(3c
: 0)24 Y qi impedanla internd, ega,ld, cu 50Q. Valoarea tensiunii la bornele
:Bd0rB,e2p'4teesiYted, ectousccamarcraaiincdtteenrdissinituaicnmaeicas5t,apt(eidcdeD, pTaaDn,1Tti5s,(et-ig1p.o14a2.te"4)0dbde)ut;esrrie,mzduiniltna5,pppuruinnnccitntuutlel rV1seopceolina:-
trn care va:0,036 Y, In:4,08 mA qi care constituie starea de echili-
brn a circuitului in intervalul r.--t.--3t ln continuarea analizei autorul

146







rlti]rzeazil rela!,iile existente intre diferite componente a,le tensiunilor ryi
cnren{,ilor la termin:llele (irornele)
unei linii (r'ezi paragrafu} 2. 2.2}

Il1 4 V,: 7, , (4.x12)

I, -f Ir: Iti (4"r 13)
{4.11,4}
lVrllrl :7'", i1:',lI,l : fr", i4.tr f.i.r)
r, : f1t''),

I

h A*f--'--11-='

i

+t,_.,1 *
t*

'*t*l

L*i

+u z_- --.Jr.^.- t 1,____0,,r5i rJ , _,.1.
Fi-g-.r"1.39
0,a U.7 \\l)

precum gi o relalie leferitoa,re la,,r-a,ria!iilet' t'ensiunii

A l/a -f AI/" : AY', (4.11ti]

Df {a) nntle tsr, Itl LY, au Bemn;-tir:a,!ir,r,
unor m[rimi md,surate pe ter]r:ri-
nltesa,l,reIe:.Bl0i3n'0'i3n6adYYceomdnintVac1re[:llaalOia7te1.r(24n.rT1inLr9ri-)i
ur:re2erznk,ul4ral!trrii"elulorl1rA'r,1(r4i::a.1r 11-104,,16,)08:I8um6,4:,YA08.QI m,ScI)oaAfnll'1ufpp6Qrrrii-.lrenl
iur tn1-a:,rle$2lier-fsA,,inAntc'ppaurronlipdaael grlelafs,lepmcrteoamtteee;.nnrntcui--l

0.1 0.2 0.3 a,/, ferindu-ne nurnai la tensiuni, se
rc) aDt<r+rlei.bTeaZst\ee,rre)annrsvl-lsooisiamuc-rne[eVea0nc,z,otlc6ouea:4lfri:LpcIT'ri:eoi(snV-neIt3lun,urcr-le:mdfalZaee0cr"creer)0etsl5is(ftlE-aestslxprtaVui-l,eci.ltl
ajunge la terminaiele BB'. Pent,ru
determinarea noului punct de eehi-
libru se procedeazd' analog ca, l:u
punctul 1 : releaua din stinga t,er'-
Fig. 4.40 xrinalelor BB' se inlocuie.ste
.pflr"fu.r:-
tr-un generator echivalent aljntl tem Tzo=:6,108 \,'qi impedan{a interni,
O ; din punctul I considerat
:50 ca origine Be t'r:aseazdpe axa tensiunilor un

150

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