Nghiên cứu và phát triển lý thuyết đường dây ghép để chế tạo một số phần tử thụ động siêu cao tần

CHU'ONG I-LY THUYET DUCNG DAY TRUYEN SONG 1 1.1 Khai niem va dinh nghTa 1 1.2 MO hinh mach dien tuang duong gom cae phan tu tap trung cua mot mach dien phan bo 1 1.3 Truyen so'ng tren du

T R A N ANHTUAN

NGHIEN CUD VA PHAT TRIFN

LY THUVET DUONG DA\ (;HF:P D E T H I E T K E CHE TAO

M O T SO PHAN T L I T H U DONG SIEU CAO TAN

Nganh; Ky ihiial Dion Ui-Vicn ihoiig

Chuyen nganh: K.y ihuat \ 6 lu\en dicn lir \a thong tin \\cu lac

T6i xin cam doan day la cong trinh cua rieng toi Nhung k^t qua dugc

trinh bay trong luan van khong sao chep ttr bk cu tai lieu nao khac Toi xin chiu

hoan toan trach nhiem toan ve lai cam doan cua minh

Ngudi cam doan

Tran Anh Tuan

LOI CAM ON

Dau tien, toi xin chan thanh cam an toan th^ gia dinh toi, nhCrng nguai iuon luoi

ung ho dong vien khich le toi, ho trg toi ki ca vat chat va tinh thSn trong su6t cupc da

hoc tap, phan dau va trirong thanh cua toi

Tiep theo toi xin chan thanh cam an GS.TSKH Phan Anh la ngircri Tha> dans

kinh nhat ciia toi Thay Iuon Iuon ung ho tao moi di^u kicn thuan Igi nhk de toi cc

the tien hanh nhung nghien cuu ciia minh Han tat ca Tha\ da nhan ra duac nhCmi

dicMii manh cua toi de dinh huang cho toi di vao ITnh \ ue nghien cuu phu hop \ a di truycn dat cho toi nhOng kien thuc \a kinh nghicMTi vd cung qu\ gia khong ehi irom

ITnh vue boat dong khoa hoc ma trong ca nhung van d(} cua cuoc song \a hoi Nhuni kel qua ma toi dat dugc ngay hom na\ da mang nang dAu An cua Tha\

Tiep theo toi xin chan thanh cam on GS.VS Ngu\en Van ilieu mot nguoi lha\ het long vi cae the he hoe sinh, sinh \ ien va dugc rat nhieu ihe he hoe smh kmh iiong Thay da danh cho toi rat nhieu su quan lam lo cho i6i loan bo kinh phi hoe lap e.u

hoe tai truong Nhung khoan kinh phi do du khong Ion nhung eimg da giup io\ eo IIK

danh nhieu thoi gian ban cho hoc tap \ a hoal dong nghien cuu khoa hoe cua minh

Toi cung chan thanh cam on tai ca cae lha\ giao eo giao ivong Khoa Dien

lu-Vien thong, cae ban dong nghiep cae ban cung lop da danh cho loi rat nhieu su quan tam, giup do" va ehi bao cho toi rat nhieu trong qua trinh hoe tap

CHU'ONG I-LY THUYET DUC)NG DAY TRUYEN SONG 1

1.1 Khai niem va dinh nghTa 1

1.2 MO hinh mach dien tuang duong gom cae phan tu tap trung cua

mot mach dien phan bo 1 1.3 Truyen so'ng tren duang day Nghicm cua phuang trinh \ i phan 4

1.4 Duang truyen khong ton hao c6 mac tai dau cuoi 7

1.4.1 He so phan xa 8 1.4.2 He so song dung 9 1.4.3 Bicu thuc cua he so sonu dunu I 1

1.4.4 Bieu thuc eiia he so phan xa tai \ i iri bat ky I I 1.4.5 Cong suat trung binh theo duong da\ tru\en song 12 1.4.6 Ton hao do phan xa 12 1.4.7 Tra khana vao cua dumm da\ tru\en somi 13

1.5 NghicMi cuu mot so doan da}' tru\'en song eo do dai dae biei 13

1.5.1 Duong day eo do dai nua sc^ng 14

1.5.2 Duong da\' c6 do dai mot phan lu' buoe song 15 1.6 Duoniz tru\en dan sona eo ton hao 16

1.6.1 Duong tru\en ton hao thap 16 1.6.2 Duong tru\en khong ecS tan song \ a eo tan song 18

1.6.3 Duong tru\en dan khong lam bien dang song 19 1.7 Duong tru>en eo ton hao dugc mac tai dau cuoi 19

1.7.1 Tro khang vao cua duong tru\en eo ion hao 20

1.7.2 Cdm suat trii\en \ a o duona tru\en tai dau \ a o 2 1

1.7.3 C'onu sual lru\ en \ a o tai 21

1.7.4 Cdmj sual mal mal Iren duonu lru\en

^ »

-1.8 Duonu da\ mach dai

1.8.1 I lang so dien moi -3 1.8.2 Iro khani: dae inih cua duonu da\ mach dai 2^

21

CHU'ONG 2- LY THUYET MANG VI BA 27

2.1 Khai niem chung 27 2.2 Khai niem ve tra khang dong dien va dien ap tuang duong 27

2.2.1 Dien ap va dong dien tuang duang 28 2.2.2 Khai niem tra khang 29 2.3 Dinh luat Kirchoff ma rong doi vai mang vi ba 30

2.4 Phan tich moi quan he giua cae tham so cua mang vi ba 31

2.4.1 Mang nhieu cua 31 2.4.2 Mang mot cua 33 2.5 Ma tran tra khang, ma Iran dan nap ma Iran tan xa

ma tran truyen dan 34 2.5.1 Ma tran trcT khang fZ] 34

2.5.2 Ma tran dan nap [Y] 34 2.5.3 Ma tran tan xa |S] 38 2.5.4 Cach xac djnh ma tran |S] tu ma Iran |/.| hoae [Y| 40

2.5.5 Ma tran truyen dan |ABCD| 41 2.5.6 Quan he ciia ma Iran ABCD \6i ma Iran tro khang | / | 4 4

2.6 Khai nicMii tro khami anh \ a ham tru\en cho mane hai cone 44

2.7 Bg dcio dan nap va bg dao Iro khang 48

ClIUdNG 3- LY THUYET DUONG DAY GHEP VA PII.AT TRIEN 50

3.1 Khai nicMii dirong day ghep 50

3.1.1 Phan tich mode kich Ihieh chan le cua

duone da\ ehep 52 3.1.2 Tro" khang mode le \ a mode chan cua moi duong da\

ghep CO eau true mach dai 57 3.2 Dae tinh lira ebon tan so cua duong da\ ghep 62

3.4 Phat irien Iv thuvet duone dav ehep eo eau true mach dai 63

3.4.1 1 le so ghep song cua duong da\ ghep 63

3.4.1.1 Duong da\ dan song khong ion hao 64 3.4.1.2 Duonu dav dan sons c6 ton hao 66 3.4.2 Phan lieh mot doan duong da> ghep \ oi mot phan lu

lap trime mac neane qua hai duone da\ dan sone sone 67 3.4.3 De xual mot ihiei ke moi cua mach cong huong

sieu cao lan 3.4.3.1 Khai niem mach cong huvvng

-3.4.3.2 Xa\ dung ihiel ke bo cong huong

dirong da\ ghep

->

4.1.2 Bo loc thong dai 85 4.1.3 Xay dung thiet ke cua bo loc duang day ghep bang r6ng86

KET LUAN : 94

CAC CONG TRINH D A CONG BO 97

TAI LIEU THAM KHAO 97

DANH MUC CAC BANG BIEU

Bang 2.1 Cae tham so ABCD ciia mot so mang hai c6ng di^n hinh 46

Bang 2.2 Bang chuyen doi cae tham so cua mang hai cong 50 Bang 2.3 Tra khang anh va cae tham so khac ciia mang hinh T va TT 52

Bang 3.1 Cae dai lugng dae trung ciia mot mach cgng huong 77 Bang 4.1 Gia tri cae phan tu trong mach loc thong thap chuan boa

(gO - 1 , o)C=l, N=E 9, CO do ggn song la 3dB) 89 Bang 4.2 Bang tham so hinh hoc cua duang day ghep bang rong 95

DANH MUC HINH VE

Hinh 1 - 1 Mo hinh dien ap dong dien va mach tuang duong ciia mot

duang day dan song c6 chieu dai vi phan 2 Hinh 1-2 So do duang truyen khong ton hao c6 mac tai dau cuoi 7

Hinh 1-3 Do thi bieu dien a) Dien ap, b) dong dien c) tra khang

phan bo doc theo duong day truyen song ngan mach 10 Hinh 1-4 Doan day truyen song (1= l=X/2) c6 mac tai 15

1 linh 1-6 Duong truyen song c6 ton hao c6 mac tai 20

Hinh 1-7 Duong day mach dai 23

Hinh 1-8 Cau true hinh hoe ciia duong day mach dai vai bue tuong

ngan each y 26

Hinh 2-1 Mode dien truong ngang T\-M 3 1

I linh 2-2 Cau true mang n cua dien hinh 34

I linh 2-3 Mo hinh manu mot cua dien hinh 36

Hinh 2-4 Mane hai eonii 45

I linh 2-5 So do ang hai cong c6 mac lai dau cuoi \ oi hai tro khang anh 49

I linh 2-6 Mieu la hoal dong eiia mgl bo bien doi iro khang \ a dan nap 53

Hinh 3-1 Mot so cau true dien hinh cua duone da\ ehep 55

I linh 3-2 Duone truvcMi sone eom 3 dai dan dien \ a mach tuo'ne duone 55

1 linh 3-3 Mode kich thich chan \ a le eua duong da> ghep 56

I linh 3-4 1)6 thi thiet ke eua duone dav ehep dane truven del 5><

1 linh 3-5 Do thi cua duong da\ ghep eo eau triie \ i dai 58

1 linh 3-6 Bieu dien dien ap \ a dong dien tren doan duong da\ ghep

CO cau triie \i dai 62 Hinh 3-7 Phan thuc eiia tro khang anh doi voi mach thong dai 66

I linh 3-8 Mach tuong duong eua moi doan duong da\ ghep 6''

I linh 3-9 1)6 thi bieu dien su phu thuoc ciia |S31| so \di ZOe-ZOo 70

Hinh 3-10 Cau triic mot doan duong da\' ghep eo mot phan lu khang

mac ngang qua 71

1 linh 3-1 I Phep bien doi mach lirong dirong trong mode chan '^2

I linh 3-12 So do mach tirone duone eua 1 linh 3-8 a mode le "3

Hinh 3-13 Mach dien tuong duong cuoi eiing eua mach Hinh 3-8 "4

1 linh 3-14 Phep bien doi tuong duone eua doAn dirong da> ghep eo mot

phan lu khang mac ngang qua hai duong da} \ i dai song song r ?

1 linh 3-15 Mach cone hirong \a dap ung eua no 76

Hinh 3-16 Phat trien thiet ke ciia bg cong huang duong day ghep 79

Hinh 3-17 Phep bien doi tuong duong mot mach cong huang

RLC mac song song 79 Hinh 3-18 Dap ung tan so ciia bg cgng huang duang day ghep 86

Hinh 4-1 Dap ung tan so cua mot so bg Igc ly tuong 87

Hinh 4-2 Cau true ciia mot bg loc thong thap chuan boa 88

Hinh 4-3 Cae phep bien doi tu bg loc thong thap chuan boa d^n

cae dang bg Igc khac 90 Hinh 4-4 Quy trinh thiet ke mot bo Igc duang day ghep bang rong 92

Hinh 4-5 Mot so ket qua mo phong eiia mach Igc duong

day ghep bang rong 96

I linh 4-6 Mot mau bo loc duong day ghep bang rong 97

MdOAU

Trong nhung thap nien truac viec nghien cuu ky thuat va ly thuy^ sieu cao dn

thuang tap trung vao viec nghien cuu va giai cae bai toan phuc tap ciia truong dien tu cho cae phan tu ong dan song bang viec ap dung he cae phuang trinh Maxwell, nhung ngay nay cae ky su lam viec trong ITnh vue sieu cao chii yeu thi^t k^ mach dien sieu cao tan eo cau true phang (plarmar) va cae mach tich hgp (intergrated eircuitrx) do

do khong can quan tam nhieu den viec phan tich ly thu\et truong dien tu nua Thay cho nhijng phuang trinh ciia Maxwell, la nhung cong cu rat dae lire khac do la phan mem thiet ke sieu cao tan CAD(Computer -Aid Design) \ a ma\ phan tich mang (Network Analyzer) Tuy nhien, mgl euon sach dugc coi la cam nang eua cae ky su thiet ke sieu cao tan va la cong cu khong the ihieu do la euon sach Miero\\a\e I-ngineering eua tac gia David Po/ar giao su eiia Truong Dai hoe Massaehusel My Neu khone eo mot trone ba cone cu quan trone na\ thi \ ice nehien cuu che lao cae phan tu sieu cao tan bien dai se gap ral kho khan, eon neu khong eo ca ba cone eu na\' thi chiine la khone the nehl toi vice thiet ke che tao cae phan lu sieu cao uin

Ba nam truoc do su ra doi eua Trung tam nghien cuu Dien ur-\'ien thong thuge Khoa Cong nghe na\ la truong DH Cong nghe DHQG Ha noi \ ice nghien cuu

ky ihual \ a ly thuyet sieu cao tan bien dai da dugc thiie da\ lai \'iet UAm lai da\

ehune loi, nhCrne kv sir thiet ke sieu cao tan da c6 co" hoi lam \ iee \ oi nhune cone eu cue ky quan trgng nhir la ma\ phan lieh mang \ a phan mem ihiet ke ADS2003 luy nhien phan IIKMU na\ ehi dugc diing ihu irong thoi gian la ba thang

I.uan \'an Thae sv na\ trinh ba\ cae eiai phap cho nhune \an de ma ehiine toi gap Irong qua Irinh nghien eiru ihiei ke che lao cae phan ur ihii dong sieu cao lan eo cau triie mach dai Vi du nhir lam the nao de che tao dugc bo loc duong da\ doi bang rong trong khi \oi plurong phap lru\LMi ihong bang lan dai dugc eua bo loc ehi nho hon

20%, hay lam the nao de che tao che IAO dirge bo loc sieu hep \oi nhung \al lieu eo he

Luan van gom bon chuong Chuong 1 Chuang 2 trinh bay nhiJng net ca ban eua ly thuyet duang day dan song, va ly thuyet mang Vi ba No la co so Iv thuvit

de di den cae ket qua ciia chuang 3 \ a chuong 4 Chuang 3 trinh bay co sa ly thuvet duang day doi nh&ng cong thuc bo xung cho no Chuang 4 de xuat mot thi^t k^ moi eiia mot bo Igc duang day doi bang rong ket qua nay dat dugc do \ iee ung dung nhung ket qua phat trien ly thuyet duong day doi da dugc trinh ba\ 6 chuong 3 Noi dung eiia chuong 1 chuang 2, va mot phan chuong 3 dugc trich dan lu euon sach:

^'Microwave Engineering'" ciia tac gia David Pozar xuat ban nam 1998 \ a Bai Giang

Ky thuat viba eiia GS.TSKH Phan Anh xuat ban nam 2005

1.1 Khai niem va djnh nghla

Duang day truyen song la duong truyen dan nang lugng song dien tir, la hinh thuc qua do giiia mach dien gom cae phan tu tap trung a tan so thap (L C R) \a ong dan song a sieu cao tan Duong day truyen song dugc coi la mach dien eo phan

tu phan bo bai vi nang lugng song dien tu truyen trong mach dugc dan trai Ien uit

ca cae phan tu trong mach NhiJug khap noi trong mach cung it nhieu ga> anh hucVng den qua trinh truyen song trong mach De phan lieh dugc mot mach phan

bo, tat ca cae phan tu trong mach deu can dugc xet den No khac ban \6i mach gom cae phan tu tap trung la: nang lugng eiia song dien tu dugc tap trung tai cae phan lu

L, R,C Khi phan tich mach gom cae phan tu tap trung nguoi la khong can xet den sir tieu hao nang lugng cua cae dirong day noi va cae khcrp noi Ien qua irinh lru\en song trong mach Do do sir dung cae ly thuyet vat ly kinh dien la eo the phan lieh

dirge mot mach dien gom cae phan tu lap trung mot each da\ du Mae dii eo sir khac nbau Ion giua mot mach dien tap trung voi mot mach dien phan bo la \an eo

the phan lieh mot mach dien phan bo bang each phan tich mach dien tap trung bieu dien no

Ta cung co the hieu mot mach dien phan bo nhu sau: Khi mot song truxen trong mach dien eo birae song ma chieu dai eiia no so sanh dugc \ oi chieu dai cae da\ noi ihi tai cae dicMii khac nhau Irong mach dong dien (\a dien ap) se eo pha khac nhau Do la do co bien lugng tre theo thoi gian Do do khi phan tich cae mach dien co phan tu phan bo ta khong ihe bo qua dugc su anh huong eua cae doan da> noi nay Ien mach dien Khai niem cam khang dung khang cung khong dung nua Khi \'iee tru\en nang lugng Irong mot mach dien phai mat moi thoi gian dang ke

nao do thi mach dien do dugc \ep \ ao loai mach eo phan lu phan bo I a eo the hieu

song dung ciia dien ap (va dong dien), dong thai tro khang vao ciia duang da\ thay doi theo tan so ^

1.2 Mo hinh mach dien twang duong gom cae phan tir tap trung cua

m9t mach dien phan bo

Thong thuang mot duang day truyen song co the dugc mo ta nhu mot he g6m

he gom 2 day dan song song Do la vi khi truyen dan song TEM ta phai eo it nhat 2

vat dan Mot phan tu rat ngan eiia duong day co do dai AZ (Hinh 1-la) co the dugc

bieu dien bai mot mang 4 cum don gian gom cae phan lu tap trung (Hinh 1-lb)

linh I-I Mo hinh dien ap, dong dien \a mach tuong duong eiia niol duong da> dan song

CO chieu dai vi phan a) Mo hinh dien ap \a dong dien h) Mach dien gom cae phan tir tirone dlron^ voi duone da\ dan sonu

Tronsi d()

R - Dien tro noi tiep tren moi don \ i dai eua ca hai da> il m

Cach bieu dien nay la co the chap nhan dugc vi nhu tren ta da gia thiet doan

day CO chieu dai rat ngan nen thai gian song truyen qua la khong dang k^ gidng

nhu khi truyen qua mang co phan tu tap trung Mot duong day truyen song dai se

dugc bieu dien bai v6 so cae mach dien nhu hinh 1-l.b ghep lien tiep vai nhau

Ap dung dinh luat Kirehhoff, la co the viet cae he thiic sau day d6i vai dien ap

va dong dien tren doan mach AZ, tai cae thai diem t:

- Doi vai dien ap ta co:

Chia (1.1) va (1.2) cho \Z va cho \ / -> dz ta nhan dugc:

^5IH) _ « / , , , ) - i * H l ,1,3)

& Si

'l^.^av(.o-c^l^^ ,1.4,

& St Doi vai tin hieu hinh sin co tan so o la co the viei:

SJ cW

(V Si

Thay vao (1.3) va (1.4) ta nhan dirge:

^^^=^-{R^i(oL)I(z) ( 1 5 )

De tach rieng bien so, ta dem vi phan (1.8) theo vat lieu va bien doi don gian se

nhan duac 2 phuang trinh rieng biet doi vai V va 1:

^ = ( Z r ) r ( r ) , (1.9a)

Sz^

^ ^ ^ - ( / T ) / ( r ) (l-9b)

Sz^

(1.9) la cae phuong trinh vi phan bae 2 eua V \'a 1 cho phep tinh W I tai cae diem

bat ky tren duong da}' khi biet cae thong so Z Y eua duong da\ \a cae dieu kien

bien

1.3 Truyen song tren duong day Nghiem ciia phuong trinh vi phan

Bay gio ta lim nghiem eua phuong trinh \ i phan (1.9)

He phuong trinh (1.9) eo the dugc viet lai nhu sau:

^ ^ ^ - r r ( - ) = o (i.ioa)

dz"

^ ^ - ^ - y - / ( r ) = 0 (1.10b)

dz- '

trong do y la mot hang so phuc do do ta co the bicu dicn y nhu sau:

y^a + iP^ J{R + i(oL)(<J + loC '1

/(z) = /;e-^ + /,-é^ (1.12b) (1.12a) va (1.12b) bieu thi cae song dien ap va dong dien tren duang daỵ trong do,

so hang chua é^ bieu thj cho song truyen theo huang +z (song thuan), con so hang

chua ế bieu thi cho song truyen theo huang -z (song nguge), vai y\h he so tru\en

song phuc dugc xac dinh theo ( M l )

V^^ va ll bieu thi cho bien do dien ap va dong dien song thuan

FQ" va ll bieu thj cho bien do dien ap va dong dien song ngugc

ham mu t'"" nghia la

K = K

Dodo:

T/+ -yz lol

Vfi e ^ e Vo e^ e e ^ e idt* -az -ipz lot

Neu viet duai dang ham lugng giae ta co bieu thuc ciia song dien ap tren duong

day:

F(r,0 = |C|cos(f/j/-^2 + ^*)c^"'^+|F,;|cos(r/^/ + /i: + ^")e'" (1.17 Van dung cae phep chung minh va suy luan nhu khi nghien cuu ly thuvet song dien

tu phang trong giao trinh "Ly thuyet truong dien tu" ta xac dinh dugc y nghia \at

ly ciing nhu cae moi quan he eiia cae so hang trong (1.17):

/3 - he so pha ciia song, co quan he voi buoe song cong tac x bai

2;r

va CO quan he voi van toe pha eua song bai

(1.19)

Cae bieu thuc nhan dugc o tren la cae cong thuc long quat cho truong hop duong

truyen dan song thuc te co ton hao, nghTa la khi cae da> dan khong phai la \ at dan

ly tuong (R^^O) VA dien moi trong khong gian giua cae da> dan khong phai la dien

moi ly lirong (6^0)

Doi voi dmrng day khong ton hao

Doi voi trirong hgp dirong da\ tru\'en song ly tuxrng ta eo:

R=0;

5=0 Thav vao (1.11) ta nhan dugc:

a = 0 (1.21b) Tra khang dae tinh cua duang truyen dugc xac dinh theo (1.15):

Z , = j | (1.22)

la dai lugng thuc

Nghiem tong quat ciia V va I tren duong day truyen song khong ton hao, theo

(1.12a) va (1.13a) se co dang:

J/(r) = ^;;c-'^^->Ko, (1.23a)

Buoe song trong ducmg day, theo (1.18) bang:

A = ^ ^ - ^ (1.24) /3 ojfLC

va v^n toe pha ciia song:

(0

1.4 Duong truyen khong ton hao co mac tai dau cuoi

Sa do cua dutnig truyen khong ton hao co mac tai tai diem cuoi cung \ ai true

toa dp dugc ve a Hinh 1-2

Trong do

Z/ la tra khang tai, trong truong hgp tong quat do la dai lugng phuc

Z,, la tra khang dae tinh ciia duang day va la dai lugng thuc (vi la duong day

khong ton hao)

Do tra khang ZL va Zo khac nhau, nen khi dat vao duang day mot ngu6n dao dong

tai vj tri Z<0, tren duang day se xuat hien song toi (truyen theo huong Z>0) va song

phan xa (truyen theo huang Z<0) dugc mo ta ha\:

Neu dinh nghia he so phan xa la ty so ciia song phan xa tren song toi ihi lir

(1.28) ta xac djnh dugc he so phan xa lai Z ^Q (lai \ i tri mac tai):

r(0) = Z - Z

' 0 ^ I ^ 1 1

(1.29)

Ro rang la bien do ciia he so phan xa |r| co gia tri bang hoae nho hon L |ri < I

Ap dung (1.29) ta se viet lai (1.26) nhu sau:

Cae biCni thuc (\.}0) cho thay rani; dicn ap \a done dicn tren duang lru>cn Juov

xac djnh bai su "'xep chong" cua hai song la song tai \a song phan \a Do \ a \ bicn

do \V\ va |/| tai moi vj tri Z se co gia tri khac nhau Co nhijng di^m bien dp \V\

hoac |/| Iuon dat gia tri cue dai, ngugc lai co nhijng diem Iuon co gia tri cue ti^u

nghTa la bien do dien ap (hoac dong dien) co dang giao dong theo Z Song nay

dugc gpi la ''song dung"

Nhu vay song diing se xay ra khi he so phan xa r ?^ 0

Khi r = 0, tren duong truyen ehi c6 mot song la song tai eo dang song ehay

Nhu vay song ehay se xay ra khi

r = 0 hay Z/ = Z,,

Ta noi duang truyen dugc phoi hgp tra khang

1.4.2 Hien tugng song diing

Sau day se giai thich ky hon ve hien lugng song dung tren ducrng truyen lay

song dien ap lam vi du (1.30a) co the dugc viet lai nhu sau:

Tu (1.34) ta xac dinh dugc khoang each giQa hai diem cue dai ke nhau AL.=— vol

duang truyen khong ton hao, /] = — , do do AI, = —

A 2

- A \

t 3A

Tu (1.34) va (1.35) ta xac djnh duoe khoang each giua diem cue dai \a diem cue

ti6u ke nhau la 2/?(/_, - / _ , ) - TT , hoac 2/^AL = TT Txx do: IL = ~ = Y^

Ta CO hinh anh eua song dung dicMi ap tren duong da\ iru\en song khong ton hao dugc ve 6 hinh l-3a

D6i voi song dong dien, eiing khao sat tuong tu nhu trCMi ta nhan dugc hinh anh eua song dung ecS dang tuong tu nhu song diing dien ap \e trC-n hinh l-3a Dieu khae

nhau o day la d6i vai cae vj tri V^^u ibi ta eo I^un^ ngiroc lai tai cae v\ tri \',„n, ta lai

c6 Imax- Hinh anh ciia song dung dong dien va song dung dien ap dugc ve chung

tren Hinh l-3b

Cae diem ma bien do dien ap co gia tri cue tieu dugc goi la diem "niit" ciia song

dung dien ap, con cae diem ma bien do dien ap eo gia tri cue dai dugc goi la diem

"bung" Cae diem mil va diem bung ciia song dung dien ap se tuong ung \ oi diem

bung ciia song dung dong dien va ngugc lai Tai cae diem bung va diem mil cua

song dung ta co:

Ty s6 bien dp eiia dien ap tai diem bung va diem mil dugc goi la he so song

dung (USD), viet tat la S

1+r

HSD = S i i i a \

Khi r = 0 ph5i hgp tra khang ta ccS he s6 song dung V = 1 nghia la bien do cua

song dien ap (hoac dong dien) co gia tri nhu nhau tren toan bg chieu dai cua duang

tru\en Song trcMi duang truNcMi dugc coi la song cha>

1.4.4 Bieu thiic he so phan xa tai \ j tri bat ky

Bay gicr ta xac dinh he so phan \a tai \ i tri bat k> tren duang tru>cn imh lu dau

cu6i / - 0 Thay Z = -/ vao cong thuc (1.26a) ta co

r(/) = r;,v^ + F„>-'^ " ^ i >

He s6 phan xa theo djnh nghTa se bang:

1.4.5 Cong suat trung binh truyen theo du-cmg day truyen song

Ta khao sat cong su^t trung binh truyen theo duong tru\en qua diem eo toa do

Z nao do Theo cong thuc kinh dien eua ly thuyet mach, ta co the viet:

Khi r - 0 (phoi hc:rp tro khang), loan bo cong suat dugc truyen cho tai

Khi r ^ 1 cong suat ciia song toi \ a song phan xa eo gia tri bang nhau do do cong

su5t truyen cho tai bang khong

Khi r ^ 0 (khong ph6i hop tro khang) khong phai toan bo cong suat dugc tru\en cho tai ma co mot bo phan bi phan xa tro lai, gay ton hao cong sual Ta goi ton hao

do la *l6n hao do phan xa'\

1.4.6 Ton hao do phan xa

Vi ton hao do phan xa eo quan he mat ihiet \oi he so phan xa r nen nguoi ta

dinh nghTa ton bao do phan xa (thec^ dB) boi cong ihire

Kl^-2iM\\dD <' -^-^'

Khi r = 0, ta nhan dugc RL - -<^ilB (truong hgp khong co cong suat phan xa tra

lai)

Khi r = 1, RL^ OdB (truang hgp toan bo cong suat bi phan xa tra lai)

1.4.7 Trtf khang vao ciia dircmg day truyen song

Tra khang nhin ve tai tai moi diem bat ky tren duang day truyen song dugc

xac dinh bai ty so cua dien ap V(z) va dong dien I{Z) tai vj tri khao sat Khi xay ra

hien tugng song dung tren duang day, tra khang tai moi diem khao sat se khac nhau Tai khoang each / b4t ky (tinh lu tai) ta co tra khang vao nhin ve phia tai se bang:

1.5 Nghien ci'iii mot so doan day truyen song co do dai dae biet

Cae doan duang day co do dai Y^ xa ^ co rit nhiCni img dung trone x ice

thiet ke cae mach dien sieu cao tSn Prong mot sA truang hop cae doan duong da>

niy CO the dugc su dung nhu mot so phan tu quan trong trong mach dien sieu cao

tan

1.5.1 Tru-irng hop du-cmg day co do dai nira song

Apdung (1.47), va luu y pi = —.—= ;r, ta nhan dugc:

A 2

Z _ = 2 / - (1-48) Di^u nay co nghia tra khang vao nhin tu diem each tai mot khoang bang ^ se gia

tri dung bang tra khang tai

ZL-Khi Zl =0, doan duang day ^ ngan mach tro khang vao bang 0 Tinh chat na>'

gi6ng nhu tinh chat ciia mot mach cong huang LC noi tiep co tan so cong huong

Khi ducmg day co t6n hao (a>0) thi duang day ^ ngdn mach lucTiig dm^ng \ ai

mach cong huang RLC m k ndi tiep trong do L.C dugc xac dinh boi cong ilurc

(1.68a, b) va R dugc xac djnh bai

Khi ZL= 00, duong day y^ ha mach, tra khang Zm =x Tinh chat nay giong nhu

tinh chat cua mot mach cong huang LC mac song song co tin so cong huong fc

Neu duong day co ton hao, duong day truyen song ^ ha mach se tuong duong

voi mach cgng huong RLC mac song song noi tiep trong do

/? = ^ (1.50c)

a/

1.5.2 Truong hop duong day co do dai mot phan tu buoe song

Ap dung (1-47) va luu y pi = — - = - < ^^ "han dugc

7 - ^ -^ Z Z ^Z~ (1-^1)

^ I

Nhu \'ay, doan day truyen song y^ eo \hh dong vai tro cua bo bien doi tro khang

Khi cho truac Z,, ta eo th6 nlian dugc Z,,,, luy y bang each lua ebon tro khang dae

linh Zocua day truxcMi song mot each phu hgp

'0 (?=>

in

A/4

Hinh 1-5 Bo bien doi khang tra phin lu song (l-}74)

1.6 Duang truySn dan song co ton hao

Trong thuc te tat ca cae duong truyen dan song deu la cae duong truyen co ton hao do cae vat dan khong phai la cae vat dan dien ly tuong va dien moi trong duong truyen cung khong phai la dien moi ly tuong Trong nhieu bai toan loan thuc te nguoi ta co th^ bo qua cae ton hao nay va duong tru>en dugc coi nhu khong co KHI

hao Tuy nhien khi dn tinh chinh xac su suy giam song trong duang tru\en ha\ khi

tinh toan he s6 phim chat cua khoi cong huong lam tir mot bo phan duimg iru\cn lai khong the bo qua ton hao nay

1.6.1 Dutrng truyen ton hao thap

nau hk cae duong truyen vi ba thuang gap trong thuc te la cae duong tru>en

CO ton hao thdp Do chinh la ddi tugng khao sat cua chung ta trong muc na>:

Nhu da biet, he s6 truyen song trong truang hgp tong quat dugc xac dinh bai: boi (1.11)

y = J{R + i('x){S + i(oc) ^a + ip

Ta CO the vi^t lai bieni thuc na\ duoi dang

i(oL

R G

y = MicoL)(io)C)(\ + -:^)(1 + ) = i(oJIcJ\ - i(^ + ) RG (1.52)

i(oC (t)L (oC ol.C

Doi vai duang truyen co ton hao thap, ta co the gia thiet:

R«(oL\G«€oC, (1.53)

RG «oj'LC, (1.54)

Do do, RJCOL vkGIa)C la cae v6 cung be bac 1 con RGIo^LCXk cae v6 ciing be

bac 2 Neu bo qua dai lugng v6 cung be bac 2 trong (1.52) ta nhan dugc:

R6 rang la neu bo qua cae dai lugng v6 cijng be bac 1 thi (L55) se la cae dai lugng

thu4n ao va tro v^ cong thuc he so truyen song eua duong tru>en khong ton hao

Ta tiep tuc khao sat (1.55) bSng each khai trien gan diing theo chuoi Taylor

V I T 7 = 1 + A:/2 + n va ehi giir lai 2 so hang dau, ta nhan dugc:

Doi voi duong day ton hao thi tro khang dae tinh dugc xac dinh thirc tong

quat (1.15) se la dai lumig thuc TUN nhien khi tdn hao thap ta cung co the bo qua

ic v6 cung be bac 1 khi do (1.15) cung se la dai lucmg thuc:

Cae ket qua tren cho phep ta di tai cae ket luan khi duang truyen co ton hao thap thi

he so pha pvk tra khang dae tinh Zo co the dugc coi nhu gan diing vai truang hgp

day khong ton hao

1.6.2 Dir^Tig truyen khong co tan song va co tan song

Cong thuc (1.58) cho thay he so pha/?(trong truang hgp duang truyen co ton hao thAp) la dai lugng thuc va la ham tuyen tinh theo tan so:

P = A(o, vai A = -JTc = hang so

Do do, van t6e pha cua song v, = ~ = const, khong phu thuoc tan so Khi mot tin

hieu CO ph6 rong truyen theo duang truyen thi cae thanh phan tan so khac nhau eua pho se dugc truyen di vai cung van toe nhu nhau, do do khi chung hcrp voi nhau tai dau thu, ph6 cua tin hieu se dugc bao toan va tin hieu khong bi bien dang Day la truang hgp duong truyen khong eo tan song

Trong thuc ik sir phu thuoc ciia p vd'\ tan s6 la mot ham phuc tap hon (1.54) nghia

\kP((t))khdng phai la ham tuy^n linh eua r.;(e6ng ihue 1.54) do vayv^ = - k h o n g

phai la hang s6 ma la mot ham theo (o Khi moi tin hieu eo pho rong tru>C'n theo

duong truyen thi cae thanh pbdn tan s6 khae nhau eua pho se dugc iru\ en di \ oi cae

van toe khae nhau, do do khi chung hgp vd\ nhau lai dau ihu pho eua im hieu cung

se thay d6i, khong con nhu lue dau \a kCn qua la tin hieu bi bien dang Da> la truang hgp duang tru\en eo tan song

Tom lai, khi truyen tin hieu tren cae dud^^g ixuyhn dan song thuc te eo ton hao thi it nhxcn deu co xay ra tan song \ a kem theo bi^n dang song, muc do nhieu ha> it

la tuy thuoc vao muc do t^n hao eu the eua dirong tru>en

1.6.3 Dirong dan co ton hao nhirng khong lam bien dang song

Ve ly thuyet, co the thiet lap dugc duang truyen dan (co ton hao) khong lam

bien dang song hay khong? De tra lai cau hoi nay ta hay quay tra lai cong thuc

Trong truong hgp nay a = R — \d dai lucrng khong phu thuoc tan so con

P = (OyJTc la ham lu>cn tinh theo o giong nhu doi voi duong tru>en song khong co

tdn hao K^t qua la khi co tin hieu dai rong truyen tren duong tru\en dan noi tren thi

tin hieu song se bi su\- giam nhung khong bi bien dang

1.7 Duong truyen co t6n hao duoc mac tai dau cuoi

Trong iruong hgp nay he so iru>tMi song via dai lucmg phuc y^a + ip \'oi

gia thiCn duong \x\.\\'cn co ton hao nho thi a va /?se dugc xac dinh theo (1.57) \a

(1.58), con tro khang dae tinh Z, duoc xac dinh theo (1.59) la dai lugng thuc Bieu

thirc cua song dien ap va dong dien tien duong tru>en dugc xac dinh theo cong thuc

tong quat (1.23)

yu^=y:[e-'+re-\ (1.62a)

trong do: V la he so phan xa tai tai (* = 0) Vi tri phan xa img voi vj tri = tren duong

truyen dugc xac dinh boi ty so song phan xa va song toi tai diem kkhao sat nghia la:

1.7.1 Tro* khang vao ciia duong truyen co ton hao

Ap dung dinh nghia long quai iro khang vao.ta biet dugc:

Hinh 1-6 Duong trii\en song co ton hao co mac tai

Thay V boi (1-39) sau khi bien doi ta dugc

/ +Zjhyi

" Z^,^Zph}i

(1.66)

1.7.2 Cong suat truyen vao dvcmg truyen tai dau vao

Cong thuc tong quat de xac dinh cong su^t trung binh tru\Sn vao duang truyen tai dau vao, co dang:

(1.69)

(1.70)

(1.71

r \

1.7.3 Cong suat truyen vao tai

Tuang tu nhu tren, ta \ae dinh dugc cong suat trung binh dua den lai khi thay /=0 trong cae cong thuc a doan tren Ket qua ta dugc:

' :

1.7.4 Cong suat mat mat tren duong truyen co ton hao

Biet cong suat truyen qua dau \ao VA cong sual dua dugc den tai ta xac dinh

dugc cong suat mit mat tren duong lrii>en (ha\ cong suat ton hao ky hieu la P,h)

Thay (1.69) va (1.71) vao (1.72), ta dugc

Cong suat mat mat ciia song phan xa, bang hieu cua cong suat song phan xa

tai vi tri ciia tai

)

1.8 Duong day mach dai

Duong day mach dai la mot irong nhung loai duong da\ lru\en song phang thong dung nhSt, ehu y^u la vi no eo the dugc che lao de dang nho ky thuat in khae

kim loai va de dang tich hgp dugc \oi cae thiet bi sieu cao tan tich cue va ihu dong

khae Tinh chdt hinh hoe ciia mot duong day \i dai dugc \e trong Hinh l-8a Mot

day dan co do rong W duac in khae tren mot mat eua \ at lieu sieu cao tan mat phang d6i dien dugc n6i dat va do dA>- vat lieu each dien giua hai mat dan dien la d hang so dien moi la £,\ Phae thao eua cae dirong sue triRmg dien tu dugc bieu dien

trong Ilinh l-7b

( J )

inh I -7 Duong da\ mach dai, a) cau ink hinh hoc b) phan bo dirong sue tir eua dirong dav

N6u khong co chat dien moi (^v=^l) ehiing ta co the coi duong day nhu la mot

duong day hai sgi bao gom hai dirong day phang eo do rong la ll\ each nhau mot doan la 2d (mat phang dat co the bi loai trir do ly thuyet anh) Trong truong hop nay ehiing ta co the co mot duong lrii\'en song mode TEM vd'\ c,, = c vix p = A,,

1.8.1 Hslng so dien moi

Su CO mat cua chSt dien moi, \'a dae biet \'di thuc te la chat dien moi khong

lam dhy mi^n khong khi ben tren duong da\ C > d), da lam cho \ iee xem set \ a

phan tich duang da>' \'i dai them phire tap Khong nhu cae doan diroiig da> tru\en det (stripline), trong do truang dien ur dirge giir trong mot mien dien moi dong nhat cae duang day vi dai co phAn lan cae duong sue tir trong \ iing dien moi tap trung giua doan duong day dan \'a mat phang ddl mot phan cae dirimg sire tir nam a \ ung khong khi phia tren tSm vat lieu Vi ly do nay cae dirong day \ i dai khong the cung c^p mot song mode TEM thuan tu\ Vi van tck pha eua trucmg TEM trong \ung dicMi moi se la e / ^ ^ , nhimg van lOe pha eiia trircmg TEM trong vimg khong khi eo

the la e Do vay, mpt su phoi hgp pha tai giao dien ciia chat dien moi va khong khi

se khong the dat dugc doi vai song lEM

Tuy nhien, trong hau bet cae img dung cu the, vai vat lieu dien moi rat

mong id«A) ve mat dien, va vi vay tmang la TEM goc phan tu Noi each khac,

truang dien tir ciia duang day vi dai ve eo ban giong nhu truang tinh Do va\' cae

phep gan diing se dugc sir dung de xac dinh van toe pha va hang so truyen song, tra

khang dae tinh co the dat dugc tir nhilng ket qua ciia truang tinh hoac truang gan

nhu iTnh Vay van toe pha va van toe truyen song co the dugc tinh nhu sau:

v ^ , = - ^ , (1.75a)

trong do^,*^ la hSng so dien moi hieu dung eua duimg da\ mach dai Vi mot trong

cae duang sue cua truang trong vimg dien moi va mot so khac thi nam trong \ img

kliong khi, hSng so dien moi hieu dung thoa man moi lien he sau:

1<^- < ^ , , (1-76)

va doe lap vai do day eua vat lieu dicn moi d va do dong da> dan (C

Dau lien, chung la se xay dung bieu thuc cho hang so moi hieu dung \ a tro

khang dae tinh cua duong da> vi dai; nhung kcH qua na\ la nhirng phuong trmh \ap

xi phu hgp voi nhung k^l qua khSt khe cua truong gan linh Sau do sc phac thao ra

mgl s6 phucmg phap loan hoc de lim loi giai cho dien dung tren mot don \ i chieu

dai cua duang day vi dai, cae phuong trinh hing so dien moi hieu dung, iro khang

dae tinh va do suy giam Hang so dien moi hieu dung eua mot duong da> \i dai

dugc cho trude xap si bang :

2 2 ^\ + \2d W

imng so dicMi moi hieu dung co the dugc dicn dai nhu hang so dien moi cua \ai lieu

trung gian dong chil co the thay the miCn dicn moi \a mien khong khi cua duong

day vi dai, nhu ehi trong Hinh 1-9 Van toe pha va hang so truyen song co the dugc

cho bai phuang trinh (1.75)

1.8.2 Tra khang dae tinh ciia duong day mach dai

Neu cho truac do rong ciia duong day vi dai tra khang dae tinh co the dugc tinh nhu sau:

Neu cho truac mot dudng day co trd khang dae tinh Z(, va hang so dien moi /, ihi li

le W/d CO the duac tinh nhu sau

" 2 , / , ( , - l ) Phuang trinh nay giai thich cho moi ihuc le rfing truong dien lu xung quanh duong day vi dai cd mot phiin nam trong khong khi( mat mal) xa mot phan nam trong chai

diCMi moi Su suy giam cho m^t mat tren dudng da> dan co the dw^ unh xap xi

biing

a^ =—^—Nplm, (1.82)

trong do R^ = yjco/u^^ 125 la tra khang be mat ciia chat dan dien Doi vai hau bet vat

lieu vi dai, do mat mat dan dien la nhieu hon nhieu mat mat dien moi: ngoai tru nhirng dieu xay ra vai chat ban dan

Hinh 1-8 C^u true hinh hoc cua duong day mach dai vdi hire tuong ng^n each y

2 ChiFO'ng 2

LY THUYET MANG VI BA [1,2]

2.1 Khai niem chung

0 tan so thap, kich thudc cua mach dien tu rat nho so vdi bude song \ a bao

gom cae phan tu tap trung Tren dudng day noi giijra hai phan tir tap trung dienap

va dong dien tai mgi diem dugc coi la nhu nhau nghia la ta co the bd qua su ire pha ttj diem nay den diem kia Truong dien tir tdn tai trong mach dien co the dugc coi la truang dien tir ngang (TEM) Trudng nay dugc duy tri boi 2 hoae nhieu day dan Co nhi^u each d^ phan tich mach dien lan so thap, pho bien la sir dung phuong trinh Kirchoff ddi vdi dien ap, ddng dien va diing khai niem trd khang eua ly thuyet mach d t4n so cao, kich thudc ciia mach dien so sanh dugc \di bude song nen cae qua trinh xay ra trong dd la phire lap Phuang phap long quat la diing he phucmg trinh Maxwell va ap dung dieu kien bd cho cae bai loan cu the: Cae bai loan bcr

Tuy nhien, viec giai true tiCp bai loan bd cung khong dan gian \a khong phai liic

nao cung dat dugc Vi vay, cd the tuong nhdm ly luan ve mang \ iba khong the dem lai mot sir de dang nao ve mat phan tich loan hoc ma chi la mo phong theo mach dien tdn thSp da cho quan niem dugc cu the ban \a de hinh dung hcTn so \di khi ap

dung ly thuySt trudng dien tir ma thoi Qua trinh phan tich mang \ i co the duoc hicu

nhu sau: Dau tien ta nghien eiru moi loat cae vdn de kinh dien mot each chi lici \ oi viec sir dung cae phuang trinh Maxwell Khi lam nhu the la co the luxmg hoa dugc nhirng nhan td cd lien quan true ti^p d^n cae tham sd cua duong da> truyen song, ur

do cd th^ tinh ra dugc hang s6 lru>en song \a tro khang dae tinh cua duong da> Cae dudng day tru>C^n sdng ed the dugc xem nhu la mot phdn tu phan bo ma dai dicMi cho no la chiCni dai, hang sd tru>>}n song va tro khang dae linh Tai muc do na>

ta cd th6 sir dung ly thu>(lt duimg d.i> iruy^n song \a mang \ i ba de phan iich cae mach dien gdm nhiCni loai ph^n tu khac nhau de tinh ra cae tham s6 eua mach dien

nhu la do ton hao trong mang, he so phan xa he so truyen qua tra khang vao tro

khang ra, va cae thong so lien quan khac

Luan van nay chi nghien cuu ly thuyet mang vi ba ap dung cho ducmg day

truyen song Trong do song truyen trong duang day co cae mot song la TEM hoac

gan TEM

2.2 Khai niem ve tra khang, dong dien va dien ap tuong duong

2.2.1 Dien ap va dong dien tuong duong

Doi vai mach dien sieu cao tan viec do dugc dien ap \ a dong cha\ trong mach

dien la mot di^u khong the, tru khi da xac djnh dugc ro rang dien ap tai cae diem

dau eu6i D6i vai day truyen song \ i du gom hai day dan a va b, dicMi ap giua hai

day:

V= frJl C.\)

Theo ly thuyet truong tmh thi gia Iri dien ap xac dinh iheo (2.1) la du> nhal \a

khong phu thuoc vao duang lay tich phan Dong dien cha\ trong da> dan dugc xac

dinh theo dinh luat Ampere:

Tra khang dae tinh cua day truyen song:

Zo=j- (2.3)

Sau khi xac djnh dugc dien ap V, dong dien I va tro khang dae tinh Zo, ta co the ap

dung ly thuyet mach cho duang day truyen song nhu thuc hien a chuang 1

2.2.2 Khai niem trey khang

Chiing ta da su dung khai niem ve tra khang trong mot so ling dung Trong muc

nay se thao luan ve khai niem tra khang theo mot y nghia tong quat hon Thuat ngu

tra khang da dugc Hevisaide sir dung lan dau vao the ky 19 de mo ta ty so pbiie eua

V/I trong mot mach dien xoay chieu gom eo cae dien trc7 dien cam va dien dung

"Tra khang" da nhanh chong tro thanh mot khai niem khong the thieu dugc khi

phan tich mach dien, g6m ca duong iruyen dan eo cae phan tu tap trung hoae phan

b6 Nam 1930, Schelkeenooffda nhan thSy rSng khai niem nay cung eo the ap dung

cho truang dien tu va no dugc coi la dae trung eua mot kieu trudng ha\ mot moi

truang Co thS tom ik mot vai khai niem \'6 tro khang da dirge su dung cho den

nay:

- TrcV khang eua moi truong: Z - ^pTe Tra khang na> ehi phu thuoc \ao

cae tham s6 vat lieu eua moi trirong D6i voi song phang iru>en lan irong

moi truOTg thi dai lugng na> chinh la bang tro khang song eua song phang

- Tra khang song:

7 = - ^ la ti so cua thanh pluin dien truoTig ngang \ a tu iruong ngang eua

mot song Cae song TEM, TM TE eo tro khang song khae nhau. ( Z , , M Zn-,

ZTM) phu thuoc vao loai duong iruyen vat lieu dien moi ben trong xa idn so

cong tac