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DAI HOC QUOC GIA HA NOI
TRl/dNG DAI HOC KHOA HOC TlT NHIEN

£)ETAI
TOI UU QUA TRINH TRUYEN NANG LUONG TIN HIEU
VA NANG CAO DO NHAY CUA CAC THIET BI THU
DAI TAN SO CAO CO CHON LOC

MASO:QT-05-11

CHU TRI DE TAI: VU THANH THAI
(KHOA VAT LY)

HA NOI - 2005


DAI HOC QUOC GIA HA NOI
TRUCJNG DAI HOC KHOA HOC TIT NHIEN

€)ETAI

TOI UtJ QUA TRINH TRUYEN NANG LUONG TIN HIEU
VA NANG CAO DO NHAY CUA CAC THIET BI THU
DAI TAN SO CAO CO CHON LOC
MA SO: QT-05-11

CHU TRI DE TAI:
CAC CAN BO THAM GIA:

THS. GVC. VU THANH THAI
GPS-TS VU ANH PHI

THS.GV D A N G THANH THUY

DAI HOC Q U O C GI.A HA NOl
TRUNG TArv/ THONG TIN ^HU \,/!PM

PT / 5-00

HA NOI - 2005


1. BAO CAO TOM TAT
a. Ten de tai:
Toi icu qud trinh truyen ndng luang tin hieu vd ndng cao do
nhay ciia cdc thiet bi thu ddi tdn so cao co chgn Igc .
(Ma so: QT-05-11)
b. Chu tri de tai:

ThS. Vu Thanh Thai

c. Cac can bo tham gia: POSTS VQ Anh Phi
Ths. Dang Thi Thanh Thuy
d. Muc tieu va noi dung nghien cuu:
- Xay dung bai toan toi uu truyen nang luong trong khong gian
song cao tan .
- Tdng hgfp cac mach phoi hgfp va toi uu hoa dac tfnh truyen dat
cong suat cua he thdng thu va xu li tin hieu .
- Tfnh toan va dua ra giai phap nang cao do nhay ciia thiet bi thu
tan so cao co chon loc .
e. Cac ket qua dat dugc :
• Kit qud nghien cAu khoa hgc:

* Dua tren ly thuyet v6 khong gian tuyen tfnh gia Ocht
(Mincopski) da xay dung dugc mo hinh vat ly thuc cua
khong gian tuyen tfnh - khong gian nang lugng trang thai tfn
hieu.
"^ Tren ca sa phan tfch cac toan tir trong khong gian nang
lugng trang thai tfn hieu da thiet lap dugc bieu thuc ciia he so
truyen dat cong suat cua mang 4 cue du6i dang cac cap ham
ma tran vo huang ciia cac dang toan phuang chi cua mot
bien. Dieu nay cho phep dua bai toan xay dung he thong
truyen tfn hieu voi dac tfnh truyen cong suat cue dai ve bai
toan gia tri rieng ciia dang toan phuang trong khong gian
nang lugng ciia trang thai tin hieu.
* Xay dimg bai toan truyen song cao tan trong khong gian :
da tfnh toan thanh cong van d6 toi uu nang lugng cho song
cao tan qua cac dac trung cua song tai va song phan xa .
* Tong hgp cac mach phoi hgp; tinh toan toi uu hoa dac
tfnh truyen dat cong suat ciia song sieu cao tan . Bang ly
thuyet da chi ra r^ng chi can sir dung cac mach phoi hgp 3
phan tii co thd phoi hgp dugc vcd cac phan tu M4C hoac M2C
bat ky va co the thay doi dac tuyen phoi hgp ciia he thong
b^ng each thay ddi cac tham so vat ly ciia mach phoi hgp ma
khong thay ddi thiet ke ciia no.


* Tfnh toan mot so mach cu the truyen song sieu cao tan va
dua ra cac thong so toi uu cho mach phoi hgp de dat cong
sua't truyen cue dai . Khao sat dac trung truyen nang lugng
ciia mach sieu cao tan .
• Ket qud dao tao:
*- Co 02 khoa lu|n tot nghiep dai hgc da dugc bao ve theo

hu6ng nghien cun ciia de tai
*- Khoa luan nam hgc 2005-2006 se co 2 sinh vien nghien
cuu tiep tuc theo huang de tai.
f. Tinh hinh kinh phi cua de tai:
Tdng kinh phf thuc chi
Trong do
- Tir ngan sach nha nu6c
- Kinh phf ciia DHQG
- Vay tfn dung
- Von tu CO
KHOA QUAN LY
(Ky va ghi ro ho ten)

: lO.OOO.OOOd
: Od
: lO.OOO.OOOd
: Od
: Od

CHU TRI DE TAI
(Ky va ghi ro ho ten)

TS. Nguyen The Binh

ThS. Vu Thanh Thai
TRI DE TAI
OHIEUTHUOKU

^j^.Twk^f

^ik


2. BRIEF REPORT OF PROJECT.
a. Project title:
Optimize of transmission energy of signal and to raise the
sensitivity of the receivers high-frequency selectively .
(Code: QT-05-11).
b. Project co-ordinator: MSc. Vu Thanh Thai
c. Co-operator

Pro. Dr. Vu Anh Phi
MSc. Dang Thi Thanh Thuy

d. Objectives and scientific contents:
- To solve a optimal problem of transmission energy in the
space high-frequency waves .
- To synthetize the coordinate's circuits and optimize a
partycuarity transmission power of receivers and signal processing .
- To calculate and to put foward method to raise the
sensitivity of the receivers high-frequency selectively .
e. Results :
• Science results:
* Based on the theoretical of the linear space- Euclit's false (
Mincopski's space ) , we constructed real physics model of
linear space . This is the energy space of signal state .
* We established the expressions of transmission power
coefficient of a four-pole network (M4C) to expressin the form a
pair supecalar matrix function of quadratics of the only variable
For this reason , we came to conclusions that the solution of

the combined problem on the linear system for signal
transmission will become the solution of problem on specific
values in quadratic form in the linear space - energy space of
signal state .
* We solved a problem of the transmission high frequency
waves in the space ; To solved a problem optimize of energy of
the high frequency waves in the form values of incident and
reflected waves .
* The authors calculated some of concrete circuit -super high
frequency and disgnated parameters for to obtain a maximium
power
..« •» v:
• Training results:
There are 02 graduation theses having been defended from
the project's goal . In the next year , will be 02 graduation
continues .


PHAN CHINH BAO CAO
1. MUC LUC
Bao cao tom tit
1
Brief report of project
3
Phan chfnh bao cao
4
1. Muc luc
4
2. Lai mordau
4

3. Noi dung chfnh
5
3.1. Xay dung bai toan truyen nang lugng toi uu trong
khong gian song cao tan
5
3.2. Tdng hgp cac mach phoi hgp va toi uu hoa dac tfnh
truyen dat cong suat ciia he thong thu va xir If tfn hieu. S
3.3 Tfnh toan va dua ra giai phap nang cao do nhay ciia
thiet bi thu tan so cao co chgn Igc
i§
4. Ket luan
J.5
5. Tai heu tham khao
J|3

2, LCil MO DAU
Trong kl thuat viln thong , mot trong nhirng chi tieu ki thuat ca ban
khi xay dung he thong thu va xir If tfn hieu la viec dam bao he sd truyen
tai cong suat tac dung cam iing vao anten thu tod phu tai dat gia tri 16n
nhat . Nang cao he sd truyen cong suat se lam tang chat lugng va cir ly
thong tin ( khi cong suat phat cung nhu cau true he thdng anten khong
thay ddi) .Giai quyet nhiem vu dat ra din tdi viec giai bai toan phdi hgp
giira cac khdi chiic nang ciia may thu , dac biet la tuyen sieu cao tan .
Ngay nay, vdi nhiJng tien bg nhay vgt ciia ky thuat mdri va c6ng
nghe che tao cac linh kien dien tu, hang loat linh kien mdi dugc dua vao
sii* dung. Viec su dung cac linh kien mdi nhu cac ph& ttr td hop cao, cic
linh kien lam viec d giai song sieu cao tan cang can phai doi hoi ngJu^
cuu cac thuat toan tdi uu de phdi hgp chiing.
De tai nay la tiep ndi ciia de tai " Tdi iru hoa qua trinh truyoi nafl^
lugng tfn hieu dien trong mach dien tuyen tfnh va trong khdng gia" "• ^

sd : TN 03-05 cung do chinh nhdm tac gia nay thirc hien .
Ket qua ciia de tai ma sd TN 03-05 da dat Auoc Ja:
1. Xay dung mot mo hinh vat ly thirc cua khong g^an'WF^^^
chfnh la khong gian nang lirgng trang thai tin hi^u. G^ ^
*

|
J


sang giai bai toan ve tri ridng, vec ta rieng trong khong gian gia Oclit
(khOng gian mincopski)
2. Vdi mo hinh tren chiing toi da xay dung va giai bai toan match
dien voi cac thong sd la U, I cua dong dien. Dua bai toan cong suat cue
dai ve viec quay vecta khong gian.
3. Tfnh toan cho mot sd mach phdi hgp 3 phin tu
De tai QT-05-11 nay se giai quyet tiep nhOtig van de sau :
1. Xay dung bai toan truyen nang lugng tdi uu trong khong gian
song cao tan .
2. Tdng hgp cac mach phdi hgp , nang cao cong suat thu ciia he
thdng thu va xir li tfn hieu .
3. Tfnh toan va dua ra giai phap nang cao do nhay cho cac thiet bi
thu tin sd cao cd chon loc .
3. NOI DUNG CHINH
3.1.

Xay dung bai toan truyen nang lugng tdi uu trong khong
gian song cao tan .

3.1.1, Cdc todn tu: truyen dat trong khong gian song cao tdn .

Trong dai sdng sieu cao tan , khi giai bai toan truyen tfn hieu cQng
nhu bai toan ly thuyet mach , ngu6i ta diing cac tham sd sdng: sdng tai va
song phan xa thay cho cac tham sd dien ap va dong dien . Trong truang
hgp nay , dac tfnh ciia cac M2C va M4C cung dugc dac trung bdi cac
tham sd sdng : Mang 2 cue dugc dac trung bdi he sd phan xa . M4C dac
trung bdi ma tran tan xa S va ma tran truyen dat T.
Tdng quat, quan he giua dien ap U^, dong dien I^ vai sdng tai va
sdng phan xa tren cac cue ciia MnC dugc xac dinh :
Uk = ak + bk
Ik - ^k '

\

Trong dd a^, b^ la sdng tdi va song phan xa chuan hoa tren cue thu
k ciia MnC
Xet vdi mang 2 cue nhu hinh ve
1 fc

U

V

p

Hinh 1

VaiM2Cahmh(l)tac6:


U =a+b

I-a-b
Trong dd:

b=ap

p = — - : la he sd phan xa ciia M2C
z+p
*
z: Tdng trd ciia M2C
p: Trd khang song ciia doan day ndi vdi M2C
Neu ta ggi khong gian sdng ciia trang thai tfn hieu ciia M4C bao
gdm cac vecta: C^ = ae^ + be^ (1)
Trong dd €3,6^ la vecta ca sd khong gian sdng trang thai tfn hieu,
thi dt dang thay ring, khong gian sdng (1) va khong gian kinh dien
v^ = ue, +ie2 la dang cau, va ma tran chuyen T tir ca sd (€,,62) sang ca sd
(€3,6^) CO cau true:
^1 I

V^

(2)

Trong khong gian sdng trang thai tfn hieu, cong suat tac dung ciia
M2C, hay binh phuang do dai vecta trang thai tfn hieu dugc xac dinh bdi
bieu thiic:
|V| =P a^-b^ (3)
Hay P = C,+JC, (4)
Trong do J - ma tran gramma ciia vecta ca sd true giao chuan hoa
trong khong gian song trang thai tfn hieu. Ma tran J co ket cau:
(5)

Trong trudng hgp xet ta cd:
(ea.eb) = (eb,ej=0
Do dd khi nay ma tran J co ket cau:
1

J-

0

(6)

Trong mat phing Oclit, phuang trinh (3) la phuang trinh ciia dudng
hypecbol vai cac dudng tiem can la cac dudng phan giac ciia cac gdc toa
do (hinh 2).


Hinh 2
Tir hinh ve, dt thay ring: gia tri khong doi cua cong suat tac dung
ciia M2C cd the nhan dugc v6i cac gia tri khac nhau ciia cac toa do a, b.
Han the nua, cac toa do a, b lien he v6i nhau bdi bieu thiic (3). TCr sir phu
thuoc giua cac toa do a, b co the tha'y ring, viec chuyen tir toa do nay sang
toa do khac cd the dugc thuc hien bing viec quay dudng hypecbol mot
gdc 9 nao dd, ma viec quay dd hoan toan khong lam thay ddi do dai
vecta.
3.1.2 . Gidi bdi todn cong sudt cue dai:

Neu mang 2 cue da cho dugc ndi vdi M4C tuyen tfnh vdi ma tran
sdng T. Thiet lap mdi lien he giira song tai va sdng phan xa tren dau vao
va dau ra ciia M4C (hinh 3)

a,

32
•<

b>i
T

c.

P
ba

F>

-

—^ c,.
Hinh 3

Tacd
hay

'a,'

T

kJ

T

CI

~

T.C:,

T
M2

\ '

T22J .^2_
(7;)

Trong dd Cj =(aib,)^,C2 =(b2a2)^ la vecta ma tran cot ciia cac sdng
tdi va sdng phan xa tren dau vao va dau ra ciia M4C.
va T =

T
Ml

T

T

la ma tran truyen sdng ciia M4C

thi ta se nhan dugc M2C mdi vdi he sd phan xa P,.
Dac tfnh ciia M2C mdi dugc dac tnmg bdi cac bien mdi aj, bj. Cac

bien aj, bi lai dugc xem nhu la toa do ciia vecta C, cung trong khong gian


nang lugng trang thai tfn hieu. Va trong trudng hgp nay, ma tran truyen
sdng T cia M4C dugc xem nhu toarftir tuyen tfnh trong khong gian sdng
2 chilu, thi6't l|p mdi quan ht giiia cac vecta trang thai tfn hieu tren diu
vao va dau ra ciia M4C.
Trong khong gian sdng trang thai tfn hieu, cong suat tac dung len
diu vao va diu ra ciia M4C dugc xac dinh bdi hieu cua cong suat sdng tdfi
va cong suit sdng phan xa.
P.=a/-b,^

(8)

P,=a,'~b,'

(9)

Cac bieu thiic (8), (9) cd the viet dudi dang bieu thiic ciia cac dang
toan phuang:
Pi =C/JC,

(10)

P2=C2^JC2

(11)

Hay vdi chii y (7), nd se dugc dua ve dang:
P, =C2^(T^JT)C2 (12)

P2=C/(TJT'^)-'C, (13)

Ddi vdi cac M4C tuyen tfnh tich cue, khong tdn hao, co tdn hao,
cong suit tac dung tren diu vao P, tuang iing se nhd han, bing, lan han
cong suat tac dung tren diu ra Pj ciia nd. Nghia la, toan tir T co the la toan
tii gian, Unitar, toan tii co. Tren quan diem toan hgc, ma tran truyen sdng
T CLia M4C khong tdn hao thuc hien phep bien ddi toa do ciia vecta trong
khong gian sdng nang lugng trang thai tfn hieu, nhung khong lam thay
ddi do dai ciia vecta. Cdn trong ky thuat thu va truyen tfn hieu, cac M4C
khong tdn hao dugc diing de phdi hgp cac phan tii (cac khdi chiic nang)
ciia he, dam bao he sd truyen tai cong suit tir ngudn tfn hieu tdi phu tai
dat gia tri Idn va de chgn Igc tfn hieu theo phd tin cua nd.
Phil hgp v6i cac bi^u thiic (10) -H (13), he sd truyen cong suat ciia
mang 4 cue cung dugc viet dudi dang bieu thiic ciia cac dang toan phuang
ciia cimg mot bien ma tran C, hoac C2:
P2.

C2^JC2

C;(TJT-)-'C,

Pi

C2^(T-'JT)C2

Ci^JC,

Bieu thiic (14) cho phep dua viec giai bai toan xay dung he thdng
tuyen tfnh truyin tfn hieu vdi dac tfnh truyen dat tdi uu ve viec giai bai
toan tri rieng ciia cac dang toan phuang trong khong gian sdng nang

lugng trang thai tfn hieu va phan loai cac M4C theo dac tfnh nang lugng
ciia nd.


5.i.3. Mot so kei ludn:
Vdi cac k^t qua nh$n dugc cd the dua ra mot sd ket luan sau day:
1. Khong gian nang lugng trang thai tfn hi6u cua mach dien tuyen
tfnh la mo hinh vki ly thuc cua khong gian tuyen tfnh. Ddi vai M2C thu
dgng, khong gian nang lugng trang thai tfn hieu la khong gian tuyen tfnh
vdi me-tric hypecbol. Trong khong gian binh phuong do dai vecta xac
dinh cong suit tac dung dugc biic xa hoac hap thu cua M2C. Mdi tuang
quan nay cd y nghia quan trgng trong thuc te xay dung he thdng truyen
tfn hieu, vi nd cho phep thiet lap mdi lien he giua viec quay vecta trong
khong gian vai viec bien doi cac mang 2 cue bing cac mang 4 cue khong
tdn hao ma vin dam bao dac tfnh biic xa, hoac hip thu nang lugng ciia nd.
2. Tir viec phan tfch cac toan tir tuyen tfnh trong khong gian nang
lugng trang thai tfn hieu da thiet lap mdi lien he giira viec bien ddi cac
vecta bao toan do dai cua nd vai viec bien ddi cac M2C nhd cac M4C
tuyen tfnh khong tdn hao, va do do co the coi ma tran truyen dat ciia cac
M4C khong tdn hao nhu la ma tran ciia phep bien ddi tuyen tfnh khong
lam thay ddi do dai vecta.
3. Tren ca sd phan tfch cac toan tir trong khong gian nang lugng
trang thai tin hieu da thiet lap dugc bieu thiic ciia he sd truyen dat cong
suit ciia M2C dudi dang cac cap ham ma tran vo hu6ng cua dang toan
phuang chi ciia 1 bien sd. Di6u dd cho phep dua viec giai bai toan xay
dung he thdng truyen tfn hieu vdi dac tfnh truyen dat cong suat cue dai ve
bai toan tri rieng ciia dang toan phuang trong khong gian nang lugng
trang thai tfn hieu. Dieu nay co y nghia thuc te Idn trong linh vuc dien tir
viSn thong,
3.2. Tong hgp cac mach phdi hgp va tdi uu dac tinh truyen dat

cong suat ciia he thdng thu va xir ly tin hieu .
3.2.1. Bdi todn cong sudt cue dai:
Trong kl thuat vi6n thong , khi xay dung he thong thu va xir If tfn
hieu phai dam bao dugc he ssd truyin cong suit cue dai . Dieu nay cd y
ngliTa rat Idn la : trong khi cong suit phat va cau true ciia he thdng anten
khong thay ddi , neu ta nang dugc cong suit thu se lam tang chat lugng va
tang cu ly thong tin . Trong ki thuat rada , nang cao he sd truyen cong
suit se lam tang cu ly phat hien muc tieu , ddng thdi cung tang kha nang
phat hien muc tieu cd dien tfch phan xa nhd .
Giai bai toan cong suit cue dai nay ciia may thu cao tin din den
bai toan phdi hgp giira cac khdi chiic nang ( hoac cac phin tir chiic nang )
ciia tuyen sieu cao tin ciia may thu .
De sang td dieu nay , ta xet mot bai toan dan gian :


Xet viec truyen cong suit tac dung til ngudn tfn hieu cd tdng trd
trong ZQ = Ro + JXQ den phu tai Zt = Rt + jX^. (Xem hinh 4 )

1=^
z„

6

J

Zt

Hinh 4
Cong suit tii ngudn truyen den phu tai dugc xac dinh la :
Pt=PRt

TUT

(15)

sa dd ta cd :
I-

Zo+Z,

(16)

(Ro+RO + J(Xo+XJ

Thay gia tri ciia I tir (16) vao (15) ta cd :
E^R,
(Ro+Rt)'+(Xo+X,)^

(17)

De cong suit tren phu tai dat gia tri Idn n h i t , trudc het miu sd phai
cue tieu ; hay :
(18)

X o + X j =0

Nghia la thanh phin khang ciia tdng trd ngudn va tdng trd phu tai
ddi nhau - Bing nhau ve tri sd nhung ngugc tfnh nhau . Khi dieu kien
(18) dugc thuc hien , ta se co :
E^R

(19)

(Ro + Rt)'
Dao ham bieu thiic (19) theo R, va cho dao ham triet tieu , ta se tim
dugc dieu kien , khi dd cong suit tac dung truyen tir ngudn tfn hieu den
phu tai dat gia tri cue d a i . Dd chfnh la :
RpRo

(20)

Khi dd cong suit cue dai tren phu tai la :
P=P
^ t

=

^ t max

4Ro

(21)

Ket hgp dilu kien (18) vdi dilu kien (20), ta cd ;
P =P
*^t

'

tl

z,-z,

10

4R.

(22)


Trong thuc te , khi xay dung he thdng thu va xir ly tfn hieu , dilu
kien Z, = Z* thudng khong dugc thuc hien , nen ngudi ta phai dung cac
mach (thudng la cac mach khong tdn hao ) mic giua ngudn tfn hieu va
phu tai (hinh 5).

Hinh 5
Cac mach dien nay lam chii:c nang bien ddi tdng trd phu tai thanh
tdng trd cd gia tri mong mudn dam bao cong suit tac dung len phu tai dat
cue dai. Chiing dugc ggi la cac M4C phdi hgp .
Cdn vl mat toan hgc , nhu tfnh toan ly thuyet da chi ra d tren : viec
mic cac phin tir phdi hgp ding tri vdi cac phep bien ddi tuyen tfnh trong
khong gian nang lugng trang thai tin hieu , khong lam thay ddi do dai vec
ta.
3.2.2. Mo hinh tong qudt cua he thong thu vd xii ly tin hieu
He thdng thu va xir ly tin hieu n kenh bat ky dugc mo ta bing mo
hinh tdng quat (hinh 6).

s,

Sx

s,

s„

S2

Hinh 6
Trong dd cac mang nhilu cue loai phan xa S^ dac trung cho khdi
ngudn tfn hieu ; St dac trung cho khdi phu tai ,c6n cac MnC loai true
thong Si,S2, ...Sn dac trung cho cac khdi chiic nang ciia he thdng (phan
kenh, khuech dai ... ) .
Ddi vci he thu va xir ly mot kenh ( he thdng dang dugc sir dung
rong rai) dd la cac M2C va M4C nhu hinh 7 .
p,

p„
Zn

s,

S2

Hinh 7

11

s„

z,

-.^

Trong dd cac M2C dac tnmg cho ngudn tfn hieu va phu tai , tfnh
chit cua nd dugc dac trung bdi he sd phan xa P^, P, hoac tdng trd phiic Z^
va Zt. De he sd truyen dat cong suit tac dung tii ngudn tdi phu tai dat gia
tri Idn nhit , cin phai thuc hien phdi hgp giua cac M2C va M4C , cung
nhu giiia cac M4C . Bai toan phdi hgp gdm 3 loai sau day:
1. Bai toan phdi hgp giira cac M2C
2. Bai toan phdi hgp giira M2C va M4C
3. Bai toan phdi hgp giiia cac M4C vdi nhau .
Xet M4C tuyen tfnh bit ki dugc dac tnmg bing ma tran truyin sdng
IT] nhu hinh 8 . Diu vao va diu ra ciia M4C dugc ndi v6i ngudn tfn hieu
va p hu tai vdi he sd phan xa phiic P^ va P^ tuang iing .
a,—p-

p„

-«—a^

[T]

Pt

^b,

-1—b,

Hinh 8
Theo ket qua tfnh toan (14) da cho ta :

K p , = ^'
PI

C2^JC2

(23)

C2^{T^n)C2

?2 _C,^(TJT-')"'Ci

hoac Kp^^ =

(24)

Bai toan xac dinh dilu kien truyin tai cong suit tac dung cue dai
cua M4C dugc dua vl giai bai toan gia tri rieng ddi vai cac dang toan
phuang tuong img vdi cong suit tac dung tren dau vao va diu ra ciia M4C
trong khong gian trang thai tfn hieu . dilu nay da chiing minh trong 3.1.
Tir If thuyet ma tran , gia tri cue dai ciia bieu thii:c (23) va (24) triing
vdi gia tri rieng ciia cac ma tran dac trung :
Kp=JTJT

(25)

Ka=TJrj

(26)

Dl dang thay ring , cac ma tran J , T^JT , TJT^ la cac ma tran

Hecmit , do dd cac tri rieng Xi {\Xi) cua ma tran dac trung Kp (K^) la sd
thuc . Mot trong cac gia tri dd X\ ([i\) xac dinh he sd truyin cue dai cua
M4C cd the dat dugc khi truyin tfn hieu theo chilu thuan , gia tri cdn lai
^2(1^2) - khi truyin theo chilu ngugc lai.

12


Ivr-

Co the chiing minh dugfc ring gia tri truyen dat cong suat cue dai
cua M4C la khong doi , doi voi cac bien doi khong ton hao . Thuc vay ,
gia sir trfin dSu vao va dau ra cua mang 4 cue T duoc mdc hen thong voi
cac mang 4 cue khdng ton hao Ta, Tp voi cac ma trSn truyen song [Ta] ,
[Tp] (xem hinh 9) . Khi nay , doi v6i he thong truyen tin hieu nay , ma
tran dac trung se co dang :
[T]

[Ta]

[Tp]

Hinh 9

Trong do:

K„ =TJT*J

(27)

Kp=JT-'JT

(28)

T = T,rT^

(29)

Bieu thiic (27) va (28) co the viet lai dudi dang :
K

K,

=T„TT„JT„*T*T:J

(30)

JT;T*T;JT„TTP

(31)

Vi cac ma tran Ta va Tp ciia M4C khong ton hao la gia Unita nen :
TpJT; = J
T:J = JT„-'

(32)

T;JT„=J
JT;=Tp-'j

Cac bieu thiic (30), (31) duoc viet lai :
K,

(33)

K,

Trong dd : Ka=TJT J
Kp=JT^JT
Bieu thiic (33) chiing td cac ma tran K^ , K^ (Kp, Kp) la ddng dang ,
tii:c la cac gia tri rieng ciia chiing la triing nhau .
VI y nghia vat If, dilu nay cd nghia la khi thiet lap cac mach
phdi hgp khong tdn hao vai diu vao va diu ra ciia M4C thi dac tfnh truyin
tai cong suit tac dung cue dai ciia M4C la khong thay ddi; nhung nd cho
phep phdi hgp dugc M4C theo ca diu vao va diu ra . M4C khong ton hao
chfnh la nhung bg bien ddi tdng trd If tudng , bg quay pha If tudng .
13


B6 bien doi tong trd li tudng lam thay ddi mdi tuang quan giira
sdng tdi va sdng phan xa, nhung khong lam thay ddi do dai vecta, do dd
nd xac dinh dugc dilu kien phdi hgp giira ngudn va tai, ciing nhu giira cac
M2C va M4C. Nhu vay he thdng xir ly tfn hieu ed dac trung truyin dat
cue dai hoac dac tfnh tap tdi uu.
Cac bg quay pha If tudng khong lam thay ddi tuang quan sdng tdi
va sdng phan xa. Nghia la khong lam thay ddi ti sd U,hAJ,ap diing de xay
dung he thu va xir ly tfn hieu vdi dac tfnh chgn Igc tdi uu.
3.2.3 Tinh tri rieng vd vec ta rieng cho M4C khong ton hao
Viec tfnh toan cac tham sd ciia M4C khong ton hao (de dat cong
suit truyin dat cue dai) din tdi viec tfnh cac tri rieng va cac ham rieng

ciia ma tran truyin sdng , ma tran tan xa .
Trong he thdng thu tfn hieu (hinh 9) ta thay the cac M2C ngudn va
phu tai bing viec ndi giira ngudn va phu tai v6i cac M4C khong tdn hao
cd cac ma tran tan xa [S„] , [SJ hoac cac ma tran truyin sdngCT^] , [TJ ta
dugc he thdng nhu ( hinh 10 ) .
- ^w

I

1

b, ^

1 b2,

I

1

boo

[SJ
[T.]

[Sn]
[Tn]

0

I

:0

P.

P2
Hinh 10

Ta cd cac ma tran tan xa [S^] va [S,] da dugc tfnh nhu sau :
_p;ej2.p

(34)

[s„]
Pn

[s,

e^"'Vl-|Pt|'

P.

(35)

-P;eJ^'"

eJ""^l-|P,|^

Sir dung moi lien he giua cac phan tu ciia ma tran tan xa S va ma
tran truyen song T cua mang 4 cue , ta se nhan duoc eac ma tran truyen

song [TJ va [T,] tuong iing :
-jip

(36)

[T„]
; i-p„

-?y'
P.e J¥

•jv

[Tj =
^ 1-P,

P,e-J"'

14

(37)


Tiir ly thuyet cua phep bien ddi tuyen tfnh , vec ta C20 =[b20'0r
(hinh 10) cd thi dugc xem nhu vec ta rieng iing v6i gia tri rieng ^1 ciia
phep bien ddi tuyen tfnh x vdi ma tran bien ddi Kp (25) , khi mang 4 cue
da dugc phdi hgp theo diu vao .
Tuang tu , vec ta Cjo =[o,b|of (hinh 10 ) cd the xem nhu vec ta
rieng iing v6i gia tri rieng Hi ciia phep bien ddi tuyen tfnh U vdi ma tran
bien ddi K;' = (TJT''J)"' khi mang 4 cue da dugc phdi hgp theo diu ra ,

Mat khac , td hgp cac ddng toa do ciia tat ca cac vec ta rieng ciia
phep bien ddi tuyen tfnh U v6i ma tran bien ddi A , tuang iing vdfi gia tri
rieng l^ triing vdi td hgp cac nghiem khac khong ciia he phuang trinh
tuyen tfnh tren ; nen cd the viet:
(A-^E)Xo=0
Cu the vai trudng hgp dang xet, ta cd :

Trong dd:

(Kp-^,E)C2=0

(38)

( K ; ' - ^ I E ) C , =0

(39)

(40)

C,-[T;']C,O

C2=[T,]C2o

(41)

va ^i , 10., la gia tri rieng ciia cac ma tran dac trung Kp (25) va Ka (26)
^1 = T ( 1 ^ I I P ~1*^22P + V ( ^ " P "^^22p)

~4K-i2pK2ip)

-~(1*^11P ~1^22P - V ( ^ 1 1 P • ' • ^ 2 2 p )

-4K,2pK2ip)

(42)
1^1 - " ( l ^ l l a ~ 1 ^ 2 2 a + V ( ^ l l a + 1 ^ 2 2 a )

" 41^12a*^21a )

P-I - T ( K i i a - 1 ^ 2 2 a ^ ^ ( ^ I l a + ' * ^ 2 2 a )

"^K,2^^210)

^ l l p - M l 1,1

I-),1 I-,
*21

' ^ l l a ^ Ml '11

M2 M2

1^12p -

M2M1

T22T21

1^^120 -

*llT2l

M2^22

*^21p -

M I M2

^21 ^22

1^21a - T^21 Ml

T22Ti2

22p~M2M2

*22'22

I I 2- I1]
K
^ ^ 2 2 a - ^ I2TM

l-i-iin
^22^22

Dau * bieu thi mdi lien hgp phiic .
Sau khi thiet lap cac ma tran [TJ (36) va [TJ (37) , cac vec ta ma tran C,
(40), Cj (41) thay vao cac bieu thiic (38), (39) va thuc hien mot vai bien
ddi, ta nhan duac :
15

(Kjjp -A,i) + K,2pPto - 0
K21P + (K22P + ^i )Pto - 0
-(K22a+h)PnO+K,2„=0
-(K2,pPno+(Kna-^^i) = 0

Tir cac bieu thiic tren , ta tim duac :
Pfo -(A,,

K],p)K,2p

(43)

Hay
to

• ( X , + K 22P
2 2 J - ' K 2lp

PnO - ( ^ 2 2 0 + ) ^ l )

^12(

(44)

Hay
PnO -(^ila~l^l)1^21a

Trong cac bieu thiic tren P„o va P^gla cac he sd phan xa tuang

duang cua ngudn va phu tai; khi nay he thong s truyen tin hieu (hinh 10 )
cd hhe ssd truyin cong suit cue dai . Dilu nay cd nghia la M4C phdi hgp
hoan toan theo ca diu vao va diu ra .
3.2.4. Mot so kei luan :
1. Dac tfnh truyin dat cong suit cue dai cua M4C tuyen tfnh bit ki
la khong thay ddi ddi vdi cac bien ddi khong tdn hao . Cac gia
tri rieng ciia cac ma tran dac trung M4C chfnh la gia tri cue dai
cua he sd truyin cong suit cua he thdng thu tfn hieu .
2. Cac phan tii ciia ma tran truyin sdng ciia cac mach phdi hgp tren
diu vao va diu ra cua M4C dugc xac dinh nhu ddng toa do ciia
cac vec ta rieng iing v6i cac gia tri rieng ciia cac ma tran dac
trung cua M4C .
3. Tren quan diem toan hgc , viec thiet lap cac mach phdi hgp tren
diu vao va diu ra ciia M4C ( hinh 9) tuang iing vai viec dua cac
dang toan phuang (23), (24) ve true chfnh .
3.3. Mot sd tinh toan va giai phap nang cao do nhay thiet bi thu
tan sd cao,
3.3.1. Tinh cho 1 modun co SF7900 :
Xet mang 4 cue la modun khuech dai trasistor trudng cao tin
SF7900 , tai tin sd 2Ghz . Ma tran tan xa cd ket cau :
0,285eJ"^"

[s]
L^21

'22

2,19e J''"

16

0,086eJ^^"
0,59e-^''"

(45)


Dua vao mdi h^n he giua ma tran tan xa va ma tran truyin sdng cua
M4C , ta xac dinh dugc ma tran truyin sdng T cua modun transistor
SF7900 ling vdi ma tran tan xa S :
0,45662e"-'^^" 0,289406e"J^^"

[T] =

(46)

0,130I369eJ''^" 0,039046^^^'^"

Theo cdng thiic (42) , xac dinh dugc cac gia tri rieng cua ma tran
dac trung M4C:
^,=0,1059

;

>.2=0,014536

(47)

Sir dung cong thiic (43) , (44) tfnh dugc cac gia tri ciia he sd phan
xa cua ngudn vdi tai ding tri:

P„o =0,4969eJ^"'"

va

P^Q =0,69596^'^'"

(48)

Trong mot tfnh toan khac , phan tfch ciu true ciia M4C bat ki ;
chiing ta cd M4C [T] cd gia tri truyin dat cong suit cue dai tuang duang
vai 3 mang 4 cue [T,], [To] , [T2] nhu hinh 11:
[T,]

[T]

[TJ

[To]

Hinh 11
Trong dd : [TQ] la M4C " hat nhan" xac dinh gia tri truyin tai cong
suit cue dai , con cac M4C [TJ va [T2] xac dinh dieu kien phdi hgp ciia
M4C trong he thdng thu tfn hieu .
Cac ma tran truyin sdng tuang iing vdi 3 mang 4 cue nay la :
[T,l

e

il-|P„ol

lx.1

-J9

P

(49)

p ' p-"*^

V^

0

0

JA.

(50)

-JV

[T.] =
V I - | P :to

e'J'''

L

Ptoe

JM'

P pJ'''

(51)

Ap dung cu the cho trudng hgp nay , ta cd :

17

0 A I H O C Q U 6 > GIA H4 i-M,
TRUNG TAM THONG T\i-i TH. r v/.

D/ /5-61)


-J(P

[T,]=

0,49696^^2'^''-'''''

1,152

(52)

0,4969e"J*-"'""^'
0.32452
0

0

(53)

0.12050

0.6959e

[ T . ] ^ 1,3924
0.6959e

.4^.3'-V)

(54)

.|{-»''"'.3 - V )

Nhu vay , vai cac tham sd ciia ma tran [S] biet truac ciia M4C bat
ki , chiing ta cd the tfnh dugc cac tham sd ciia cac M4C phdi hgp dl dat
dugc cong suit truyen dat cue dai .
3.3.2. Tong hgp cdc mach phoi hgp detoi itii hod cong sudt
truyen dat vd tdng do nhay cua he thong thu tin hieu cao tdn .
Bai loan dat ra la budc cudi cimg . ta phai tfnh dugc cac tham sd vat
ly ciia mach phdi hgp dl dai dugc cong suat cue dai ciui ca he ihdng ihu
tin hieu . Ve nguyen tic . mach phdi hgp cang dan gian . cang ft phan lir.
cang lot . Dac biet la vdi dai song sieu cao tan .
Trong mot cong trinh khac . chung toi da chirng minh dugc rang :
-

Khi phdi hgp cac much 3 phan tir ( hinh T hoac hinh 11 } . neu

chgn cac tham sd pha cp , \\f khac nhau thi gia tri cac tham sd
vat li ciia mach phdi hgp cung nhu tfnh chat ciia chiing sc
khac nhau .

-

Sir dung cac mach phdi hgp 3 phan tir cho phep thuc hien \ ice
tdi uu hoa dac tuyen truyen dat cong suai ciia he thdng trii\cn
tfn l-iieu . Dieu khien dugc dac tuyen bien do tan sd . pha tan
sdciia he thdng .

-

Neu sir dung cac mach phdi hgp 2 phan tir khong the tdi uu
hoa dac tuyen truyen dat ciui he thdng . Hcyn the nCra . cac
mach phdi hgp 2 phan lir chi co the sir dung lam mach phdi
hgp trong ciic dieu kien xac dinh .

Vdi modun khuech dai ciia (3.3.1) chiing ta da tfnh dugc cac tham
s d c a ban . (hinh 12)
_/' _ ^_______,,

,

,
A,

T

Hinh 12

Y2„=-jHp-'[sin(Y + (p)-|Pn|sin(Y + G.+(p)]
Z.. =

H[cos(Y + (p) + |Pjcos(y + 9, +(p)]-l

(55)
(56)

^H,[cos(a-(p)-|Pjcos(a-e,-(p)]-l
Y.

Y:3=-jQ,p"'[sin(v' + M')-|P.|sin(v' + e,+v|;)]

(58)

Q[cos(v-vi;)-|P lcos(v-0, - v|y)J-l
7

=

(59)

Y„
Qi [cos(\'' + v|j) + jP, [cos(v' + 9-, + \\i)\-

y7„

(60)

Trong do cac gia tri : H , H, . Q, Q, ,a . y . v , v' la cac gia tri diroc
tinh theo cac cong thiic sau day :
P„„cosO+P„„

U

(61)

(i-ii',„r)(i-ip„r)
i i + 2 l P „ cosO+ P

(62)

\ (i-ip„orKi-ip„i")
1 + : P , „ COS(3 4- P,

0

(63)

\ (l-jp,J")(J~lp,i")
l-2|P,„|cos(l + |P„

\ (i-iPnlHl

(64)

IP,!")

ll',JsinO

y = arctg—

(65)

l-|P„„!cosO
|P„„JMnO

a - arcli!

|P.„jsinP
V = arctu

l + [P,„|cosP
P.JsinP

\' = arctu

(66)

(67)

(68)

Ncii chon mach phoi hop hinh T va chon cac ihani so jiha (p=vj/=90
ta SC xac dinh diroc ;


C,a=7,32.10-''F

;

C,a=l,76.10-^'F

;

L.„=2,22.10-^H
'2a"

C,p=19,85.10-'-F

;

^^=1,26.10'-?

;

L2(3=2,67.10-^H

Lap trinh cho cac tham sd (p va y cac gia tri khac nhau , tii dd tinh
dugc cac gia tri tham sd vat If ciia cac phan tir ciia mach phdi hgp . Ta cd
bang ket qua sau day :
Bang 1. Mach phdi hgp hinh T
9

V

Mach phdi hgp tren dau vao
Ket cau

Giii tri tham sd

C, = 1.1.10'-

145*'

Mach phdi hgp tren dau ra
Ket cau

0

CfiV

Gia tri tham
sd^
L| = 1,2.10"

L, = 2,6.10'

L, = 3,0.10-"

20"

C.= 1.2.10'-

L, = 3.1.10'"

147"

C, = 1.1.10'=

L, = 1,2.10"

L, = 2.7.i()-"

^ = 2,7.10"

28'

C,= 1.2.10"

C, = 2,3.10"

149"

C, = 1.0.10'-

L| = 1,2.10"

L: = 2.8.10"

L, = 2,5.10"

C. = 1.2.10' =

C. = 7,8.10'^

C,-9.6.10"

L| = 1.1.10"

L, = 2.9.10"

L, = 2.4.10"

C= 1.1.10' =

C, = 4.7.10'=

36"

.SI" I -"
45"

51.

20


Cl

C:
II
II

II
II

153"

,

>L2

53"

0—

156" ^ h

0

C, = 9,1.10"

0

CTfL

L, =9,6.10'"

L2 = 3,0.10"

L2 = 2,3.10"

C, = 1,1.10"

Q = 3,4.10"

C, = 8,5.10

13

L, = 7,8.10

-i()

L2 = 3,1.10"

L. = 2,3.10"

61"

C.= 1.0.10'=

C, = 2,1.10'=

158"

C, = 8.0.10'-

L, = 5.5.10 Id
L, = 2,3.10"

L, = 3.2.10"
70"

C,= 1.0.10'=

160"

C, = 7.5.10

5

C, = 2,1.10'=

-•

L, = 2,5.10'"

L, = 3.4.10"

j L, = 2.4.10"

78"

C = 9.7.10"

, ' C-, = 1.7.10'=

162"

C, = 7.0.10"

C, =4.7.10"

L, = 3.6.10"

L, = 2.6.10"

86"

C, = 9.2.10'=

C,= l,4.10-'=

cii

C, = 6.5.10"

C, = 9.9.10'=

L: = 3.8.10"

L, = 2.8.10"

C, = 8.8.10'=

C-,= 1.1.10'=

165
C'l

95

21


Bang 2. Mach phdi hgp hinh 11

Mach Igc phdi hgp dau ra ap

Mach Igc phdi hgp dau vao a^

9

Kit ca'u mach
loc phdi hgp
145"

0

20"

.

,

Gia tri phan tir

C, = 5,2.10"
L. = 2.4.10'"
C, = 5.6.10'"

0

AVI

T-

Ke't cau mach
loc phdi hgp

I

L, = 1,6.10"
L , = 1,7.10"
L-, = 4.0.10"

i-

i-

Gia tri tham so

•

C, = 3.2.10"
L, = 3,9.10'"
C, = 3.5.10"

i_

147"
28"
!

•

^

C, = 2.3.10"
L, = 5.4.10'"
C, = 2.6.10"

149"
T "
i

36"
1 i: |t>

151

•: '^^ [

=
1

1

45" !

T ""
1

C, = 1.8.10"
L, = 6.9.10-'"
C, = 2,1.10"

^

[

f ^

T ••

V1

1

.

1

=

1

^: .
II

1

=

,
>

•

•

C, = 7,8.10'L, = 8,4.10'"
L , = 1,8.10"
L, = 5.2.10"
C, = 2,4.10'"
r , = 5 6 10'"
L, = 5.2.10"
C, = 2.4.10'"
C^ = 5.6.10'"

—

1
15.3"

C, = 1.5.10"
L, = 8.4.10'"
C,= 1.8.10"

3

5.3"
1

C, = 1.3.10"
L, = 9.9.10'"
C,= 1.5.10"

iTy-ll

i 156
^

±

•,

61"

C, = 1.1.10"
L, = 1.1.10"
C,= 1.4.10"

1 CO*'

1-^8
70"

1
J-

••'•

i
-1- 1

160" ! '

—""--1

J_ ...

-L .

C, =9.6.10'=
L,= 1.1.10"
C,= 1.2.10"

=

78" i
^

1

C| = 8.5.10'=
L , = 1.4.10'"
C , = 1.1.10"

162"
86"

-

-

•

=

* .

i

c''

-

L, = 2.4.10"
C, = 2.5.10'=
C = 8.6.10'''

7

L, =5.5.10'"
C = 1.9.10'=
C-, = 4.6.10"

~^

L, = 2.5.10"
C,= 1.6.10'=
C-= 1.7.10"

:^

{•-•-

L, = 2.5.10"
C = 1.4.10"
L-, = 8.7.10'

j

165"
95"

:

€, = 2.1.10"
L, = 3.7.10'=
C,= 1.5.10'=

=

C, = 7.7.10'L , - 1.6.10"
C - 1.0.10"

11

:

:

L, = 2.5.10"
C, = 3.1.10'=
L; = 2.2.10'

^

4. K E T LUAN

De tai QT-05-11 da giai quyet dugc cac va'n de sau :
1. xay dung bai toan tdi uu truyen nang lugng trong khong gian sdng
cao tan : Bai toan nang lugng tdi uu dugc quy ve bai toan tfnh tri
rieng cua dang toan phuang trong khong gian nang lugng trang thai
tin hieu .
2. Tdng hgp cac mach phdi hgp va tdi uu dac tfnh truyen dat cong suat
ciia he thdng thu va xir If tfn hieu : Bai toan tdi uu cong suat trong he
thdng thu tfn hieu chfnh la bai toan phdi hgp giua cac M4C vai nhau .
M2C va M4C , M2C vdi nhau di khong cd tdn hao d dau vao va dau
ra , nhirng dat cong suat tac dung cue dai . Cac M4C khong tdn hao
dat dugc cac yeu cau tren la M4C khong tdn hao gdm bg bien ddi
tdng trd h' tudng , bg quay pha va bg bien ddi tdng trd If tudng .
Tliam sd ciia M4C nay dugc tfnh qua cac gia tri rieng va vec ta rieng
3. Mot sd tfnh toan va giai phap nang cao dg nhay thiet bi thu sieu cao
tan : Tir cac tham sd ciia 1 modul cu the cd the xay dimg dugc cac
M4C phdi hgp khong tdn hao gdm 3 phan tir de nang cao do nhay va
cong suat ciia he thdng thu va xir If tin hieu .

5. Tai lieu tham khao.
[I]. Vu Thanh Thai va cac tac gia - Tdi uu hoa qua tiinh truyen
nang luang tfn hieu dien trong mach dien tuyen tfnh va trong
khong gian . De tai TN 03-05 - DHKHTN nam 2004
[2]. Dd Huy Giac . Vu Thanh Thai - Khong gian nang hrang trang
thai tfn hieu ciia mach dien tuyen tfnh va cac dac trung co" ban

ciia no .- Tap chi khoa hgc va cong nghe ( Tap XXXVl . 1 .
1998 )
*
|3].Dd Huy Giac , Vu Thanh Thai - Khong gian nang lugng song
trang thai tin hieu ciia mach dien tuyen tfnh va cac dac tfnh co'
biin ciia nd .- Tap chi khoa hgc va cong nghe (Tap XXXVIl. 6
.1999).

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