, chi~u ~ai I = 5Ocm Uri giai :
d) ndi tiI dt;zng d{Ji slf sang d{Jng mil
a + jb = CeiCl
trang do:
b
a =arctg-
a
Vi~c dOi nlly thqc hi~n d~ dlrng tren mc1y Hnh.
2. MOl ,6 phep linh d61 vOi .6 ph"c
a) C9ng, tril
G~p trubng hqp ph8.i c(mg (trir) s6 ph1l'c, ta bi€n dOi chung v~ d~ng d<.ti. s6,
r6i cOng (1m) phtln Ihqc vOi ph4n thqc, phtln 00 vm ph'n 00. (4 + i2) + (3 + il) = (4 + 3) + i(2 + I) = 7 + i3 (4 + i2) -(3 + il)= (4- 3)+ i(2·1) = I + il
b) Nhdn, chia
Khi phai nh4n, chia, ta Den dua v~ d~g mu: NhAn (chia) hai s6 ph1l'c, ta nM.n (chia) mOdun con acgumen (g6c) thi c(mg (tru) cho nhau.
68
6ej20" .2ej10" = 6.2ei(20° +10") = I2ej3O"
'1ft'
~=~ej(200-10") = 3ej10"
2ejICf 2
NhAn cilng co the thqc hi~n dum d~ng d~i s6 nhu blnh thubng (a + jb) (c + jd) =ac + jbc+jad + lbd
= (ac - bd) + i (bc +ad)
vi j2=_1
Khi chia ta ohan tir s6 W mAu s6 vOi 86 phuc lien hgp cua mAu s6.
a+jb (a+jb)(e-jdj (ac+ bd)+j(bc-ad)
--= -
c+jd (e+jd)(e-jd) e2+d2
3. Bil. di~n de d~i h'qng di~n blob sin bAng .6 phlle
C4eh bi~u dil!n cAe d!).i hrQIlg di¢n hlnh sin bang s6 ph6'c nhu. sau: mOdun (d" 16n) eua s6 phuc III tri s6 hi¢u dlJng ;
aegumen (g6e) clla s6 phU'c 18. pha ban d~u.
. . .
Dong di¢n phue : 1= IL<pj = leNt
Di¢n Ap phue:
Tdng trc,; phli'c ella nMnh R, XL' Xc nOi tie'p
Z = rei" = zeoscp + jzsincp = R + j (XL -Xc)
Trong d6 z=~R2 +(XL-XCl' <p=arc'gXL -Xc R 4. Yilt de d!nb 1.$1 du4!l d~ng .6 phtlc a) EJlnh lu~ Om • or 1=- Z
b) i)jnh lu41 Kiicshdp I cho m~1 nul
• })=O })=O nOt • • L ZI= L E m4ch vang
ac quy u6c v~ da'u tuong tl! nhu dii lam a m(lch di¢n m"t ehi~u, di~u ehl1
j 11 dAy lA cae d~i lugng phii vi~' dum d~ 56 ph1lco
69
Vi d~ 15: Tinh d~ng di¢n i3 tren hlnh 3.27. Cho bitt:
i1 = 5..fi sin (wt+400)A
i2 = lO..fi sin (WI - 300)A Lili giai : Bieu di!n cae d~ng di¢n bang s6 phll'c
• 0
II = 5ej40 = 5cos40° + j5sin4O" = 3.83+ j3.21
I~ '" IDe -j3O" '" IOcos( -30") + jsin(-30o) '" ~ 66 - j5
Ap dy.ng dinh lU$t KieeshOp 1 tl!i nut:
I: '" il+ I~ -= 3,83 + j3,21 + 8.66 - j5 '" 12,49 - jl, 79", 12,6Ie-j8.lS" V4y tIi s6 hi~u dl,lng vA pha ddu ella V4y tIi s6 hi~u dl,lng vA pha ddu ella
d~ng di¢n iJ III l3 = 12.61A '¥) = _8,15° r, Trt s6 t1h: thili i3 = 12.61...fi sin(WI - 8.15°) . • Vi dl.l 16: M¢t m{lch di¢n g6m R = mnl! 1.27
100; Xl. = 160; Xc = 110 n6i tie'p. Di¢n tip ngu6n u = 200..fi sin(rot+500). Tin'
d~ng di¢n trong mq.eh.
70
Uri gial: T6ng trO phlk clla m{lch
Z = R + j(X, -Xc) = 10 +j(16 - 11)
= 10 + j5 = ll,lSL26,56° Di¢n lip phiie Clla ngOOn
• U "" 2OOL50" Ap d1,lng djnh IU$t ()m • i= U '" 200LSOo _17,88L23,440 Z 1l.18L26,56
Trj s6 hi¢u dl}ng vA g6e pha d4u eua d~ng di¢n IA: I=17,88A
'Pi = 23,44° Trj sO" tll'c thb-i ella d~ng di¢n Ill.:
i = 17,8S..fi sin(wt + 23,44°)
3.9. PHUONG PHAp GIAI M~CH DI/i:N XOAY CHItu HINH SIN HINH SIN
De' giiH ffil;lCh di~n xoay chi~u ta thuang dung cAe phuong pM.p sau.
1. Phuong phap d6 th! vecta
.
NQi dung eua phuong pMp nAy It .. bie'u di~n dong di~n. di~n Lip, sue di¢n
dQng bang' vecta, vi!!t cAe dinh lu~t dum. d~ng vecta va. th'!C hi¢n tinh toan tr~n
do thi vecto.
2. Phuong ph8p 56 philc
Bieu di~n dong di¢n, di¢n Lip. sue di¢n d"ng,tOng trO bang s6 phuc, vit!~ cae
dinh lu~t du6i d .... ng 56 phii'c. D6i vOi m~ch di¢n phdc tl;lP, sir d1,log cae phuong phap dii hQC a chuang m .... ch di¢n mQt chi.!U de gilli nhu phuong phlip bil!n dOi
wong duang. phuong pUp dong di¢n nh4nh. phuong pMp dong di¢n ffil;lCh
Yang. phuong pUp di¢n ap cae out, phuong pMp x/!p chOng ... an eM. '9 rhng, khi sir d\lng cae phuong phap ntly ph8i bi~u di~n cae d .... i luqng bAng 56 phuc.
D6i vOi cae m .... ch di¢n don gian, nhi~u khi ta trvc til!p sa dqng dinh lu~t
Om III phuong ph8.p cOng sua't d~ giai ml}-ch di~n.
Vi dl} 17: Clto ml:lch di¢n hlnh 3.28a. Hay tinh dong di¢n cac nhr:inh, cong sulft p. Q. S va CDS<p ClIa ml:lch di¢n.
Lbi giai: ~ h¢ th6ng l~i kitn tMc ta gilii ml:lch di¢n bAng cac phlWng phap khac nhall. 1!XlV .) I. R Ion
aJ PhuOJI8 phdp 46 thi vectCl
Dong di¢n trong cac nhanh
I, X. X. Ion Hillh 3.28 ... - - T b) 71
U 100 IL==-=-=20A IL==-=-=20A XL 5 U 100 IC=-=-zIOA Xc to
ViS (ld thi vec(a eua m{lch dj~n tr~n hlob 3.28b. ChQD pha dil:u cua di¢n tp
q>"u = D. vecto Cr trilDg v6i trl}C ox vi! vecta dbng di¢n IR trung pha v6"i vecta di¢n lip U, vectO' dbog di~n IL ch.m sau vecta dien lip D m(\t g6c 900. vecta dMg di~ ic vuqt tnroc vecta di¢n lip D mQt g6c 90°,
Ap dl,mg d!nh lu~t Ki~cshOp 1 t~i nut A ta c6: I=IR+IL+1c
TrJ/C tie'p c(lng vecta teen dtS th, ta c6 i a m~h chfnh.
Trjs6hi¢udl,lDg I=~I02+102=14,14A.
COng sua't tAc d\Ul8 P CUR m~h
P=RI~ =10.102 =IOOOW. COng sua:t phin kh.4ng Q CUB m/ilch COng sua:t phin kh.4ng Q CUB m/ilch
Q = QL + Qc = XLIl-XcI~ = .5.202 _10.102 = IOOOVAr. COng suIt bi~u kien cua m~h; COng suIt bi~u kien cua m~h;
s.N' +Q2 =~rlooo2~-+-looo2--;;-. =1414VA. H¢ s6 cOng sulft coscp cUa m~h: H¢ s6 cOng sulft coscp cUa m~h:
P 1000
COSlpz-=--=O,707 .
S 1414
Ta ding c6 tht! t!nh P. Q. S nhu sau:
p= IDcoscp = 100. 14.14cos4SO = lOOOW Q = UIsincp = 100. 14,14sin4SO = lQOQVAr
S = VI = 100. 14.14 = 1414VA
b) Phllcmg phap ctJng suat
~ tfnh dOng di¢n [ trong nMnh chfnh ta c6 tM khOng sir d1;mg dd th! 'Iecta m~
sit dl).ng phuong philp cOng su!t nhu sau:
Til dOng di¢n. tinh cOng suIt P. Q. S cua m{lch nhu dill~m 0 m\lC a. sau d6 tfnh dOng di¢n I iJ m{lch chInh theo bi~u thli"c:
72
S 1414
I=-=--=14,14A
U 100
c) Phuan8 phQp so' phiic bi/II diln cdc dt;Ji lU,!lIg lIa dinh lu~; MIl8 so' phiic
Ap dlmg·dinh lu~t Om
•
iL "'...!:!.,..'" lOOLOo "" lOOLOo =20L-9O"
jXL jS 5':::::90° • ic=~=IOOLO" '= 100'::::0" =IOL900 -jXc -jlO IOL-90° Ap dl.lng lGecshOp 1 t~i nllt A • • • •
1= IR+ IL+ Ie '" lOLO+20L-9O" + lOL90°
'" 10+ jO+O- j20+ 0+ j1O= 10- jlO '" 14,14L _450
Tri s6 hi~u dl.lng cAc dOng di~n Ill:
III. = lOA; IL = 20A; Ie = lOA
i= 14,14A
C4ch tinh cOng su!"t P, Q. s. cosq> nhu 0 myc a. Vi dl.l18: Tinh dOng di~n trong m~clt di~n hlnh 3.29.
Day Ill. m~h di¢n phllc ~p, ra c6 th~ sir dyng cAc phuong pMp dA hqc 0 chuong 1.
Du~i da.y ta x~t 2 phuong pbAp sau: