Antenna W4 - 國立中興大學
Transcript of Antenna W4 - 國立中興大學
33
The Reciprocity Theorem
• Equivalent of the Tx and Rx patterns ofan Antenna– a set: Antenna 1: Tx, Antenna 2: Rx– b set: Antenna 1: Rx, Antenna 2: Tx– On cross-section of transmission lines
an
a1 H1K a
n1
0a
1m E1K a
na2 H1K a
n1
0a
2m E1K b
nb1 H1K b
n1
0b
1m E1K b
nb2 H1K b
n1
0b
2m E1K
dS
dS
SS
SS
21
21
bm
aba
am
bab
KBKE
KBKE
44
The Reciprocity Theorem
• Equivalent of the Tx and Rx patterns of an Antenna dSdS
SSSS
2121
bn
abn
aan
ban
b E1HH1EE1HH1E
)143.1(
yxzIzyx
yxzVzyx
, ,,
, ,,:moden Propagatio
tang
tang
hH
gE
1 ,,z dSyxyx
Shg1
b
b
a
a
RRn
an
bn
n
bn
an I
VKIVZZZZIVIV
1
2
2
1212211
2
1
2
1 ,,, difiningby
,, 21
21
aa
bb I
VKVI
linear.) bemust (Material antenna. theof or type shape, size, theofindepent
proof general a is This identical. are patterns fieldRx Tx / Normalized
55
The Reciprocity Theorem
• For the power patterns of Tx and Rx antennas
2
2
2
2
1
2
2
11
2
1 ,21,
21
Ra
a
b
R
RR
b RIV
KVRRRI
66
Directivity and Gain
• Directivity
– If the radiation intensity is defined by
• Gain
)160.1(
0
2
0sin,
, 4,ddP
PD
)161.1(
)162.1(
0
2
0
2 sin , ddrKP Lacc P
)163.1(
)164.1(
,, DG
77
Directivity and Gain
• Partial directivity and Partial gain
LK
DG ,,
LKDG 101010 log,log,log :dBin
)165.1(
)166.1(
,,, DDD
)167.1()168.1(
)169.1(
)170.1(
88
Receiving Cross Section
• Equivalent receiving cross-sectional area
receiver) (matchedpower absorbed :matched)ion (polarizat waveplane incoming :
,,
r
rr
PS
ASP
antenna. matchedon polarizati lossless allfor same The4
2
)172.1(
)173.1(
)171.1(
)174.1(
)175.1( )190.1(
99
Receiving Cross Section
S
situation-a
situation-b
2, 1, 12 rrba AAII
situation-a situation-b
Tx :1Ant Rx :1Ant
)(Tx :2Ant 2 dlI b1
)177.1()176.1(
)178.1(
)179.1(
)181.1()180.1(
abbaban
an
bn
n
bn
an
IVIVIV
IVIV
112211
2
1
2
1
r r
lossless ,2 :situation- 111 RVIa ga
22
2
221 RI a
1010
Receiving Cross Section
dlIrEIVIV baabba21111 ,,
2
2
22
11411
211
211211
11
1111
111111
1111111111
4
2
,
dlIEVVZ
R
dlIEVVZ
RZZZZVV
ZVZVIZVI
baba
bababa
bR
bbaa
11211
2
111
2
1 21
21:situation- R
Z
VRIPa
aa
acc
2
1112
11
2
1
2
4,,,
21
rDR
Z
VrE aa
2
21211
2112
1 , 16
dlIDr
RZV bb
:situation-b
, 4
, 42
1
1,
2
2211
211
22
1
1,
2
22
2
rbb
rb
abs
AdlIr
RZkV
AdlIr
kP
,4
, 1
2
1, DAr
4
2
rA
11211
2
111
2
1 21
21 R
Z
VRIP
bb
abs
1111
Polarization
tjeEE 11E
EjEE
EjEE
tEtEtEtE
eEjEEjEtr tj
sin cos sin cos ,,,
1111E Re
tBtAEE
EE
EEBEEA
tBtA
cos cos
tan tan
)()( )()(
in which cos cos
11
2222
11E
11E
1313
Polarization
• Circular Polarization
)-( kwisecoutercloc
sin cos90 and If o
handrightttA
BA
11E
)-e( clockwise
sin cos90 and If o
handftlttA
BA
11E
1
1
1414
Polarization
• Elliptical Polarization
2/1 2222
o
cos cos
0 and
tBtAt
BA
E
2cos2sin2tan
at Extrema
22
2
BABt
1
1
1515
• The Center-Fed Dipole
Dipole Fed-Center Simple 2.1 Fig.
Radiation Patterns of Dipoles,Loops, and Helices
2.2 Fig.
tjm exlkItxI sin,
aveformcurrent w
dl 2
d
1717
The Center-Fed Dipole
• The half-wavelength dipole, 2l = /2
sincos2cos
2
sincos2cos60
reIjH
reIjE
rktjm
rktj
m
1818
The Center-Fed Dipole
• The half-wavelength dipole, 2l = /2
2
609.02m
radIP
73609.02
609.021
4/ Since2
2
rad
mradradm
R
IPRI
l
1919
The Center-Fed Dipole
• The short dipole, 2l <<
!3)(sin :currentinput The
3klklIklII mm
2
22
20
12)(
LR
IklP
rad
rad
2424
A Dipole in Front of a Ground Plane
Homework #1Plot the field pattern of a dipole in front of a ground plane as shown in Fig. 2.7with 2l = / 2, h = / 8a) = 90o, = 0 ~ 180o
b) = 90o, = 0 ~ 180o