Nghiên cứu xử lý tín hiệu nhỏ phục vụ đo lường

DAI HOC QUOC
GIA
HA
NOI
TRITCING
DAI HOC KHOA HOC
TU^NHIEN
DE
TAI
:
NGHIEN
Ciru Xir
LY TIN
HIEU
NHO
PHUC Vy
DO
LUCING
MA SO: QT-06-45
CHU TRl
DE TAI : PGS. TS.
PHAM QLOC TRIEL
CAC
CAN
BO
THAM
GIA: ThS. Nguyen Anh
Due
HVCH.
N"uv6n
Huu

Lam
JA^I
HOC
UUOC
GlA
r^
NO;
n^
jNG
TAM
THONG
TIN THUVIEN
^VML
HA NOI - 2006
BAO CAO TOM TAT
De
tai;
NGHIEN
CUtf
XL^
LY TIN HIEU NHO PHUC VU DO
LUONG
Ma so: QT-06-45
CHU
TRI
DE TAI PGS. TS. PHAM QUOC
TRIEU
CAN
BO
THAM GIA: ThS. Nguyen Anh Due

HVCH.
Nguyen
Huu Lam
Muc
tieu
nghicn ciiu
- Nghien
cuu
cac
phuong
phap xu
ly
tin
hieu
nho, lay
vf
du tin
hieu
DLTS
ling dung vao do
luang
cac
dai lugng
vat ly, nhan manh phuang phap
Fourier, Tach song dong bo. Boxcar va Lock-in.
- Nghien cuu van
di
tang cuang
tin
hieu dong

ihoi giiim thieu
tap
nhieu
-
Tdng
hap.
khai
quat ly thuyet va ap dung thuc te
Noi dung nghien
ciiu
- Tong quan
ly
thuyet ve mot so
phirang
phap xu ly
tin hieu
DLTS
- Nghien cuu cac
guii
phap nang cao chat luang do tin hieu nho
- Nghien
cuii
cac
hieu li'ng lien
quan den xu ly tin
hieu
- Dinh
huong
xay dung phep do
-

Hudng dSn
Luan van cao hoc va viet bai bao khoa hoc
Cac ket qua dat
diroc
- Nghien cuu
tinh
chat
ciia
tin hieu nho tren ca sa moi tuang quan giua tin hieu
va tap
nhi^u
tac dong vao he do vat ly.
- Nghien cuu tap hop va khai quat boa mot so phuang phap xu ly tin hieu nho
nhu phuang phap Fourier, phuang phap Tach song dong bo, phuang phap
Boxcar, phuang phap Lock-in. Tin hieu nho duac dan chung
la
tin hieu
DLTS.
Tuy
nhien,
hoan toan c6
the
su dung cac phuang phap noi tren
dd
do
dac,
xu ly cac
tin
hieu nho khac trong he do.
- Huang

dSn
01 Luan van cao hoc theo huang
d6
tai. Ket qua
ciia
Luan van:
Thiet ke xay dung thanh cong bo khuech dai lock-in so hai pha bang phan
mem Labview (two-phase lock-in amplifier) ung dung trong nghien cuu va
dao tao tai Khoa Vat ly.
- Viet
01
bai bao khoa hoc ve cac phuong phap xu ly tin hieu nho ung dung
trong do luang DLTS.
Tinh hinh
sii
dung kinh phi
-
Kinh
phi duac cap: 20.000.000 d
-
Kinh
phi da quyet toan: 20.000.000 d
KHOA QUAN LY
(Kv va "hi
rd
ho ten
CHU TRI DE
TAI
(Ky va ghi ro ho
ten

XAC NHAN
CLA
NHA TRtONG
S.TS.^W^/J^
\y^/rh/(^^juci,
fotui/'
BRIEF REPORT
Project title:
STUDY ON TREATMENT WEEK SIGNAL FOR IMPROVING
MEASURED SYSTEMS
Project code: QT-06-45
COORDINATOR: ASSOC. PROF. DR. PHAM QUOC TRIEU
KEY IMPLEMENTORS: MSc. Nguyen Anh Due
Nguyen Huu Lam
Project purpose
- Study on signal transformation methods for applicadon in measurement
the physical quantities, focusing on methods for week signal processing
such as Fourier. Synch Rectifier, Boxcar. Lock-in.
- Study on problems of increase signals and decreace the noises
- Summarise the theories in order to apply
into
measued systems
Project content
- Review of the theories for the week signal proccessing (for example
DLTS signal)
- Study of the methods for improvement of the measured quality
- Study of the effects concerning the signal proccessing
- Orientate to build measured systems of MSc Thesis
-
Full fill

the contains of the scientific article.
Project results
-
01
research paper
- 01 MSc Thesis of
N^uven
Anh
Due
(2006).
MUC LUC
• •
Trang
Madau
2
CFIUDNG L
TIN HIEU
DLTS
TRONG
By\N
DAN
^
LI Tin
hieu nho DLTS
3
1.2 Xac dinh mot so thong so
\\i
tin hieu nho DLTS
4
1.2T

Xac dinh nong do muc
Np
4
1.2.2
Xac dinh tiet
dicn
bat 5
1.2.3 Xac dinh
miic
sau 5
CHUDNG
2- CAC PHUONG
PHy\P
XU' LY TIN
HIEU
DLTS 6
2.1 Phuang phap Fourier 6
2.1.1
Co
soTy thuyet 6
2.1.2
Tinh
Uu
viel ciia phucmg
phap 7
2.1.3 So do
khoi
va
nguyen
tac boat dong 8

2.2 Phuo'ng phap dich cu'a 9
2.2.1
Casaly
thuyet 9
2.2.2.
Uu nhuoc
diem
ciia
phuong phap dich cu'a 9
2.3.
Phuong phap tach song dong bo A
-
B
10
2.4. Phuo'ng phap Boxcar
j I
2.4.1.
Casaly
thuyet
I j
2.4.2 Sa do khoi
chii'c
nang ,
r
CHUONG
3-
PFIUONG PHy\P
KHUECH DAI LOCK-IN 17
3.1 Gioi thieu chung
17

3.2 Cac khai niem
co"
ban 17
3.3 Bo phat hien nhay pha (Phase-sensitive
deicclion)
22
3.3.1 Gioi
thieu
22
3.3.2 Nguyen ly boat dong 22
3.3.3 Cac khai niem lien quan den
bp
PSD 26
3.4 Khuech dai lock-in hai pha
(fwo-phase
Lock-in amplifier) 27
3.5 Cac nguon nhieu 28
Ket luan 33
MODAU
Trong thuc nghiem vat
ly,
phep do tin hieu nho la mot thach thuc thudng xuyen
doi
vdi ngudi
nghien cuu. So
dT
nhu vay
la
bai vi
tin

hieu nho khong phai la
tin
hieu
CO
gia tri tuyet doi nho (bien do nho, dien ap nho, cuang do nho, cong suat nho ).
Tin
hieu duac coi
la
nho khi ta xet tuang quan giua tin hieu can do vai tap nhieu di
kem theo no. Nhu vay, do
tin
hieu nho c6
nghla
la xac dinh gia tri va quy
luat ciia tin
hieu tren nen tap nhieu. Neu nen tap nhieu rat
Ian ihi tin
hieu c6 gia tri tuyet doi Ian
cung tra thanh tin hieu nho. Nguac
lai,
neu nen tap nhieu nho thi dii
tin
hieu c6 gia
tri tuyet doi rat nho cung
dugfc
goi la tin hieu
Ion.
Tuu trung lai, nhiem vu
ciia
nguai lam thi nghiem do dac cac tin hieu nho la phai

loai
bo, boc tach toi da anh huang
ciia
tap nhieu vao
tin
hieu do, phat hien ro rang
nhat tin hieu vat ly
c^n
quan tam.
De tai nay nghien cuu ve mot so phuang phap
xii'
ly
tin
hieu nho trong phep do
dai luang dien nhu phuo'ng phap Fourier, phuong phap tach song dong bo, phuang
phap
Boxcar,
phuang phap Lock-in. Day
chi
la mot so phuo'ng phap thong
dung,
mot
so cong doan trong qua trinh het
sue
da dang, phong
phii
cua thuc nghiem vat ly.
Tuy nhien
chiing
cung

gop
phan tao ra nhieu cong trinh khoa hoc co gia tri.
nhieu he do gia tri cao tren the gioi cung nhu
o
Viet nam. Nam vu'ng nguyen ly va
giai phap thuc hien cac phuang phap nay co
the giup
cac nha thuc nghiem trong
nghien cuu doi
tugng
quan tarn cua minh.
Bao cao
j^om
3 chuo'n
Chuangl trinh bay ve mot loai tin hieu nho dien hinh trong nghien cuu vat ly ban
ddn:
tin hieu qua do
ciia
cac tam sau (DLTS). Xu ly tot tin hieu nay ta co the' nhan
duac nhieu thong tin
v^
cac tam sau trong chat ban
d5n,
anh huang
ciia
no tai chat
luang
linh
kien ban dan.
Chuong

2 trinh bay ve cac phuo'ng phap xu ly tin
hieu
nho DLTS. Chuong nay
chii
yeu dua ra cac nguyen ly va
each
thuc hien
de
co
the xan
dung vao cac he do tin
hieu nho khac.
Chuong 3 trinh bay ve phuang phap Lock-in
xii'
ly
tin hieu nho rat hieu qua trong
cac phep do thuc nghiem
vdi
nguyen ly va each ap dung do tin hieu nho.
Hy vong
rang,
nhieu nguyen ly do,
nhi(!u
giai phap thuc nghiem nham nang cao
chat luang phep do se duac nghien cuu tiep
luc irong
thoi
^ian
tai.
CHUONG 1

TIN HIEU DLTS TRONG BAN DAN
1.1
Tin
hieu nho DLTS
Khi bi kich thich ( do nhiet, dien hoac quang) tam sau bi lap
d^y
dien tu va se
tra
lai
trang thai diing neu
ngiang
kich thich.
So
dien tu tren cac lam sau bi thay doi
trong qua trinh chuyen tiep va duac bieu
diln
bang phuo'ng trinh sau:
dn,
_
dp
dt
If
dn
dl
(Cp-k,
)(Nr-n,)-(e,
+
k,J.nT
( I.I )
Trong do: n, p la nong do dien

tii*
va
16
trong
Cp,
e„
:
la
toe
dp
phat hat tai bang nhiet tuong ung vai
16
trong
\a
dien
tii.
kp
,
kn
la cac hang so lien quan den ban chat dan dien.
Nj
la nong dp tam.
Co the thay doi dp lap day dien
tii'
ciia
tam sau bang chuyen tiep P - N hoac
bang hang rao Schottky.
Gia su
CO
mot

lo'p
chuyen tiep
N'-
P hoac diod Schottky loai P co tam sau nam
a niia duoi
\'ung cam. Hay vo'i chuyen tiep
P"^
- N hoac diod Schottky
loai
N co tam
sau nam
a nii'a
tren vung cam. Dien dung tren mot don vi dien tich 16p ngan la;
C-
—
\
(1.2)
2(r,
±V)
'
Trong do
V^^
la the khuech tan.
±
V
tuong ung la the phan cue nguac va thuan.
N,
la n6niz
d6 ion trong lop ngan.
N,=

(N^+N-,)-n-,
^ ^ _ _
(1.3)
Tir cong
thiic
(1.2) va
(1.3)
ta thay dien dung cua lop chuyen tiep
the
hien
miic
dp lap day dien tu
ciia
tam sau.
Neu
e^
»ep do la truang hop tam sau bat dien tu thi cong thuc
(1.1)
tra thanh
dn
dl
n,(
e„
-
nCj +
Nr.n.Cn,
(1.4)
Truang hop phan
cue
thuan cho chuyen tiep. Nong dp dien tu trong

mii^n
chuven
tiep cao. n ti
le
\(i\
N^^
\a e„
« n.Cn
thi
(1.4) se la:
N,
-n-,-(t)-
jN,
n^(0))
exp(
-n.C,.t)
Khi t
—•x
thi
np(t)—•Nj.
Tat ca cac tam deu bat dien tu.
Truang hop phan
cue nguoc
lap chuyen tiep. Cac hat tai dien bi
diy
khoi lap
ngan. Khi do
c^»x\.C^
, dien
tii'

duge
giai phong khoi tam sau.
Ta
CO
np=N-|-
e\p(
-e,^.T
).
C(t)-
qX^'.^^'i)
S
A-,
+
A
,
-exp(-c^^/)
2(f^.+rj
Trong
truc^ng
hop
NY«N^
CO dang gan
diing
(1.5)
C(t)=
?>(^,;+'V,y
_ 2{V,+V,<)
_
C(t)
=Cf

-
C,exp(-e„t)
1 —exp{-ej)
2.V„
Trong do:
C,
=
C
= C
^
2{K,+y.,)
i
~
^t
2A'
(1.6)
(1.7)
(1.8)
(1.9)
Vay trong duang dien dung qua dp C(t) mang
ddy dii
cac thong so ca ban
ciia
tam sau nhu: n6ng dp muc
Nj,
tiet
dien bat dien
tii
a,^
, nang luang tam E, ,

toe
dp
phat xa nhiet
c^.
1.2 Xac dinh mot
so
thong so
tu
tin hieu nho DLTS.
1.2.1 Xac dinh nong dp
miic
Nj.
Trong truang hop dien dung thay doi nho do qua trinh lap
d^y
hoan toan tam
bat
N[
trong vung ngheo va dp pha tap la deu theo kh6ng gian vai ban dan loai N ta
co:
N,=2(N,-N,).
\(
C la dien dung lop ngheo.
Neu tap phan bo khong dong nhat trong kh6ng gian thi nong dp tam sau duac
tinh theo cong thuc chinh xac
hon
la:
AC
<>( ) =
AC
Tron>i

do
di
—
)
la su thay d6i tuong doi cua dien
duniz
tam bat
uav
ra do su thav
('
•
•
^ - .
.
.
doi nho
the d
V
ciia
xung phan
cue
V ung vai dp rpng vung ngheo x.
N^
la nong dp tam nong.
Vav tu do thi AC va V ta co the tinh ra
noni^
d6 tam sau.
1.2.2 Xac dinh tiet dien bat.
Tu su phu thupc
ciia

dien dung theo thai gian ta
tinh
tiet dien
bdt
:
e^^cr,,
.0',
.n
doi
\oi
hat tai
co'
ban. Phuong phap
na>
cho ket qua chinh xac ma don
gian.
Doi voi qua trinh
bai
hat tai khong co' ban
ihi phiic
tap vi no phu thuoc vao co
che tiem.
De
xac dinh tiet dien bat
nguoi
ta con co
each
khac la tinh tu toe dp phat xa
trong vung ngheo
e,^

MVN^expt-^'^
kT
(1.10)
Gia tri
eiia
tiet dien bat xac dinh bang phuong phap nay cao han mot bac so
vai phuang phap quang. Dieu nay co the do cac qua trinh bat xay ra trong mot dien
truang manh
ciia
chuyen tiep.
1.2.3 Xac dinh
mure
sau.
TCr
phep do
miic
dp phat xa nhiet
e^,
ciia
hat tai ta co the xac dinh
miic
sau.
Thiet
lap
do thi In
(ej
phu thupc
I/T.
Dp
nghieng ciia

duang phu thupc chinh
la nang lugng kich boat phat hat lai.
Tuy nhien nang lugng kich boat khong phai
liic
nao cung triing vai nang lugng
do duge.
Di^u
nay co
the
do cac nguyen nhan sau:
1/
Trong c6ng thuc (1.12) phan truac
ciia
ham exp phu thupc nhiet dp.
-Tiet dien bat
a ,
phu thuoc vao nhiet do
thuanu
la
khoniz biel
truoc.
-Thanh phan
(r,,
A;
phu thupc bac 2
ciia
nhiet dp
(-
J-}.
2/

Su phu thupc vao nhiet dp la khac nhau do co'
che
bat hat tai khac nhau. De hieu
chinh su anh huong
ciia
nhiet dp trong
tinh
toan co may each sau day:
- Hieu chinh theo cac phu thupc manh trong nhu'ng khoang nhiet dp nhat dinh.
-Phu thuoc
'/r,,A -
T"
hieu chinh tir
2kT ciia do
thi
ln(eJ\aT.
CHUONG
2
CAC PHUONG PHAP
XLTLY
TIN HIEU DLTS
2.1
Phuomg
phap Fourier.
2.1.1
Casaly
thuyet.
Phuang phap qua dp tam sau Fourier
duge
xay dung voi

su
so hoa dien dung,
thai gian qua
do va
xac dinh
he
so roi
rac
Fourier. Ket qua
do
duge dieu khien
tu
dong cho dp chinh xac cao. Phuang phap nay g6m
4
dac trung co ban sau:
1-
Dat
N gia tri do
lam
mSu
tu
pho dien dung qua dp. Khai trien theo chu6i
Fourier de tim
ra
cac he so roi rac.
2-
Tinh
duge
true tiep tren ph6 qua
dp

hangd
so
tho
gian
r va
bien
dp
phd
bang moi lien he giua cac
he
so Fourier.
3-
Di^u
chinh dp rpng chu ky
T,
de dang doi voi cac nhiet dp khac nhau. Dac
biet han
che
nhieu tot.
4-
Loai nhieu
tot
bang
each
phan
lich
qua dp dien dung theo cac he so Fourier.
Thuc
te
cho ket qua chinh xac

thuong
duac tinh toan doi vai cac
he so
a nhiJng
bac
dau tien.
Phuang phap qua
dp
tam
sau
Fourier
vdn
dua tren moi tuang quan giua
cac
thong
so ban
dSn
nhu trong c6ng thuc (1.10)
va
(1.12). Tuy nhien duge phan tich
duoi dang chu6i Fourier.
f(t)='-^
- ^./,
cos(noji)
^
J^h
sminfot]
(2.1)
Vai
CO

^ ^
(2.2)
/;.
— la do bu dien dung.
2
• •
T,,,
la do rpng chu
ky
\a
co c6ng
thiic
T,=N.
A/
(2.3)
A/
la
m^u
thai gian
nghi,
N
la
so khoang thoi gian
nghi.
TCr cac
he so
Fourier
ta
tinh duge bien
dp

ph6
suy ra
tinh
duge
nong
d6
tam
sau.
A=^h^
exp
+
n'co'
1
-
-
^^p\
-
V
T ]]
- —
T
J]
(2.4)
nco
Va
h^ng
so thai gian co cong thiic:
"^/r ••
cf,
-a,

7',,
]l
k^a^
-
n'ci^
:.T
Z;
\lk~h,.
-
n'h
ZTTH
r
net.
(2.5a)
(2.5b)
(2.5c)
Tuy nhien doi vai cac he so bac cao thi ket qua tinh loan kem chinh xac ban
cac he so bac thap vi khi khai trien 6
tin
so cao theo chuoi Fourier thi mot vai cap
dau la chong kbit con cac cap bac cao hon se bi
sai
lech.
Sii'
dung phuong phap nay tin
hieu
qua dp dien dung
a
m6i nhiet dp
duge

ghi
nhan rat nhieu
giii
tri (
N-512.
1024, )trong khoang thoi gian
T,,
bang pho
ki
thuat
so.
Vi \ay
CO
N cap gia
Iri
r va
l
nen co
the
ap dung
luy \
cac phuong phap de
tinh cac thong so tam sau. Song
sii"
dung phuo'ng phap nay cac thong so ban dan duge
rut ra true tiep tu cac he so Fourier th6ng qua cac
dinh ciia
chiing.
2,1.2
Tinh uu viet

ciia
phuong phap
.
1.
Cho ket qua chinh xac ma chi can quel nhiet mot
hln,
con doi
vc'^i
cac phuang
phap khac thi phai quel nhiet hoac do it nhat la nam
Ian
moi danh gia duge ket qua.
2.
Toe
dp
xii
ly nhanh, dp nhay cao. sai so nho.
3.
Tinh toan dp bu dien dung — tu dong trong khi neu
sii'
dung phuang phap khac
thi phai thuc hien
thii
c6ng.
4.
So hod va tu dong
luu
iru'
cac so lieu.
5.

Kha nang loai nhieu cao.
6. Dt dieu chinh
b^ng
cac th6ng so nhu bien dp, dp rpng chu ky.
7.
Van hanh dan gian.
Son"
CO
han che la chi
dumz
duoc
trons
he do tu
d6n^.
7
2.1.3
Sa do khoi va nguyen tac hoat dong.
•
So
do khoi:
Mdudo
Dat nhiet
do
A
-^-
Chua
Ket thuc
phep do
Roi
^

Birdc
nhu\
0.5K
/\
The
xunu.
Nhiet do ket
(hue
chua ?
A
Khoiif.
Co
BucVc iihav
2K
•>
Nhom c() \ac
Do
dicndung
}.L
Danh
gui
nhom qua do
Hinh 2.1
S(J
do
klioi ehde
ndn^^
ei'ui
phiiwv^
phap do

cpid
do tam
sdii
Fourier.
• Nguyen
tie
hoat dong:
Dal
mSu
do vao trong buong
miu,
buong
m5u duge hiit
chan khong thong qua
may bom, sau do dat gioi ban nhiet dp cho phep do. Tac dung xung vao
mSu
do. Co
the
la xung anh sang hoac the xung. Cho qua thiet bi do dien
dung,
diing
ph6
ki
thuat
so ghi nhan va \ e d6 thi pho.
May tu dong khai trien pho dien dung theo chu6i Fourier roi tinh ra cac he so
de tii do danh gia nhom qua dp.
Neu nhom qua dp da xac dinh thi
buoc
nhay nhiet dp la 0.5K. con kh6ng xac

dinh thi buoc nhay la 2K. Qua trinh tiep luc cho den khi nhiet dp dat toi giai ban,
con khong phep do lap lai.
2.2 Phirang phap dich
cura.
2.2.1
Casaly
thuyet.
De xac dinh cac thong so'
ciia
lam sau tu duang qua dp dien dung
C(t)
= Qj.exp
(-e^t)
ta xet tai 2 thai diem
tj
va
l.^r.t,
vai
r=2.3,
Ta co:
AC
= C(/,)
-
C(i,) =
Q[exp(-
e,/,)
-
exp(-
ej'l,)]
(2.6)

Cho
t|
tang dan thi AC dat
cue
dai
a
thai diem
t,,,,
nao do.
Dt
xac dinh t
^,,
tii
dieu kien:
dAC ^ ^
ln(r)
,0-7,
=
0 Suy ra
i ^
(2.7)
dl
"""
(/•
-
1).L:^
Do
vay
e =
'I'iLL.

(2.8)
'
V -
1)./,,,,,
Vay tai mot nhiet dp T nao do. dung phuong phap dich
tj
la co duang qua dp
C(t) ma
cue
dai
ciia
no cho ta tinh duge
e,^.
Biet cap th6ng so
(e,,.
T) thi se xac dinh
duge
E]^
va
a,^
trong he do tu dong. duang C(t) duge ghi tu dong tai m thai diem khac
T
nhau m6t
each
gian doan theo
thai
gian
t,
voi t
=

CS.At,
CS =
l,2,3 m
va A/
^ -^,
m
Tgla
thai gian do dien dung qua dp.
May tinh se tu dong tinh hieu AC - C(t) - C(r.l)
a
nhu'ng thoi diem t lien tiep
nhau de ve
len
d6 thi su phu thupc C(t) tai vai
gia Iri
nhiet dp khac nhau.
Gpi phuang phap dich
ciia
la do viec quet thoi gian
duge
thuc
hien
nha may
tinh
b^ng
each dich dan cac
cii'a
Sampling.
2.2.2.
iTu

nhugc diem
ciia
phuong phap dich cua.
-
Xii
ly ket qua tu dong, tinh toan chinh xac. nhanh chong, do tin cay cao.
- Tranh sai so dpc trong trong vice xac dinh cac gia tri thai gian
ciia
c6ng Boxcar tai
cac dinh pho
(t^.^J.
- De xac dinh nang lugng
ciia
mot tam chi can ghi duang C(t) tai 4 den 5 nhiet dp
khac nhau. Yeu
cfiu
so file kh6ng nhieu.
-
Khi do nhiet dp thi dp on dinh va tinh chinh xac doi hoi rat cao.
- Trong qua trinh do chi thay doi nhiet dp mot
Ian.
- Chi ap dung tren he do tu dong.
- Pho (L6) gian doan theo
thdi
gian, neu khoang each gian doan nay cang nho (m
Idti) thi
ket qua
linh
toan cang chinh xac trong
trudng

hgp so lieu khong
chiia
tap.
- Tai mot so nhiet do chua xuat ro bieu hien tam sau.
2.3.
Phuang phap tach song dong
bp
A -
B.
Du6i su tac dong
ciia
the phan cue mot chieu gay nen mot vung dien tich qua
dp tai
mi^n
chuyen tiep. Su thay doi trang thai
tinh
dien
ciia
vung qua dp
duge
coi la
su thay doi dien dung
ciia
mot tu dien hoac dong dicn
ciia
mot mach kin
chiia viing
dien tich khong gian phd. Ghi nhan su thay doi
ciia
dong dien la pho dong qua dp.

Bieu thiic
ciia
dong qua dp la ham
ciia
thai gian.
J,^{i)
=
./,„,,.
exp[-e,,(/
-i,,)\
(2.9)
Vai
J,^,,
^
q-c,.Nr
va
L^
-
.i.7 '.
cxp(-^) (2.10)
KI
Tin hieu dong qua dp
J(t,T)
tai mot nhiet dp T nao do duoi tac dung
ciia
xung
phan cue mot chieu co dang J
=
J(t),
T

~
const.
Thuc hien
vice chia
chu ky xung kich mau lam bon phan bang nhau
a
bp
xii
ly. Tin hieu J(t) chi duge th6ng
6
hai khoang thoi gian.
T,
T,
.
37;
— <
I
< — va
—
<
I
< T,
4 2 4
Gpi tin hieu J(t)
a
khoang dau la A va khoang sau la B.
Sii
dung bp tach song
so sanh hai dien tich A va B.
Neu gpi R - R(l) la ham

truytin
dac trung cho tin hieu. R ty le vai dp
Idn ciia
A va B. Qua m6i he
sii
ly no co phuang trinh la:
R{i)
-
\C[i).F{i).di (2.11)
Trong
do
F(t)
gpi la
ham
Ipc.
voi
he
tach song dong
bp A
-B,
ham
Ipc F(t)
co
dang:
10
F(t) =
0
t"'
0
neu 0 <

/
<

4
T
neu
T.
T,
neu — < / < —
2 4
(2.12)
T.
=
-2/
neu
37;
4
<
/ <
r,
Vai
T,
la chu ky
lap
lai
ciia
xung kich
mSu.
Ham
truydn

co
dan^:
exp
^ '.^, ^
/Vy
-exp
—
[
'-fj
- exp
•
e„
]
+ exp
4/;
•
f
^^V
^^7).
2.13)
TCr (2.13) tim duge
cue
tri
ciia
ham truyen la
0.133Q,
doi voi dien dung qua dp
va
0,403C^
doi vai dong qua dp.

Qua trinh thuc nghiem la dinh truo'c
e,,^,
( bang tan so f), do nhiet dp
ciia mlu
thay doi. Dinh
cue
dai pho DLTS cho ta xac dinh nhiet dp
T^^,.
Thuc hien phep do vai
cac
e^j
khac nhau, do tuang
ling
T,^,.
Tu cac cap gia tri do duoc ve do thi su phu thupc
Ln
T:
theo
KT.
Duong bieu dien cho biet nang lugng ion boa
Ej,
tiet dien
b4t
hat tiii
ciia
cac
mii'c
sau. Vay vai phuang phap nay phep do da chuyen quan he hai
bien so
J(t,T)

sang quan he mot bien so AJ(T) bang
vice
lay hieu hai khoang A va B
tren duang tin hieu dong qua dp.
Cung
CO
the thuc hien phep do nhu
va\'
tren he analog dung tu ghi.
2.4.
Phuong phap Boxcar.
2.4.1.
Co so ly thuyet.
Xet cau
triic
P"
- N, tam bat dien
tii trouii
chat ban dan N. Ta co
cons
thuc
toe dp phat hat tai doi vai dien
tii
va cong thiic dien dung qua d6C(t) nhu sau:
(2.14)
—'- .
exp
A£ \
JT]
C{t)

=
C, -
c;.exp(-
e
I
(2.15)
11
Neu khong quan tam den thanh phan khong doi
C^
va de y
r^ng
V„ -
T~;
V^
«
T~
thi
(T,,
coi nhu khong doi theo nhiet dp va cong thiic (2.14),
(2.15)
co the viet
dang:
E,
KT
^„ =
AJ^\
exp
an
=
C,.cxp{-e,,.t)

2.16)
(2.17)
V6i
Cy,
A
la
cac hang so va A
-
a,,
va goc toa dp tai day vung
d^n
E,.
- Doi vai ban
d2n
cau
true
N^
- P, phuang trinh bieu
diem
cho tam bat 16
tro'ng
hoan
toan tuang tu (2.16) va
(2.17),
khi do
e^
duge
thay
bing
Cp.

Trong c6ng thiic
(2.16)
va (2.17) chiia cac thong tin
chii
yeu can thiet ve tam
sau hu nang lugng ion hoa
E,.
toe
dp phat xa dien
tii
e,^,
tiei dien bat dien
tii
a^
(
n^m
trong A), nong dp tam sau
.N-,
( nam trong
e^,).
Tii cac phuong trinh (2.16) va (2.17) cho ta thay
duong
dien dung qua dp phu
thupc vao hai bien so la nhiet dp va
thoi
gian. Ta \iei: C
=
C(t.T).
ky thuat
xii

ly tin
hieu qua dp dien dung bang he Boxcar kep nhu sau:
- Tin hieu dien dung qua dp dua vao bp
xii'
ly va
duge
ghi lai. dua ra chi
a
hai thai
diem la
t,
va
t
0
loi
ra cua bp
xii'
ly co hai gia tri C(t,).
C(U}
lai duge dua vao bp
khuech dai vi sai. Loi ra khuech dai vi sai cho dien ap
ling \'6i
dang duang qua dp va
vi tri
ciia
hai c6ng
t,
va
t
*

t
DoC
L(t)
D
Cil
1
Cl
>
Tu
ghi
Hinh 2.2: Mo td ky thuat Boxear kep
Tin hieu di qua m6i bp
xii
ly
duge
dac trung boi ham truyen:
R{t)
=
\C(t).F{i).dt
(2.18)
12
F(t):
La ham
loc
dac trung cho bp
xii
ly;
Tf:
La chu ky lap lai
ciia

bp xung kich
mSu.
Ham ipc F(t) doi vai he Boxcar co dang:
F(0 =
d{f,
-t,)-d(t-f)
Vdi dieu kien
T,
»
tpt.,
cong thiic
(2.18)
tra
thanh
(2.19)
lUn
-
Jr(/).[r(/„
-0-r(/
~
i.)\di
(2.20)
Qua he Boxcar kep a
loi
ra ta nhan duge:
R{i) = C(/,)-C(/,)
Mat
khac theo (2.17), ta co the viet (2.21) nhu sau;
Rif)
=

(::.[exp(-
e,,./,
) - exp( -
.',./
)]
(2.21)
(2.22)
Do
(2.16)
ta thay toe dp phat dien
tiie^
lai phu thupc vao nhiet dp:
e^
-
e,/T).
Khi do R theo su thay doi nhiet dp
ciia miu
( co nghla
e„
thay doi ) thi R se di qua
cue
tri thoa man
di6u
kien:
dR
de
cj-
/,
. e
xp(-

c^,./,
)
4-
expi-
e ,.i
)|
=
0 (2.23)
Suy ra:
hay
[-
V
exp(-
e^,.i,)
+
/
exp(-
e,,.t,)]
= 0
nen
^.^
I
J
•^^(max)
e U.
- /,
in
^i.)
(2.24)
I,

-/.
Vay ghi nhan tai hai thoi diem
tj,
t-,
thong qua he Boxcar kep va thay doi nhiet
dp
m3u
thi ham truyen R se dat gia tri cue dai.
Toe
dp phat xa dien
tii
tinh
duge
tu
gia tri cue dai do la
e,^.
Neu dinh san hai thoi diem
t,, t.
co
nghia
la an dinh mot gia
tri
to'c
dp
phai
xa. Ghi nhan ham truyen R theo su thay doi nhiet dp
ciia mSu
thi se
xac dinh
duge

c\xc
dai
ciia
R tai mot nhiet dp nao do. Su phu thupc
ciia
ham truyen R
vao nhiet dp gpi
la
ph6 DLTS.
- Gia tri
e^
duge
lua
chpn
trudc
do gpi la su
lua
chpn
ciia
s6
toe
dp. Khi cho
nhiet dp thay d6i thi
e^
sx thay doi den gia tri
e^^
da djnh truac
ciia ciia
so toe do.
13

Khi do ham truyen R dat
cue
dai, ky thuat DLTS co tinh uu viet
a
dac diem nay. No
da bien su phu thupc C(t,T) ba chieu thanh R(T) hai
chi^u
cho ta
xii
ly
di.
dang ban.
- Trong qua
trinh
thuc nghiem cho nhiet dp
ciia m3u
thay doi va gia tri
e^
dinh
trudc
( cac vi tri
t,,
t2
dinh truac ).
Tir
pho DLTS xac dinh duge nhiet dp
T^^
a cue dai
pho.
Tu cong

ihiic (2.16)
co:
AJ-
exp
K.T
(2.25)
Vai
e^i
cung lam tuang
lU
de xac dinh
T^j
tii cong thuc
A.T^;^.
exp
K.T.
(2.26)
Lap lai phep do cho
c,^,
de xac dinh
T,^
4.T^~.
exp
^•T;,,
j
(2.27)
Tii cac cap
(e,,,,
T,,)
ta lap do thi

Ln\
~ \
theo
'
Du6n2
bieu dien se la duang
thdng
ma dp doc la nang lugng ion hoa
E,
va giao
dicm ciia
duong thang voi true
tung cho ta thong so
\'6
tiet dien bat
hai
tai.
- N6ng dp cac tam co
the'
tinh true tiep tu su thay d6i dien dung
ling
vai su lap day
hoan toan cac tam
b^ng
xung tiem bao hoa doi vai truang hgp hat tai khong ca ban
hoac
bing
xung hat tai co' ban rpng nhat co the co doi voi truang hgp tam hat tai ca
ban.
-

Doi vai cau
Iriic
N^
- P thi bieu thiic nong do lam bat
dien
tu la:
AC
-V,
=2
C
.(A-, Vj
(2.28)
Trong do:
C: La dien dung cua diod khi phan
cue
ngugc
tinh;
AC:
La su thay d6i dien dung tai t = 0 gay boi xung
tiem
bao hoa;
(N^
-
ND):
La n6ng dp aceptor tong cong
a
phia P
ciia
vung
tiep

giap.
14
Ln(e/r2)
C(t,)-C(t,)
KT
•>
Nhiet
do
Hinh
2.3:
Minh
hoa
phep
do
DLTS
vdi nam
ci'ra
so toe do
kluic
nhau
vd
edeli
xde
dinh
ndnq
luang
ion hod cua tam sau.
Bang
phucmg
phap DLTS

cac
thong
so
duge
xac
dinh
co sai
so
kh6ng vugt
qua
10%.
Uu
diem
ciia
phuang phap
nay la chi can xac
dinh dinh
cua tin
hieu
de
tim
T^^^
ma khong
cin
quan
lam
bien
dp tin
hieu
la

bao
nhieu
nen anh
huang
ciia
hang
so
truyen tren
he
dien
tii
den
phep
do la
khong
he co.
Vay viec
dat cac
ciia
s6
t|, t.
(co
nghla
dat
truoc e„
) da
chuyen quan
he 2
bien
AC{LT)

sang thanh quan
he
mpl
bien
A((/) mot
each
tu
dong
\a co
the
xay
dung
duge tren
he
analog
tu ghi.
2.4.2
So do
khoi
chijc
nang.
Phuong phiip Boxcar dung trong
he do
DLTS
co sa do
khoi
sau:
Phat(l)
•
QP(4)

1
TH
chuan(6)
^Vi(9) ^^
Boxcar
Hinh
2.4 Sa do
khoi
ehue
nang
ei'ia
he do
dien dung DLTS.
15
Neu chi
sir
dung cac khoi tii (l)den (9) cho he do dien dung DLTS thi ta co he
do dien dung nho
duge
chi thi
b^ng
dong ho mot chieu . Hinh tren
la
sa do khoi
chiic
nang
ciia
he do dien dung DLTS dung ky thuat
xii
ly Boxcar kep.

Chiic
nang ciia tiing khoi nhu sau:
Khoi (I)
la
khoi phat tin hieu hinh sin cao tan lam viec
a tdn
so 5.6 MHz.
Mach phat
sii
dung bp dao dong thach anh vai cac cong
NAND ciia
vi mach
SN7400. Tin hieu
hinh
sin 5.6 MHz sau khi qua cac tang
Ipc
lua se duge dua vao cau
dien dung (2), khoi quay pha (4).
a
do
edu
(2)
duge
nuoi
b4ng
nguon 5.6MHz. Tin
hieu sau cau (2)
lai
duge dua vao khoi khuech dai
Ipc lua

(5). Khoi nay duge xay
dung
b^ng
vi mach SC2929 va cac khung cong huang lam viec a
tdn
so' 5.6MHz sao
cho dp truyen qua
ciia
khoi dat 0.5 MHz. Khoi co nhiem vu
Ipc
ra duang dien dung
tii song cao tan hay noi
each
khac
Ipc
duang bao bien dp tii song mang.
Khoi TSNP (7) duge dieu
chinh
de nhay nhat voi bien doi do thanh phan dien
tra. Vi
ly
do nay ma bp quay pha (4) nam truac khoi tin hieu
chuain
co vai tro quan
trpng trong giai doan
tit^n
xu ly
ciia
he do.
Tin hieu thu

duge
(duong qua dp) sau khoi TSNP co dp trung thuc phu thupc
dp don
sdc ciia
tin hieu cao tan hinh sin 5.6 MHz.
Khoi khuech dai mot
chi^u
(8) co loi ra dua vao dong h6 chi thi mot chieu (9).
a
day ta co
th6
quan sat sU thay doi gia tri
tuyel
doi cua
dien
dung mau do theo cac
tac nhan tu ben ngoai.
Bp
xii
ly tin hieu hai cong la khoi Boxcar, khoi co 3 loi A, B, C. Trong do
loi
A la
loi
phiit xung phan cue
mdu
do trong khoi cau dien dung. Loi B la loi nhan tin
hieu qua dp dien dung sau khoi khuech dai. Khoi C la loi ra tu ghi sau qua trinh
xii
ly tin hieu tu dong tai 2 thai diem dat
s5n.

16
CHl/ONG
3
PHiroNG
PHAP
KHUECH
DAI
LOCK-IN
3.1 Gioi thieu chung
Khuech dai Lock-in (Lock-in amplifier) duoc dung de phat hien va khuech dai
nhirng
tin hieu AC cue nho, co the dat toi ca vai nanovolt. No co the do chinh xac
nhirng
tin hieu nho ban nhieu nhieu
Ian
Khuech dai Lock-in
sii
dung ky thuat phat hien nhay pha, no
chi
giii lai
nhimg
thanh
phan tin hieu co
ciing
tan so voi tin hieu chuan, con nhung thanh phan tan so khac
vai tan so tin hieu chuan se bi loai nen khong anh
hucrng
gi den phep do
Xet vi du sau:
Gia

six
tin hieu can do co dang sin voi bien dp
10
nV.
tan so
10
kflz.
Neu
sii
dung bp
khuech dai tap am thap voi nhieu loi vao khoang 5
nV/VlI/,
dai tan
ciia
bp khuech
dai la 100 kHz va he so khuech dai la
1000
thi
a
loi ra cua bp khuech dai chiing ta
co:
dp
Ian ciia
tin hieu la 10
|.iV
(10 nV x 1000) va dp
Ian ciia
nhieu la 1.6 mV (5
UV/VHZ
X

x/lOO
kHz x 1000). Nhu vay chiing ta se khong thuc hien duge phep do
neu nhu khong tach duge thanh phan tan so quan tam ra khoi nhieu
Neu chiing ta dung mot bp
Ipc
dai voi dp pham chat Q
^ 100
(day la thong so
ciia
bp
Ipc cue
tot),
tan so trung tam la 10 kHz thi tin hieu nam trong dai tan 100 Hz (10
kHz/Q) se duge truyen qua. Nhieu trong truang hgp
na\
se la 50
j.iV
(5 nV/vHz x
VlOO
Hz x
1000)
va dp
Ion ciia
tin hieu van la
10
)_iV.
Nhu vay nhieu
o
loi ra van
Ian

ban tin hieu nhieu
Ian
nen chiing ta se
Ichong
thuc hien chinh xac duge phep do. Han
niia he so
kliuech
dai cung
Idiong
lam tang duge ty so tin hieu tren tap (signal to
noise)
Bay gia chung ta se khao sat vai tro cua bp phat hien nhay pha PSD (Phase-sensitive
detector). Bp phat hien nhay pha co the phat hien tin hieu a tan so
10
kHz voi dai
rpng hep co khoang 0.01 Hz! Trong truong hgp nay nhieu o trong dai chi eon
khoang 0.5
|.iV
(5 nV/VHz x
Vo.Ol
kHz x 1000) trong khi do do
Ian
tin bieu van
la
10
|aV.
Ty so tin hieu tren tap bay gia la
10/0.5 =
20 nhu vay chung ta hoan toan c6
the thuc hien duge phep do mot each chinh xac

Mot bp phat hien nhay pha PSD khong nhung co tac dong voi bien dp tin hieu cung
tan so vai tin hieu chuan ma con nhay voi su sai khac pha giiia tin hieu va tin hieu
chuan. Vi the nen mot he thong
dira
tren hoat dong cua bp PSD co the do duge ca ve
bien dp va pha cua tin hieu luan hoan tat nhien la co su hien dien cua nhieu. Cac he
thong dua tren nguyen ly boat dong cua bp PSD duge gpi la cac he Lock-in. Neu
trone
cac he khuech dai co su dung
nauven Iv
hoat
doim
cua bo PSD thi duoc
lioi
la
khuech dai lock-in [ |
3.2 Cac khai niem
co
ban
So do
klioi
CO ban cua mot he kbuech dai lock-in duge trinh bay tren hinh 1.1. Viec
chia chiing thanh cac khoi rieng biet
giiip ehiing
ta de hieu va co the tiep can mot
each CO
hieu qua va nhanh nhat.
u^.TU^Ouoc^^TT^'
RUNGTAV IHONG
IJ-

ihU ,/ihfN
i£
17
Mot he khuech dai lock-in bao gom
nhimg
bp phan nhu: tang tien khuech dai, bo
nhan, bo loc tan thap va kenh tin hieu chuan. Sau day chiing ta se tim hieu mot so
cac khai niem
lien
quan:
3.2.1 Kenh tin hieu (The signal channel)
Tac dung
ciia
bp tien khuech dai (preamplifier) la khuech dai tin hieu dat tai gia tri
phii
hgp vai dai
ciia
bp nhan (multiplier) hay gia tri tin hieu la vugt trpi so vai nhieu
ciia
bo nhan, ngoai ra no con cho phep thay doi he so khuech dai
ciia
he hay la thay
doi dp nhay
ciia
he khuech dai.
Signal
input
o
Bo
nh;

m
Fiher
Preanip
Kenh tin
hieu
Lowjiass
Fihcr
He so KD
Ref
input
OLllpUl
Kenh
Ref
Hinh 3.1 - Bp khuech dai lock-in co ban.
Nha tang tien kliuech dai ma chiing ta co the chpn duge he so khuech dai phu hgp.
Muc dich o day khong chi lam tang he so khuech dai ma con phai tang
duge
ti so tin
hieu tren tap. Voi
each
do thi chung ta se dam bao giam toi thieu nhung thanh phan
nhieu khong can thiet ra khoi tin hieu. Nhu
\'ay
doi voi cac he thi nghiem ta phai
chpn tang tien khuech dai
phii
hgp va co tap am thap
(lov\-noise).
3.2.2 Bo tach song dong bo
Hinh 1.2 la cau tao cua mot bp tach song dong bp (synchronous detector). No bao

gom mot bp loc tan thap (low-pass filter) va mot bp nhan ly tuong (ideal multiplier).
Sau day chiing ta se khao sat theo quan diem toan hpc
{I)
-
V
2/
cosU't /
+'l)
)
<x}
\'p(ri
1
W'O)
/•/ I
ou
Output
Lin\
-pass filter
/•(O =
v2r,
cosioj,^
+(t).)
Hinh 3.2
-
Bo tach
sone dons
bo
Tin hieu va tin hieu chuan a loi vao bp nhan co dang hinh sin, co the hieu dung
l4n
lugt

la
Vs
va
V,.
Chiing duoc bieu dien boi cac phuong trinh:
18
j(0 =
V2V,cos[6?,/
+ ^J
r(0 =
V2V^cos[6i>,^
+ ^,]
d
loi ra
ciia
bp nhan chiing ta nhan duge tich
ciia
tin hieu s(t) va tin hieu chuan r(t)
CO
dang
la
tong
ciia
cac thanh phan tan so khac nhau:
V^(0
=
V,K,
COs[(a;,
+
W,

)t
4-
^^ + ^J
+
Vy^.
COS[{CO^
-
CO,.
)t
+
{(j)^
-
(I),
)]
Vai thuat toan nay se duge de cap lai a cac phan sau. Neu chpn tan so cat cua bp loc
tan thap thoa man nho
ho'n
tan so
03^
thi cac thanh tin hieu co tan so la tong
ciia
cac
thanh phan
(ojr "*' cor)
se khong xuat hien a loi ra. Ngoai ra neu dai tan
ciia
bp loc tan
thap
Ion
ban nhimg thanh phan tan so

Aco ^
|(o,
-
O),!
thi o loi ra cua bp
Ipc
se chi
xuat hien nhiing thanh phan tan so
Aoj.
De tinh bien dp
ciia
thanh phan tin hieu do
thi chiing ta phai biet ham dap
ling
tan so cua bp
Ipc
HLO*^^)-
Dp Ion
bien dp loi ra
duge bieu dien bang phuong trinh:
khV,K,./i,(A^)
trong do
AI(CO)^\Hi(joj)\
Do
AL((O)
CO
tan so cat nho hon rat nhieu so voi
oj,-
nen chiing ta thay rang he chi co
the chap nhan nhCmg thanh phan tin hieu co tan so gan voi tan so tin hieu chuan.

Dieu nay co the duge mo ta theo khai niem cua so truyen (transmission window),
vai tan so trung tam la tan so tin hieu chuan. Dac
trung
AL(CO)
phu thupc vao tan so
(co) duge mo la tren hinh 1.3. Tom lai chung ta thay rang voi su ket hgp
ciia
tin hieu
chuan, bp nhan va bp
Ipc
tan thap thi tin hieu loi ra chi con lai
nhQ*ng
thanh phan tan
so
Ian
can tan so tin hieu chuan.
-3dB
bcindu idlh
\^,
-3dB
\ bandwidth
\
(*
Hinh
3.2>
-
(a) Dap ung bien dp - tan so cua bo loc
Ian
thap
(b) Cua so

truven
cua bp loc tan thap
\ai lan
so trung tam
oj^
• Giiii dieu che
vdi
tin hieu chuan dong bo (Demodulation with a
synchronous reference)
Xet so
d6 CO
dang nhu hinh 3.4. Bay gio chiing ta se khao sat y
nghia
thuc tien
ciia
phuang phap. Tin hieu dua vao he thi nghiem va tin hieu chuan duge lay tu mot
nguon.
Ta
CO
mot nguon tin hieu dang sin co tan so
cOr
duge diing lam nguon kich dong thi
nghiem va lam tin hieu chuan. Tin hieu loi ra
ciia
he tbi nghiem co cung tan so vai
19
nguon kich dong va
bj
dich pha di
^^.

Tin hieu chuan duge dua qua bp dich pha sau
do
duge
dua tai bo nhan cung tin hieu tu tbi nghiem.
6
day chung ta thay
cOs ~ cOr
boi vi chiing duge nhan tu mot nguon. Nhu vay a loi ra
chi con lai thanh phan mot chieu co dang:
trongdo:
(p =
(/>^
-^,
k^
^K-AtiO)
Thong thuong thi bien dp tin hieu chuan duge co dinh nen
k,-
cung la mot hang so.
Nhu vay bien dp loi ra bay gio ti le thuan voi bien dp tin hieu va dp lech pha
ciia
tin
hieu va tin hieu chuan. Sau day chung la se khao sat tac dung cua bp dich pha trong
viec do cac thong so
ciia
tin hieu nhu bien dp va pha.
V2^''
cos to
/
r^
Ky

He
thi
nghiem ^
.•*
(l)
/
v'"f/;
!
.(X)
vi^^
L'()S((0
/
^
0, )
Lou
-pas>
Filter
'
; \
r-
\
O
1
Synchronous detector
Hinh 3.4 - Detector dong bp vai bp dich pha
• Giai dieu che bien do (amplitude demodulation)
Khi chiing ta dieu chinh sao cho pha cua tin hieu chuan cung pha voi tin hieu thi loi
ra cua bp nhan se la:
Vo =
k,V,

voi
(t),-
^^.
0 loi ra muon dam bao de thu duoc nhimg thay doi cua bien dp tin hieu thi dai
truyen
ciia
bp loc tan thap phai du rpng de cho phep truyen nhu'ng tin hieu dieu che
ma khong bi bien dang. Vi du, khi
tin
hieu co dang:
v^,(/)
= /?7(0cos(.ri;,/)
thi the loi ra se co dang:
v,(0-^.vn,,
(0
trong do:
/??,(/) ^ ^??(^)®h^{i)
h^(t):
dap
ling
xung cua bp Ipc
ni(t):
tin hieu dieu che
®; phep nhan chap
Trong truong hgp nay pho tin hieu loi ra cua bp tach song dong bp co dang:
V^Xfco)
=
k,.M(faj)H^{jaj)
^M{jco)H^{fCo)^
d

day:
M(j(o)
la bien doi Fourier
ciia
tin hieu dieu che,
Hgifoj) = kJT^{jco)
la ham dap
ling
tan so
ciia
bp tach song
20