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DAI HOC OUOC GIA HA NOI
TRUONG DAI HOC CONG NGHE

TRAN

ANHTUAN

NGHIEN CUD VA PHAT TRIFN
LY THUVET DUONG DA\ (;HF:P D E THIET K E CHE TAO
MOT SO PHAN TLITHU 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
Ma so:
2.07.00

LIAN \ AN THAC SV

Nca oi III ( ) \ ( , i ) \ \ k i i c n IHH.: ( . s ISKH I'll \ \ A M I

.V-Lr/66L
HA NOI, 3-2006


LQI CAM DOAN
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


u

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 luVien 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.


Hi

MUC LUC
TRANGPHUBIA
LOI CAM DOAN

LOI CAM ON
MUC LUC
DANH MUC CAC BANG
DANH MUC CAC HINH VE
MODAU

Trana
i
ii
iii
vi
vii
ix

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 \ao duona tru\en tai dau \ao
21

1.7.3
C'onu sual lru\ en \ao tai
21
1.7.4
Cdmj. sual mal mal Iren duonu lru\en
21
^-

»-

-

1.8 Duonu da\ mach dai
1.8.1 I lang so dien moi
1.8.2 Iro khani: dae inih cua duonu da\ mach dai

-3
2^


IV

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
3.1 Khai nicMii dirong day ghep
3.1.1
Phan tich mode kich Ihieh chan. le cua
duone da\ ehep
3.1.2 Tro" khang mode le \ a mode chan cua moi duong da\
ghep CO eau true mach dai
3.2 Dae tinh lira ebon tan so cua duong da\ ghep
3.4 Phat irien Iv thuvet duone dav ehep eo eau true mach dai
3.4.1 1 le so ghep song cua duong da\ ghep
3.4.1.1 Duong da\ dan song khong ion hao
3.4.1.2 Duonu dav dan sons c6 ton hao
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
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

50
50
52
57

62
63
63
64
66
67
->


CHU'ONG 4- U"NG DUNG KET QUA PHAT TRIEN LY THUYET
pU'ONG DAY GHEP
83
4.1 De xuat mot thiet ke moi ciia bo loc duang day ghep bang rone 85
4.1.1 Ly thuyet mach loc
83
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
CAC CONG TRINH D A CONG BO
TAI LIEU THAM KHAO

:

94
97
97


VI

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

Bang 3.1 Cae dai lugng dae trung ciia mot mach cgng huong

.....52
77

Bang 4.1 Gia tri cae phan tu trong mach loc thong thap chuan boa

Bang 4.2

(gO - 1 , o)C=l, N=E..9, CO do ggn song la 3dB)

89

Bang tham so hinh hoc cua duang day ghep bang rong

95


Vll

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
Hinh 1-5 Bg bien doi khang tro phan tu song (1=A/4
16
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
31
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


Vlll

Hinh 3-16 Phat trien thiet ke ciia bg cong huang duong day ghep
Hinh 3-17 Phep bien doi tuong duong mot mach cong huang
RLC mac song song
Hinh 3-18 Dap ung tan so ciia bg cgng huang duang day ghep
Hinh 4-1 Dap ung tan so cua mot so bg Igc ly tuong
Hinh 4-2 Cau true ciia mot bg loc thong thap chuan boa
Hinh 4-3 Cae phep bien doi tu bg loc thong thap chuan boa d^n
cae dang bg Igc khac
Hinh 4-4 Quy trinh thiet ke mot bo Igc duang day ghep bang rong
Hinh 4-5 Mot so ket qua mo phong eiia mach Igc duong
day ghep bang rong
I linh 4-6 Mot mau bo loc duong day ghep bang rong

79
79
86

87
88
90
92
96
97


IX

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


so pham chat thap. Ngoai ra luan van nay cung neu ra mot s6 cong thuc moi va phep
bien doi tuang duang moi bo xung vao ly thuyet duang day doi hien nay. Nhij-ne k^t
qua nay cung da dugc cae hoi nghi quoc te cong nhan.
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.


CHL^aNG 1
LY THUYET ve OLKQNG DAY TRUYEN SONG [1, 2]

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


rang khi trong mach dien cao tan co duang day truyen song ma chieu dai ciia day co

gia trj bang mot phan so dang ke cua buoe song thi mach do dugc coi la mot he c6
phan tu phan bo. The hien chinh eua khai niem nay la tren duong da\ xuat bien
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).

Uz. f)

viz. t)
i i C

• •

•

' •

(a)
i{z. t)
o
•^
z. f)

i(z +Az, r)
^Z"
\A
V VV V

LAz

1
GAz >

+

= = CA:

v(i + A;, t)

1

o
A T

o

(b)

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


L - Dien cam noi tiep tren mot dan vj dai ciia ca 2 day. Him
G - Dien dan song song tren mot don vj dai, sIm
C - Dien dung song song tren mot don vi dai. FIm

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:
F(z,0-O^A2/(z,/)-Izir^^^^^~/'(r + Az,/) = 0 .
St
Doi voi dong dien:
/(z,/)-GArr(r,/)-(Ar'^i-^^-/(r^.\_-./)-0 .
St

(1.1)

(1.2)

Ky hieu
V{z^.\zj)-\\z,t)^\W
I{z +

\za)~I(zj):^M.

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

^5IH). _«/,,,)-i*Hl.
&

,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)


^

= -iG + icoC)Viz).

(1.6)

Thay
Z = R + icoL,
Y = G + io)C,

(1.7a)
'

(1.7b)

ta CO the viet lai (1.5) va (1.6):
SV
= -IZ,

52
SI

(1.8a)

= -VY.

(1.8b)

SZ
/

/

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:
^

= (Zr)r(r),

(1.9a)

^^^-(/T)/(r) .
Sz^

(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.
dz'

(1.10b)

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)(
'1


»

«

Theo ly thuyet ve phuang trinh vi phan, ta co nghiem cua (1.11)
K(z) = ^;V^+^;-e^

(1.12a)

/(z) = /;e-^ + /,-e'^ .

(1.12b)

(1.12a) va (1.12b) bieu thi cae song dien ap va dong dien tren duang day. trong do,
so hang chua e'^ bieu thj cho song truyen theo huang +z (song thuan), con so hang
chua e^' 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.
Tir(1.5)tarutra:
I{z) =

:—.
R^-i(oL dz

Ap dung (1.12a) ta nhan dugc:
/(z) = - ^ { ^ ; , V ^ - - - ^ o V - • ) .
R + uoL

(1.13a)

Ky hieu 1^ = R^icoL, ta viet lai (1.13a)
I{z)^-^(r;e-'=-V^e'=).

(1.13b)

So sanh (1.13a) vai (1.12b) ta riit ra dugc cae moi quan he sau:

/^;=li^; / ; = ^ ^ .

(1.14)

trong do

Tu(1.14)c6th^viet
Z,=l^ =- ^ .

(1.16

Khi chuyen bieu thirc bi^u thi ham song vc mien thai gian. ta can nhan them \ai
ham mu t'"". nghia la


Luu y rang bien do cua dien ap VQ (hoac dong dien IQ) cung la cae dai lugng phuc,
vi du:

K= K

.'f

Dodo:
T/+

-yz

lol

Vfi e ^ e

idt* -az

Vo e^ e

-ipz

lot

e ^ e

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
A=

(l.lSi

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:


y = a + i/S = ia}ylLC,

(1.20)

suy ra:
P = (OJLC,

(1.21a)

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=^ ^ - ^ .
/3 ojfLC

(1.24)

va v^n toe pha ciia song:
(0

(1.25)

' P uc
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.
V{z\ /(z)

—. ,

o^k

•

Zz.

J
'

0

Hinh i-2. So do duonu tru\en khong ton hao eo mac tai dau euoi


8

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\:
V(z) = V;c-''^V,e"\

(1.26a)

/(^^).!l,-/^--+!iL^,.A.-^
7

26b)

7

Tai Z = 0 (vi tri mac tai) ta co:
Zr

^
V;^V,

J

V - V~

MO)

M)

z

(1.27)

M)

Tir (1.27) ta co the riit ra;
Z -Z

(1.28)

z, + z„
1.4.1 He so phan \a

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):
Z -Z

r(0) =
' 0

^

I

(1.29)

^11

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:
V =V^ .'''^-- + iv"--J,
,/t

""

z.

-n

Ilk

(1.30a
(1.3()b

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


9

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:

1 + re•>>/iz
Bien do ciia dien ap tren duong day

1 + rc-'/'^

(/)

(1.31)

Vi^t lai (1.31) theo toa do /. luu y rang khi a>' I = -:. ta co

1 + Ve-"^'

(/)

(1.32)

Co the bi^u thi duai dang V = \r\e'". khi do biau thuc (1.32) se co dang:
' • ( / )

=

^o' 1 + r

^,'U)-2/ll)

(1.33)

Ta nhan thay /'se dat dugc gia trj cue dai I „,aN khi t'"""^' = • • "E'lla la ung \ai;
{0 - 2/31) = 0; ± 2;r; ± 4;r ; ± 2/;.T .

(1 -34)

va V CO gia tri cue titni V„„„ khi e'^"''^'^ = - 1 . NghTa la ung \a\
{e-2pi)^±n:

±3.T; ±5.T; ... ; ±(2/; + 1)T.

(135)

10

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
]

t
3A

-A\

1

^

A
4

2

I

-1

(«)
1

1

A /a)Zo
2v:

1

3 \
" 4 \.

-A

A

J

2

/ "4

i.

-1

(b)
1

Zo

V^
-/C\

u

2

^

A

A\

z

^
\ 1
\l
\l
•l

(c)

Hinh 1-3. Do thi bieni dien a) Dien ap. h) dong dien. c) tro khang phan bo doe theo duong
day truyen song ngan mach.
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

11

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:

^.ax=k1(i+|r|),

I =fl('-in)-

(1.36)
(1.37)

Con lai cae diem nut ta co
mm

^

(i-|r|)-

(1.38

^(i^rl).

(1.39)

X

1.4.3 Bieu thiic ciia he so song dung
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.
HSD = S

iiia\

mm

1+r
i-lr

(1.40)

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>

12

He s6 phan xa theo djnh nghTa se bang:
0

r(/) =

^-e^ - 2 » / ? /

(1.42)

'^ 0

Trong do r = - ^ la he so phan xa tai dau cuoi / = 0.
K
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:
P.,.^

R6 rang: - - ^
2 Z

2 Z.

(i-lrh

(1.43)

la cong suat trung binh eiia song toi.

Irf la cong suat trung binh eiia song phan xa,
2 Z„
Nhu vay cong suat trung binh tru>en theo dirong truyen se la hieu eua cong suat
trung binh song toi trir di cong sual Irung binh song phan xa.
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.

<' -^-^'


13

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:

Z

=

c'

V{1) K
/(/)

+ 1 C '/'/

(1.45)

^V r^//'/_ p^,'/'/

Khi cho /=0, bieu thirc (1.45) se xac djnh gia trj ciia tai Z,
2,=

\+V^

1-r

(1.46)

0-

Thay bi^u thuc cua r (cong thuc 1.42) vao (1.45) la nhan dugc

7 ^7 {z,^z,y" + {z,-z,)c-^'

''^-

%Z,+Z,)e'^''-(Z,-Zo).-'^""

-z,

Z, cos/?/ + /Z,|Sin/?/
Z(, cosy5/ + /Z^sin/^/

hay
^ ^ Z, + iZ,,i^pl

(1.4-)

'z, + iz,t^pi
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>


14

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 ZLKhi 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
f(; = y..

Trong do
2Z
z/.()

(1.49a)

'U
C =

7r

(1.49b)

2ZQU.'Q

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
R = Z,,ol .

fi':

in

>

ZQ?

(1-49C)

/?•

^0

o
-/

Hinh 1-4. Doan day truyen song (/= /-/L2) ed mac tai

0