2- Dinh Iv ve tinh duv nhat
2.5.2 Ma tran dan nap
Ma Iran dan nap cua mang x iba md ta m6i quan he giua dong dien x a dien ap. Theo (2.16) ta \ iet dugc:
)'.., ^.: ... ) . ' ... ) . ' ... K , . . . ) \ v . ['•,1 r. i \ ( 2 . 1 8
hoac viet duai dang ma tran:
[I]-[Y\[V\
Ta nhan thay [Z] va [7] la cae ma tran nghjch dao cua nhau: [y] = [Z]-'
Tu (2.17) ta cd the nhan dugc phan tu ma tran:
V Z = - ^ P'l J (2.19) (2.20) (2.21) /j, =0 \fk*(f
Cong thuc (2.21) dugc phat bieu nhu sau: Tra khang Z^,^ dugc xac dinh khi tiep dien
cho cua q vai dong 7,^ va de ha mach eac cua con lai (/;, ^ 0 \ oi mgi k ^ cj). dong
thai cho dien ap ha mach tai eua p.
Tuang tu nhu vay, tu (2.18) ta co the nhan dugc phan tu ma tran:
/
Y ='^
PU y
O 1 O
Cong thuc (2.22) dugc phat bieu nhir sau: Dan nap )],,f duac xac dinh khi cap dien cho cua/? vai dien ap Vp va ngan mach tat ca cae cua con lai {l\^ 0 voi nigi ^ ^^y), đng thai do dong dien ngan mach lai CUA p.
Trong truang hgp tong quat, cae phiin tu ma tran Z^^ ha\ )]„f la cae dai lugng phuc.
Trong thuc te eo nhi^u mang viba la mang khong ton haọ mang thuan nghieh. hoae CO ca hai tinh ehdt khong ton hao \ a ihuan nghieh.
Doi vai mang thuan nghieh (mang khong chua ferrit hoae plasma), ta eo the chung minh: Z w ỵ p^ '<4P QP (2.23) -> - i 4
Doi voi man^ khon^ ton hao (cong sudt huu cong trong mang bang 0). ta eo the
chung minh: hoac RcfZ,J = 0 Rc|),,J = () (2.25) (2.26)
Nhu vay, doi vai mang khong ton hao va thuan nghieh thi ma tran tra khang va ma tran dan nap se la cae ma tran doi xung va thuan aọ De hieu can ke ban eac tinh chat (2.25) va (2.26), ta c6 the tim bieu trong cae phan chung minh sau day:
Doi vai mang thuan nghieh
Ta khao sat mot mang thuan nghjch bat ky dugc mo ta 6 Hinh 2-3. nghia la mang ma trong do khong co eac phan tu tich cue, ferrite hay plasma, dong thoi tat
ca eac cong deu dugc ngan mach tai mat tham khao tru cong 1 va 2. Gpi Ệ H^ va £^, ///,1a truang a trong mang do 2 nguon doc lap a \a h dat a hai v\ tri nao do
trong mang tao rạ Theo dinh ly tuong ho ta co the viet:
j(Êx n,,)clS = j(E,xH„)cJS (2.27)
a day, S la mat kin, phu hcTp vai mat bien cua mang va bao gom eac mat iham khao tai cae c6ng. Neu mang va duong truyen dan la cae cau true kim loai kin thi thanh ph5n tiep tuyen tren be mat phai bang 0 (gia su vat dan ly tucmg). Neu mang \a duang truyen dan la cae cSu true hó, vi du mach dai hoae khe daị ihi mach kin cua mang se dugc ebon tuy y sao cho tai do Á, la nho, khong dang kẹ Ba\ gio se ehi eo
cae thanh phan khac 0 cua truong lai mat tham khao a cong 1 \a 2 la tham du \AO
tich phan (2.27).
Ap dung nguyen ly va tinh duy nhiil. ta eo the bieu ihi truong tai cae mat tham khao 1 va 2 nhu sau: F =V "e- ^ i . i ' i r r E = r c • F -V ¥ - F =V 7 H,„ =/,./(: (2.28)
trong đ e,, h.xhc,. Tu la eac ham xecto eu dien trudng ^a tu iruong lai cong i Na
2. cdn V va I la cae dien ap \a dong dicn tuong duong. Tha> the eac bieu ihuc trudng cija (2.28) vao (2.27) ta dugc:
trong dọ Si, S2 la dien tich eac mat tham khao tai cong 1 va 2.
Mat khac ej, h^ va ^2, h2 la cae vecto chuan boa, ta viet dugc:
l(e,xh,)dS= l{e,xh,)dS=\ (2.30)
Nhu vay, (2.29) dugc rut ggn lai:
( ^ u A - ' ; . A j + (f^2./2.-^^./:J-0 (2.31)
Tiep theo, ta sir dung ma tran dan nap ciia mot mang hai cua de \ iet cae bieu thuc Is tai cae cua:
J =y y -Y V
' " • '• ^ (2.32) roi thay vao (2.31), ta dugc:
Bai vi cae ngu6n a va b la doe lap nhau nen cae dien ap V|;,. V,^,. V:,. V2b co the nhan cae gia trj bat kỵ Do vay, de (2.33) eo the thoa man \oi sir lira chon luy y eac
ngu6n, cAn co yi2 ^ yix- Mot each tong quat, la nhan dugc:
hay Zp, = Z„p. (235) Do đ, eac ma Iran [Y] va [Z] la eac ma tran đi xung.
Doi vai man}:, khong Ion hao
Ta khao sal mgl mang N cua khong ton haọ Neu mang khong ton hao thi cong suiil huu cong tru\en \ao mang phai bang 0.
Ap dung cdng thirc (2.17) ta suy ra dugc bieu thuc cong suat phuc tru>en cho mang N cua:
(0 day ta da ap dung cdng thtjrc cua dai sd ma tran ([A][B])' = [B]'[A]'). Vi eac !„ la
doc lap nen ta phai ed phan thuc cua moi s6 hang tu lien hiep Re{/„Z„/:{ bang khong, vi ta cd th§ thiet lap đng dien bang 0 tai eac cong khac trir cdng thir n. nhu vay:
Re(/„Z„„/:}=|/„|^Re{Z,J = 0. (2.37) hoac:
Re{Z,J = 0.
Bay gia, ta cho tat ca eac dong dien bang 0, tru I„, va /„. Khi do, tir (2.36) se rut ggn
lai con:
Re!(/ C + / r)z U o . (2.38) (do Z,„„ = Zfjftj) tuy nhien, (/„/*, + /„,/,*) la dai lugng thuc thuan tuy \ a noi chung la
khac 0. Do do, ta phai co:
Rc{Z ] - 0 . (2.39) Cae ket qua (2.38) va (2.39) cho tha\ rang Re{Z,„„j = 0 doi voi m VA n bat kỵ