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22
Phân
Phân t
tí
ích
ch t
tầ
ần
ns
số
ố
)
2
cos()()(
π
ωω
n
tntmJVtm mc
nnc ++= ∑
∞
−∞=
∑
∞
−∞=
++=+
nn
n
nmJm )
2
cos()()coscos(
π
βαβα
z
zĐi
Điề
ều
uch
chế
ếs
só
óng
ng sin
sin m
mộ
ột
tt
tầ
ần
ns
số
ố
z
zC
Cá
ác
cth
thà
ành
nh ph
phầ
ần
nt
tầ
ần
ns
số
ốriêng
riêng r
rẻ
ẻth
thì
ìkhông
không rõ
rõ r
rà
àng
ng
(Individual freq components are not obviously)
(Individual freq components are not obviously)
J
Jn
n(m
(m)
) l
là
àh
hà
àm
mBessel function of the 1
Bessel function of the 1st
st kind of nth order
kind of nth order
with argument m
with argument m
z
zSo,
So,
)]cos(cos[)( tmtVtm mcc
ω
ω
+
=
/4
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23
Phân
Phân t
tí
ích
ch t
tầ
ần
ns
số
ố
•
•Expanding:
Expanding:
•
•J
J-
-n
n(m
(m)=(
)=(-
-1)
1)n
nJ
Jn
n(m)
(m)
•
•m(t
m(t)=
)=s
só
óng
ng đã
đãđi
điề
ều
uch
chế
ếg
gó
óc
c
•
•m=
m=h
hệ
ệs
số
ốđi
điề
ều
uch
chế
ế
•
•V
Vc
c=
=biên
biên đ
độ
ộs
só
óng
ng mang
mang đ
đỉ
ỉnh
nh
•
•J
J0
0(m)=carrier component
(m)=carrier component
•
•J
J1
1(m)=1
(m)=1st
st set of side
set of side freqs
freqs displaced from the carrier by
displaced from the carrier by ω
ωm
m
•
•J
J2
2(m)=2
(m)=2nd
nd set of side
set of side freqs
freqs displaced from the carrier by 2
displaced from the carrier by 2ω
ωm
m
[][]
}
....)2(cos)()2(cos)(
)
2
)(cos)()
2
)(cos)(cos)()(
22
110
+−−+−
⎩
⎨
⎧⎥
⎦
⎤
⎢
⎣
⎡−−−
⎥
⎦
⎤
⎢
⎣
⎡+++=
tmJtmJ
tmJtmJtmJVtm
mcmc
mcmccc
ωωωω
π
ωω
π
ωωω
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24
Phân
Phân t
tí
ích
ch t
tầ
ần
ns
số
ố
•
•Sideband set (
Sideband set (ƒ
ƒc
c±
±ƒ
ƒm
m,
, ƒ
ƒc
c±
±2
2ƒ
ƒm
m,
,…
…,
, ƒ
ƒc
c±
±n
nƒ
ƒm
m)
)
•
•First
First-
-order
order sidebands
sidebands, second
, second-
-order sidebands,
order sidebands,…
…
•
•J
J1
1(m),J
(m),J2
2(m),
(m),…
…magnitudes of sidebands
magnitudes of sidebands
•
•J
Jn
n(m
(m) can be solved by:
) can be solved by:
•
•Table 6
Table 6-
-3
3
•
•m
mincreases, the number of significant side
increases, the number of significant side freqs
freqs
increase
increase⇒
⇒bandwidth
bandwidth increases
increases
•
•Example 6
Example 6-
-2
2
⎥
⎦
⎤
⎢
⎣
⎡+
+
−
+
+
+
−
⎟
⎠
⎞
⎜
⎝
⎛
=...
)!1(!3
)2/(
)!2(!2
)2/(
)!1(!1
)2/(1
2
)( 642
n
m
n
m
n
m
n
m
mJ
n
n
/4
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25
Bessel functions of the First Kind
Bessel functions of the First Kind
Modulation
Modulation
index
index
Carrier
Carrier Side freq pairs
Side freq pairs
m
mJ
J0
0J
J1
1J
J2
2J
J3
3J
J4
4J
J5
5J
J6
6
0
01.00
1.00 -
--
--
--
--
--
-
0.25
0.25 0.98
0.98 0.12
0.12 -
--
--
--
--
-
0.5
0.5 0.94
0.94 0.24
0.24 0.03
0.03 -
--
--
--
-
1
10.77
0.77 0.44
0.44 0.11
0.11 0.02
0.02 -
--
--
-
1.5
1.5 0.51
0.51 0.56
0.56 0.23
0.23 0.06
0.06 0.01
0.01 -
--
-
2
20.22
0.22 0.58
0.58 0.35
0.35 0.13
0.13 0.03
0.03 -
--
-
2.4
2.4 0
00.52
0.52 0.43
0.43 0.2
0.2 0.06
0.06 0.02
0.02 -
-
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26
Bessel function versus m
Bessel function versus m