近傍磁界の測定による アンテナ電流分布の推定 河村 暁子 電気通信 ...

()

()

2007

Estimation of Current Distributions on Antennas
by Measuring the Magnetic Near Fields
Akiko KOHMURA
Abstract
The estimation of current distributions on antennas is required to make clear
behaviors of designed and fabricated antennas. It also contributes to specify unexpected
electromagnetic sources and to cope with the emission problems. Generally,
the requirement arises in practical uses, for example, in the case of trouble on an
attachment circuit and so on. Therefore, it is necessary to investigate these issues
not only by computer simulations in ideal state but also by measurements in the
practical state. However, it is dicult to measure the current directly, because a
current sensor cannot touch an antenna under test in order to avoid disturbing its
behavior.
In this paper, a method for estimating the current with the measurements of
magnetic near eld is proposed. The method has the potential to estimate the
distributions of the complex current values (both real and imaginary part). The
objective in this study is to conrm an availability of the method by computer
simulations and experiments.
The principle of estimation is based on an expression of the relationship between
the current and the magnetic near eld derived by Maxwell s equations. The
objective current is composed of small dipole segments with constant current. The
magnetic near eld can be expressed as a composition of magnetic elds made from
these segments. Thus, the current and the magnetic near eld are related in linear
equations. It means that the current distributions can be estimated by solving the
linear equations with the measured magnetic near eld.
In this estimation method, it is important to obtain magnetic eld data with suf-
cient small errors to solve the inverse problem stably. A double-output shielded
loop probe is introduced as a small magnetic eld sensor. The omni-directional

characteristic of the small loop is appropriate to the magnetic near eld measurement
for this estimation. A novel determination method of the magnetic complex
antenna factor (M-CAF), that is a characteristic of eld-measurement antennas,
for the introduced probe is also proposed. The M-CAF is dened as a ratio of
incident magnetic eld to antenna output voltage. The magnetic near eld must
be measured accurately to estimate the current distributions. The measurement
accuracy depends on the determination of the M-CAF. The proposed determination
method is based on an equivalent circuit of the small loop probe. The M-CAF
can be determined with the calculated eective length and the reection coecient
at the output port.
As the rst step, the current distribution on an element of a simple dipole antenna
is estimated from the magnetic near eld measured by the double-output
shielded loop probe. Appropriate positions of the probe, which does not disturb
the current and also provides enough output amplitude, are investigated using
computer simulations considering the existence of the small probe. The estimated
complex current distribution and the values are conrmed by a comparison to the
theoretical current distributions calculated by the method of moments. In this
comparison, a new technique to calibrate the excited voltage of the dipole element
is developed. As the result, it is made clear that the presented method can estimate
not only the current distribution form but also its absolute values.
Furthermore, current distributions of leaking along a surface on feeder lines of
dipole antennas are also estimated. The method can estimate the small currents
of leakages. The usefulness of the estimation method in the analysis of actual antennas
and the specication of unexpected emissions is shown by the experimental
investigations.
Finally, the current estimation method is extended for two-dimensional objects.
The method is based on the characteristic of the small loop probe, that is, only the
magnetic component perpendicular to the loop plane is measured. The possibility
is examined through the estimation of current distributions on a two-element Yagi-
Uda antenna. This result can be the base of more general two-dimensional current
estimations in future.

Maxwell
1
2
(Magnetic Complex Antenna Factor)

1
2
2
2
2

1 1
1.1 ............. 1
1.2 .......................... 3
1.3 .............................. 4
1.4 .............................. 4
2 6
2.1 ................................. 6
2.2 ................... 6
2.3 ................................. 10
3 2 11
3.1 ................................. 11
3.2 ................... 12
3.3 ..................... 15
3.4 ............ 16
3.4.1 3 .......................... 16
3.4.2 ...................... 18
3.5 2
.......................... 20
3.5.1 ........................... 21
3.5.2 ........... 22
3.6 ............................. 24
3.6.1 ........................ 24
3.6.2 ............................. 27
3.6.3 ................. 31
3.7 ............ 34
i

3.7.1 3 ...... 34
3.7.2 .................... 36
3.8 ................................. 39
4 40
4.1 ................................. 40
4.2 .............................. 41
4.3 ......................... 44
4.4 .......................... 47
4.5 ....................... 49
4.5.1 S .......... 49
4.5.2 .................... 55
4.5.3 ..................... 60
4.6 .................. 61
4.7 ................................. 62
5 63
5.1 ................................. 63
5.2 ............... 64
5.3 ........ 65
5.3.1 ............ 65
5.3.2 .... 67
5.4 ..... 68
5.5 ..... 68
5.6 ................................. 72
6 2 73
6.1 ................................. 73
6.2 2 ........................ 74
6.3 2 ............. 80
6.4 ....... 81
6.5 2 ....... 85
6.6 ................................. 90
7 91
ii

92
A 93
A.1 ................................. 93
A.2 ......................... 94
A.3 ....................... 95
B 98
C 3 100
D 102
D.1 .................................. 102
D.2 ..................... 102
D.3 .......... 104
D.4
................................. 108
E 110
F 1+j0V 114
G 2 117
G.1 ....................... 117
G.2 .......................... 122
iii

1
1.1
1901 Marconi 1
20
LAN(Local Area Network)
(VCCI: Voluntary Control Council for Interference by Data Processing Equipment
and Electronic Oce Machines) IEC:
International Electrotechnical Commission) CISPR(
:Comite International Special des Perturbations Radioelectriques)
[1][2][3]
[4][5] 1MHz3THz
1

1820 Ampere
Faraday (1831
1864 Maxwell 4
1888
Hertz
Marconi
Maxwell
1960 (Method
of Moments)[6] FDTD (Finite-Dierence Time Domain method)[7]
1900
VSWRVoltage Standing Wave Ratio:
1)
2)
3)
-
2)
2

UWB(Ultra Wide Band: ) PLC(Power
Line Communications)
1.2
2
[8]
[9][10] LSI
Maxwell
[11][12] [13]
[8]
Maxwell
3

1.3
Maxwell
1.4
7 2
2
3
2
4 2
3
3
4

5 4
6 1
2
1 2
2
7
5

2
2.1
1
2.2
2.1 y I
1l r
P ' H ' [14]
H ' = I1le0jkr
4
jk
r + 1 r 2 !
sin (2.1)
k y '
6

x
ϕ
∆l
I
θ
r
P
z
y
H x
H x = H ϕ
H ϕ
sin ϕ
2.1:
2.2 y
2.1
y N
1ly d
M
2 3 2
32
3
H 1
11 111 1N
6 .
4
7
5 = I 1
6 .
.. . .
4
7
5
6 .
4
7
5
H M M 1 111 MN I N
(2.2)
[] mn (m =1; 2;:::;M; n =1; 2;:::;N)
(2.1) [14] 2.2
x sin = d=r mn
' = =2
d 1 1l 1 e0jkrmn jk
mn = + 1
2
4r mn r mn r mn
(m =1; 2; :::; M; n =1; 2;:::;N)
7
!
(2.3)

I n ( n =
1; 2; 3; ;N) n H m (m =1,2,3,, M) m
r mn m n
I n (n =1,2,3,, N)
(2.2) 1
M N
[15]M >N
(2.2)
[]
[] H [16][17]
2
3H2
3 2
3H2
32
3
11 111 1N
.
6 . . H 1
. .
4
7
11 111 1N
5
6 .
4
7
5 = .
6 . . 11 111 1N
. .
4
7
.
5
6 . . I 1
. .
4
7
5
6 .
4
7
5 (2.4)
M 1 111 MN H M M1 111 MN M 1 111 MN I N
(M >N)
(2.2), (2.4) 1
[16] B)
8

y
Dipole antenna
I N
H M
x
I n
r mn
Feeding
terminal
z
H m
∆l
I 1
H 1
Scanned
Magnetic
fields sensor
d
2.2:
9

2.3
1
10

3
2
3.1
2
2
2 2
(M-CAF)
3 [18]
S
FTF 3
11

[19][20]
2
3.2
3.1(a), (b)
Direction Of Arrival:DOA
[21]
3.1(a)
3.1(a)
[22]
3.1(a)
3.1(b)
3.2
[23]
12

2
2
13

Magnetic
field
Loop
Conductor
Coaxial line
Output Port
Inner conductor
Outer conductor
(a) Single-output
Magnetic
field
Loop
Two coaxial lines
Port 1
Slot
L
Inner conductor
Outer conductor
(b) Double-output
Port 2
3.1:
Slot
Semi-rigid cable
E
(a) Behaviors of current around the loop
E
Outer conductor
Inner conductor
-
+
+
I S
-
+
-
-
Slot
+
(b) Current and electric potential focused on the slot
3.2: 2
14

Loop element
Current I O
H
Coupling
circuit
Z 0
Z L
Transmission
Line
Matched
Load
(Z L = Z 0 )
3.3:
3.3
3.3 Z 0
!
H(!) Z L = Z 0 I O (!)
F M (!) = H(!)
I O (!)
(3.1)
3.1
F M I O
H H(!)=F M (!) 2 I O (!)
E(!) V O (!)
F E (!)
F E (!) = E(!)
V O (!)
(3.2)
15

F E (!) F M (!)
(120 []) Z 0
3.4
3
[18] [20] 3
(Field Transfer Factor; FTF)
3.4.1 3
3 (3-antenna method) 3
S S 21
3 2
3.4 3 3
2 S S 21 ]i
]j S S 21 A ji (i; j =1; 2; 3)
F M1 ;F M 2 ;F M3
]2
F M 1 =
vu
u
t jZ 0A 23 (R)e 0jkR
v
u
0 A 21 (R)A 13 (R)R
F M 2 = t jZ 0A 13 (R)e 0jkR
0 A 23 (R)A 21 (R)R
F M 3 =
vu
u
t jZ 0A 21 (R)e 0jkR
0 A 13 (R)A 23 (R)R
(3.3)
(3.4)
(3.5)
R 0
16

(=120 [])Z 0 k
k =2=
(3.3) (3.5)
0 =Z 0
3
(3.3) (3.5) 090 90
3.4.2
3
S S 21 R
S 21
3 S
[6] S
A 21 S 21 rR
q(r; R)
q(r;R)= A 21(R)
A 21 (r)
(3.6)
A 21 K K
q(r;R) = A 21(R)
A 21 (r)
'
'
S 21(R)K
S 21 (r)K
S 21(R)
S 21 (r)
(3.7)
S
18

(3.6)
A 21 (R) =q(r; R) 1 A 21 (r) (3.8)
S
S
(3.3) (3.5)
19

1
Coaxial Coaxial
2
3 4
-
+
Z a
V O
Z 0 Z 0 , β
Z 0 , β Z 0
Slot
1‘ 2‘
3‘ 4‘
+
-
L
L
(a)
I S
V O
Z a
3
4
+
Za ⋅ I S
Z 0 , β
Z 0 V O
3‘
4‘
Z
-
0
L
(b)
3.5: 2
3.5 2
3.1(b) 2
3.5
L
I S Z a
2
Z 0 2-2'
3-3' 1-1' 4-4' Z 0
20

V
O
= l eE
(a) The effective length in general definition
I ′
S =
l e H
(b) The effective length in this study
3.6:
3.5.1
H I S
3.9 l 0 e
I S (!) =l 0 e
(!) 1 H(!) (3.9)
l e E(!) V O (!)
V O (!) =l e 1 E(!) (3.10)
[24]3.9 3.6
(Thevenin) (Norton)
(120 [])
3.9 l 0 ""
e
21

3.5.2
3.5 2
2
1
3.2 2
2
2
1 2
2
2 I O V O V O
I O (!) = V O(!) 0f0V O (!)g
Z 0
1 1 2
(3.11)
3.1
F M (!) = I S(!)Z 0
l 0 e(!)V O (!)
(3.12)
3.5(a) 3-3' 3.5(b)
3.12
F M (!) = 1 ( )
le 0 (!) 1+ 2Z 0
e jL (3.13)
Z a (!)
l 0 e(!)
Z a 4-4'
0 1
0 1 (!) =
Z a (!)
Z a (!)+2Z 0
e 0j2L (3.14)
3.143.13 fg e j2L
3.1(b) 2
22

F M (!) =
e0jL
l 0 e(!)0 1 (!)
(3.15)
2 0 1 2
(3.15)
2 2
F M =2
23

11.5mm
Loop
Conductor
Coaxial line f = 1.5mm
Connector
60mm
(a) Single-output
Slot
(0.4mm)
11.5mm
Loop
Two coaxial lines
f = 1.5 mm
126 mm
Connector
(b) Double-output
3.6
3.7:
3.7 2
2
1.5
mm 11.5 mm Z 0 50
6cm2
0.4 mm L 12.6 cm
3.7
3.6.1
4 4.2
[6]
24

1.5 mm 24
3.7(a) (b)
3.8
3.9 l 0
e
1 GHz
0.15
=0 60 0.13 dB
1 GHz
25

E
θ
11.5 mm
H
Incident
field
k
Feeding
point
Loop
3.8:
Real part of effective length [m]
0.0098
0.0096
0.0094
0.0092
0.009
0.0088
q= 0 deg
30 deg
45 deg
60 deg
0 0.5 1 1.5 2 0 0.0005
Frequency [GHz]
0.0025
0.002
0.0015
0.001
Imaginary part of effective length [m]
3.9: l 0 e
26

3.6.2
11.5 mm
1GHz
3.7 2
3.10 = 0
3.7(a) 2 3.7(b) v o
3.10 2
3.7(a)
1ns 1 MHz
Picosecond Puls Labs Model 1000D
70 V 1GHz
6dB
1GHz 1/6 5cm
1.83 m 2 1.36 m
50 3GHz
Tektronix TDS694C 1t =0.1ns 1000
=030 45 60
3.11 (a) (b)
2 1 50 3.12
3.11 =0 =30, 45, 60
2
27

30cm
Loop antenna
port1
φ = 0 deg
Monopole
antenna
l = 5 cm
h(t)
φ = 60 deg
10 cm
port2
Ground plane
Attenuator 6dB
Impulse generator
∆t = 0.1 ns
1000 points
Ch.2 Ch.1
Oscilloscope
3.10:
28

0.01
0.005
φ = 0 deg
30 deg
45 deg
60 deg
Voltage [V]
-0.005
0
-0.01
-0.015
-4 -3 -2 -1 0 1 2 3 4
Time [ns]
(a) Shielded Coaxial Loop Antenna
0.01
0.005
φ = 0 deg
30 deg
45 deg
60 deg
Voltage [V]
-0.005
0
-0.01
-0.015
-4 -3 -2 -1 0 1 2 3 4
Time [ns]
(b) Double-Output Shielded Loop Antenna
3.11:
29

30
Ratio [%]
25
20
15
10
5
Reference
φ = 0 deg
0
0 10 20 30 40 50 60 70 80 90
Angle of the loop antenna φ [deg]
Singleoutput
Doubleoutput
3.12:
30

3.6.3
3.13 Agilent E8358A 2
0 1
0 3.9
3.133.15 0 2
1m S 21
3.14 3.15
3.14 10 cm 0 1
l 0 e
3.10
10 cm
31

0
1 [dB]
-5
-10
-15
-20
Magnitude of G
-25
0 0.5 1 1.5 2
Frequency [GHz]
200
150
100
1 [deg.]
50
0
-50
-100
-150
Phase of G
-200
0 0.5 1 1.5 2
Frequency [GHz]
3.13: 0 1 (
32

65
In free space
Magnitude of M-CAF [dB 1/m ]
60
55
50
45
With the effect of
the ground plane
(height 10cm)
40
0 0.5 1 1.5 2
Frequency [GHz]
Phase of M-CAF [deg.]
200
150
100
50
0
-50
-100
In free space
With the effect of
the ground plane
(height 10cm)
-150
-200
0 0.5 1 1.5 2
Frequency [GHz]
3.14: 2 (
33

3.7
3.7.1 3
3.15 3.4 3
2 1 50
3
3.15 690
(unwrapping) [25]
6180
100 MHz
3
S 3
S
(Extrapolation)
34

75
70
Proposed method
FTF-3antenna method
65
M-CAF [dB 1/m ]
60
55
50
45
40
35
0 0.5 1 1.5 2
Frequency [GHz]
200
150
100
Proposed method
FTF-3antenna method
FTF-3antenna method
(modified phase
from –180deg. to 180deg.)
M-CAF [deg.]
50
0
-50
-100
-150
-200
0 0.5 1 1.5 2
Frequency [GHz]
3.15: FTF-3 M-CAF (
35

3.7.2
3.15 3.14
3.10
2
h(t) i O (t)
(waveform reconstruction) [26]
i O (t) 2 v O (t), 0v O (t)
i O (t) = v O(t) 0f0v O (t)g
Z 0
1 1 2
h(t)
h i
h(t) =F 01 FM (!)Ffi O (t)g
(3.16)
(3.17)
FF 01
h(t)
h(t)
" l
1
h(t) =F 01 4 r + jk
#
0
1 I a (!) 1 e 0jk 0r
2 r
(3.18)
(2.1) sin 1=r r
k 0 I a (!)
2l
3.18 l 3.16
(a) (b) I a (!)
i a (t) 6dB v m (t)
Z in (!) Z 0
C
I a (!) =Fn
ia (t) o =
2v m (t)
Z 0 + Z in (!)
(3.19)
36

6dB Z 0
3.16 v open (t) v m (t)
Z in ! 0 1
3.17
3
V O
37

Transmission
line
Transmission
line
v open (t)
Z 0
Z 6 dB
0 Z Z 0 v m (t)
Attenuator 0
1
vm ( t)
= vopen
( t)
4
(a)
i a (t)
v open (t)
Z 0
Z 6 dB
0 Z
Attenuator 0 Z in
I
a
{ i ( )}
( ω ) = t
F
a
(b)
3.16: i a (!)
Magnetic field [A/m]
0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
Reconstruction
-M-CAF proposed
-M-CAF FTF 3ant.
Calculation
-0.06
-8 -6 -4 -2 0 2 4 6 8
Time [ns]
3.17: M-CAF
38

3.8
2
2
2
2
2
2
3
2
""
39

4
4.1
2
[6]
3 2
40

300 mm,
1mm
480 MHz
4.2
(Method of Moments : MoM)[6] Pocklington Hallen
1967 Harrington
S
4.1 a 2L
" y y
E y Maxwell
E y = 1
j!"
Z +L
0L
"
@2 V (y;y 0 )
@y 2 + 2 V (y;y 0 )
V (y;y 0 )= 1
4
r(y;y 0 )=
e 0jr(y;y0 )
r(y;y 0 )
#
I(y 0 ) dy 0 (4.1)
(4.2)
q
a 2 +(y 0 y 0 ) 2 (4.3)
I(y 0 )
y
41

y
+L
I(y’)
y’
y
0
-L
a
4.1:
E i y
0
E y + E i y
=0 (4.4)
(4.1) (4.4)
1
j!"
Z +L
0L
" #
@2 V (y;y 0 )
+ 2 V (y;y 0 ) I(y 0 )dy 0 + E
@y
y(y) i =0 (4.5)
2
(Pocklington's integral equation)[27]
V (y; y 0 ) E i y(z) R
P I(y 0 ) (4.5)
I n
" # #
Z mn
#"I n =
"V m
(4.6)
42

1+ j 0〔V〕
0.014
0.012
Real part
Imaginary part
Current [A]
0.01
0.008
0.006
0.004
0.002
0
-0.002
-15 -10 -5 0 5 10 15
y [cm]
4.2: (480 MHz)
[Z mn ](m =1; 2;:::;N;
n =1; 2;:::;N)
[V m ] N
[I n ] 1+j0V
# "I n =
"
Z mn
# 01
"
V m
#
(4.7)
1+j0V
2 1+j0V
4.2 30 cm 1mm 480 MHz
43

4.3
2.2 2
H I S
l 0 e (3.9)
2.2
I S l 0 e (3.9)
(2.4)
1) I S (y)
2) (3.9):H(y) =I S (y)=l 0 1) I e S(y) H(y)
3) H(y) (2.4): [ ] H [H] =[ ] H [ ][I]
I(y)
4) I(y) 4.2
44

Current [A]
0.016
0.014
0.012
0.01
0.008
0.006
Theoretical
(MoM)
One side of the loop
5 mm
10 mm
15 mm
20 mm
25 mm
0.004
0.002
0
-15 -10 -5 0 5 10 15
y [cm]
4.3:
(d =30 mm)
3.1(b) 2
4.3
30 mm 1.0 mm
5mm10 mm15 mm20 mm25 mm
11.5 mm 2
d
10 mm 60 mm
4.4 20 mm
3
45

0.016
Theoretical 10mm 30mm 50mm
(MoM) 20mm 40mm 60mm
Current [A]
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
Real part
I [A]
0
-0.0005
-0.001
-0.0015
-0.002
-0.0025
-0.003
5 7 9 11 13
y [cm]
-0.002
-0.004
Imaginary part
-15 -10 -5 0 5 10 15
y [cm]
4.4: d
[28]
4.5 30 mm
11.5 mm
12.5 mm
(075 mm

0.0138
0.0136
0.0134
0.0132
Theoretical(MoM)
Interval 2mm
5mm
10mm
12.5mm
20mm
Current [A]
0.013
0.0128
0.0126
0.0124
0.0122
0.012
0.0118
-5 -3 -1 0 1 3 5
y [cm]
4.5:
(d =30 mm)
4.4
480 MHz
6 (
: 7 m, : 4 m, : 2.4 m) 2.2
300 mm 1mm
1:4 (50 -200 ) (M/A Com , TP-103)
200
3 2
11.52 11.5 mm 2 4.1
S S 21 , S 31 3
(Anritsu MS4623B)
47

11.5 mm
d 20 mm 30 mm
12.5 mm 10 mm
4.1:
S
48

4.5
4.5.1 S
4.2
1+j0V
1+j0V S
1+j0V
2
4.6
3 S
S 21 , S 31 S S 11
4.7 4.6
4.7 V 1 , V d I i ( i =2,3) a i , b i (i =
1, , 4)[29]
V 1 = (a 1 + b 1 )
q
Z 0 ; V d =(a 4 + b 4 )
q
Z 0
0
(4.8)
I i = a i 0 b i
(4.9)
qZ 0
Z 0 2
Z 0 0
2 4.6
a i (i=1,2...N) b j (j=1,2...M)
2 3 2
32
3
b 1
S 11 111 S 1N
6 .
4
7
5 = .
6 . . a 1
. .
4
7
5
6 .
4
7
5
b M S M 1 111 S MN a N
(4.10)
a g a g = a 1
a 2 =0,a 3 =0 (4.10)
b 1 = S 11 a g
b 2 = S 21 a g (4.11)
b 3 = S 31 a g
49

(4.8) (4.11) V 1 I 2 , I 3
V 1 =
I 2 =
I 3 =
q
Z 0 1 (1 + S 11 ) 1 a g (4.12)
1
S 21 a g qZ 0
(4.13)
1
qZ 0
S 31 a g (4.14)
2 I O I 2 I 3
I O = I 2 0 I 3
I O =
V 1
Z 0 (1 + S 11 ) 1 (S 21 0 S 31 ) : (4.15)
(3.1) H = I O 1 F M 3 F M
1
F M =2 H V 1
H =
V 1
Z 0 1 (1 + S 11 ) 1 (S 31 0 S 21 ) 1 F M
2 (4.16)
4.6 1 (4.16)
S
V 1 1+j0V
4.7 V d
V 1 V d (4.10)
V 1 = 1+S 11B + S 14BS 41B 0 d
1 0 S 44B 0 d
! q
Z 0 1 a g (4.17)
V d = (0 d +1)1
S 41B
q
Z d 1 a g (4.18)
1 0 S 44B 0 d
(4.17) (4.18) a g V 1 V d
V 1 = (1 + S 11B)(1 0 S 44B 0 d )+S 41B S 14B 0 d
S 41B (0 d +1)
1
s
Z0
Z 0
0 1 V d (4.19)
50

0 d = Z d 0 Z 0
0
Z d + Z 0
0
(4.20)
(4.19),(4.20) Z 00 2
S ihB (i =1,4, h =1,4) S
S ihB TRL(Through Reect Line)
[30],[31] (4.16),(4.19) V d =
1+j0V
51

Z 0
Port 1
S
S
S
Port 2
a 2 b
11 12 13
2
Z
V 0
1
S 21 S 22 S 23
I 3
b 1 a 1
S 31 S 32 S 33 a 3 b 3
I 2
Z 0
Z 0
Z 0
Z 0
V g
0
V g = 2ag
Z
Port 3
Dipole antenna
Probe
4.6: 3
Port 1 Port 4
b 1 a 1
a 4 b 4
Z 0
Z 0
S
S
S
S
V g 11B
14B
V 1
0
41B
44B
V g = 2ag
Z
0
Z ′
Vd
Z d
Antenna
element
Γ d
Balun
1+j0 [V]
4.7: 2
52

Measured magnetic field [A/m]
0.06
0.05
0.04
0.03
0.02
0.01
0
Real part
Imaginary part
-0.01
-25 -20 -15 -10 -5 0 5 10 15 20 25
y [cm]
4.8: (d=3cm)
4.8 2 S (4.16)
4.9 4.8 V d =1+j0V
-15 cm y 15 cm
53

Magnetic field in 1+j0 [V] excitation [A/m]
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
-0.01
Real part
Imaginary part
-0.02
-25 -20 -15 -10 -5 0 5 10 15 20 25
y [cm]
4.9: V d =1+j0V (480MHz)
54

4.5.2
4.10
015 cm

0.015
Real
Imaginary
0.01
I [A]
0.005
0
-0.005
-15 -10 -5 0 5 10 15
y [cm]
(a) Estimated from calculated magnetic fields
0.04
0.03
Real
Imaginary
0.02
I [A]
0.01
0
-0.01
-0.02
-0.03
-15 -10 -5 0 5 10 15
y [cm]
(b) Estimated from measured magnetic fields
4.10:
56

0.025
0.02
Without error
With 1% of error
I [A]
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
-15 -10 -5 0 5 10 15
y [cm]
4.11: 1
57

0.0135
0.013
Theoretical I n
Estimated I n
’
Interpolated
points
I n (y) , I n ’(y)
0.0125
0.012
0.0115
0.011
0.0105
0.01
10 12 14 16 18 20 22
y [cm]
4.12: I n I 0 n
(N =7)
(2.4)
1I
(4.21)
1I =
vu
u
t 1 N
NX
n01
jI n 0 0 I n j 2 (4.21)
I n 31 ) N=31
I 0 n 4.12 7 I 0 n
1I =0
cm 31
16 11 7 6 4 3 4.13 7
4.13
58

0.005
0.004
I [A]
Difference D
0.003
0.002
0.001
0
0 3 7 10 16 20 30
Decreased estimation points
4.13:
59

0.015
Measurement
Calculation(MoM)
excited) [A]
0.01
Real part
Current (V d
= 1+j 0 〔
0.005
0
V〕
-0.005
Imaginary part
-15 -10 -5 0 5 10 15
Balun
y [cm]
4.14: (480 MHz)
4.5.3
(4.19) 7 (2.4)
1+j0V
4.14
(2.4)
0 10 010
( B) 4.5.1
60

0.0035
0.003
Measurement
0.0025
Real part
Actual Current [A]
0.002
0.0015
0.001
0.0005
0
-0.0005
-0.001
Imaginary part
-15 -10 -5 0 5 10 15
Balun
y [cm]
4.15:
(480 MHz)
4.6
1+j0 V
ja g j 2
(4.12), (4.19) jV d j
jV d j =
q
Z 0
0
S
41B (0 d +1)
1 (1 + S 11 ) 1jag j (4.22)
(1 + S 11B )(1 0 S 44B )+S 41B S 14B 0 d
V d V d = jV d j+j0 V
4.15 (4.22) V d
ja g j 2
0 dBm(1 mW)
61

4.7
30 cm 1mm 2
3
480MHz
2
62

5
5.1
0
63

x
(24, 15, 0)
y
z
(24, 0, 0)
Antenna
elements
(24, -15, 0)
Scanning probe
(for antenna elements)
Semi-Ridged
cable
Connector
(12, 0, 0)
Scanning probe
(for cables)
Test cable
(0, 0, 0)
Unit : [cm]
5.1:
5.2
3
2 5.1
y
x 30 cm x =24
cm
64

5.3
2
2
5.3.1
5.2
30 cm 1mm 5.2 (a) 5.2 (b)
2:1
65

Antenna element (φ = 1mm)
Semi-rigid
cable
(φ = 2mm)
12cm
Connector
x
Test cable
y
z
(a) Symmetric element (15cm, 15cm)
(b) Asymmetric element (20cm, 10cm)
5.2:
66

Antenna element (30cm, φ=1mm)
3.5mm
7cm
Parallel two
-wire line(4cm)
Soldered
3cm
Balun (TP-103)
Connector
(a) Dipole element
with detachable balun
Test cable
(b) Dipole element
with soldered balun
y
x
z
5.3:
5.3.2
5.3
4 (M/A Com , TP-103)
5.3 (a) 4
4cm 3mm 2 4
5.3(a)
5.3 (b) 2
30 cm 1mm
67

0.015
Measurement
0.01
Current [A]
0.005
0
Real part
Imaginary part
-0.005
-0.01
-15 -10 -5 0 5 10 15
y [cm]
5.4: 480 MHz
5.4
5.2 (b) 480 MHz 5.4
5.4
1+j0V
4.14
2mA
5.5
5.2 2
120 mm
68

5.5 (0cm
y 30 cm) 300 mm Symmetric,
150 mm-150 mmAsymmetric, 200 mm-100 mm
x =24cm
24 cm

(for solid line), y [cm] (for dotted line)
50
45
40
35
30
25
20
15
Asymmetric elements
Feed line
Elements
Semirigid
cable
No currents
exist.
Dipole elements
x [cm]
10
5
Test
cable
connector
0
0 0.005 0.01 0.015 0.02 0.025 0.03
| I | [A]
x
(for solid line), y [cm] (for dotted line)
50
45
40
35
30
25
20
15
(a) Asymmetric antenna elements
Symmetric elements
Feed line
Elements
Semirigid
cable
z
No currents
exist.
y
Dipole elements
x [cm]
10
5
Test
cable
connector
0
0 0.005 0.01 0.015 0.02 0.025 0.03
| I | [A]
x
(b) Symmetric antenna elements
z
y
5.5:
480 MHz
70

x [cm]
Antenna
element
Feeder
50
45
40
35
30
25
20
15
10
5
Symetric dipole (Fig. 5.2(a))
Asymetric dipole (Fig. 5.2(b))
Dipole with balun (Fig. 5.3(a))
Dipole soldered balun (Fig. 5.3(b))
0
0 10 20 30 40 50 60
I ratio [%]
5.6: 480
MHz
71

5.6
4
0
10
50
1
2
2 2
72

6
2
6.1
4 5
1
1
2
73

x
I
I 2
1
H 3
y
z
I n H1
H 2
H M
I N
H m
Plane of current
Space of measurement
6.2 2
6.1: 2
6.1
x y
y
2 (6.1) r
H ' (6.2) (2.4)
k 1l
I
H ' = I1le0jkr
4
jk
r + 1 r 2 !
sin (6.1)
74

y
x
z
Emitter element
30 cm
I (e) N
H (e) M
H (e) m
I (e) n
r (ee) mn
Dl
r (ed) mn
I (d) N
I (e) 1
w
H (e) 1
r (dd) mn
H (d) M
w’
I (d) n
H (d) m
Director element
24 cm
I (d) 1
H (d) 1
Scanned
Magnetic
fields sensor
6.2: 2
2
6
4
3
H 1
.
7
H M
2
5 = 6
4
3
11 111 1N
.
.. . .
7
5
M 1 111 MN
2
6
4
3
I 1
.
7
5
I N
(6.2)
6.2 (x 0 y
y y 0 z x
y
75

x
6.2 I (e)
n
( n =1,2,3,, N) (e) n
H (e)
m
( m =1,2,3,, M) (e)
m x I (d)
n
( n =1,2,3,, N)
(d) n H (d) ( m =1,2,3,
m
, M) (d) m x
r (ee)
mn r(ed) mn
n
m r (de)
mn
r (dd)
mn
n
m
w
w 0
1l
0
6.3(a) ' =2
I (e)
n
H (ee)
m
2
6
4
H (ee)
1.
H (ee)
M
3 2
7
5 = 6
4
(ee)
11
111 (ee)
1N
.
. . . .
(ee)
M1
111 (ee)
MN
m x
32
7
5
6
4
I (e)
1.
I (e)
N
3
7
5
(6.3)
x H x H ' sin ' ' =
=2 (6.1)
sin =
w
r (ee)
mn
(6.4)
(ee)
mn
(2.3) d w r mn r (ee)
mn
76

I (d)
n
m x
H (ed)
m
2
6
4
H (ed)
1.
H (ed)
M
3 2
7
5 = 6
4
(ed)
11
111 (ed)
1N
.
. . . .
(ed)
M1
111 (ed)
MN
x (ed)
mn
sin = w0
r (ed)
mn
32
7
5
6
4
I (d)
1.
I (d)
N
3
7
5
(6.5)
(6.6)
sin ' = w w 0 (6.7)
(2.3) mn r mn r (ed) d w
mn
x H (e)
m
2
6
4
H (e)
1
.
H (e)
M
3 2
7
5 = 6
4
H (ee)
1.
H (ee)
M
( m =1,2,3,, M)
3 2
7
5 + 6
4
H (ed)
1.
H (ed)
M
3
7
5
(6.8)
6.3(b)
I (e)
n
2
6
4
(de)
m x H
m
H (de)
1.
H (de)
M
3 2
7
5 = 6
4
I (d)
n
x H (dd)
m
2
6
4
H (dd)
1.
H (dd)
M
3 2
7
5 = 6
4
(de)
11
111 (de)
1N
.
. . . .
(de)
M1
111 (de)
MN
32
7
5
6
4
I (e)
1.
I (e)
N
3
7
5
(6.9)
m
(dd)
11
111 (dd)
1N
.
... .
(dd)
M1
111 (dd)
MN
32
7
5
6
4
I (d)
1.
I (d)
N
x H (d)
m
3
7
5
(6.10)
(6.8)
77

H (de) H (dd)
m m
2
6
4
H (d)
1
.
H (d)
M
3 2
7
5 = 6
4
H (de)
1.
H (de)
M
3 2
7
5 + 6
4
H (dd)
1.
H (dd)
M
3
7
5
(6.11)
(6.8) (6.11)
2
6
4
H (e)
1
.
H (e)
M
H (d)
1
.
H (d)
M
3
7
5
=
2
6
4
(ee)
11 111 (ee)
1N
.
.. . .
(ee)
M1
111 (ee)
MN
(de)
11
111 (de)
1N
.
.. . .
(de)
M1
111 (de)
MN
(ed)
11 111 (ed)
1N
.
.. . .
(ed)
M1
111 (ed)
MN
(dd)
11
111 (dd)
1N
.
.. . .
(dd)
M1
111 (dd)
MN
3 2
7
5
6
4
I (e)
1.
I (e)
N
I (d)
1
.
I (d)
N
3
7
5
(6.12)
(de)
mn (dd) mn
(2.3) (ee)
mn
r(ee)
mn
r(de)
mn
r(dd)
mn
x
y 0 z
x 0 z (sin ')
78

w
Elements
I (e)
e
j =p/2
H (e)
Loop probe
I (d)
j
d w’
x
y
z
(a) Probe scanning near the emitter
I (e)
e
j
w’
Elements
I (d)
d
j=p/2
H (d)
Loop probe
w
x
(b) Probe scanning near the director
y
z
6.3:
79

Emitter: 30cm
= 1mm) (f
3cm or 6cm
Director: 24cm
(f = 1mm)
y
x
z
6.4: 2
6.3 2
1926
[32]
2 1
2
6.4 2
30 cm (Emitter) 24 cm (Director) 2
1mm
2
4
80

6.4
6.2 (6.12) y 0 z
x 0 z (sin ')
6.4
30 cm 24 cm 2
1mm
0 480 MHz
3 2
11.5 mm
2
1+j0V 6.5
I S
l 0 e
(3.9)
H
l 0
e
(6.12)
[16]
2
6.6 w 3cm
1l 10 mm
M= 51,N= 51-25 cm z 25 cm
6.7 w 3cm 6cm
6.6 6.7 z -15 cm,
z 15 cmz -12 cm, z 12 cm
0
x
81

Emitter : 30cm
Director : 24cm
3cm
1.15cm
H
I s
Square small loop( l ′ )
30cm
e
z
x
y
6.5:
82

Current [A]
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
On the Emitter
Real
part
Estimated
Theoretical
-0.002
Imaginary part
-0.004
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
0.002
On the Director
Real part
Estimated
Theoretical
0
Current [A]
-0.002
-0.004
Imaginary part
-0.006
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
6.6:
3 cm)
83

0.016
0.014
0.012
0.01
On the Emitter
Estimated
Theoretical
Current [A]
0.008
0.006
0.004
0.002
0
Real
part
-0.002
Imaginary part
-0.004
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
0.002
On the Director
Estimated
Theoretical
0
Real part
Current [A]
-0.002
-0.004
Imaginary part
-0.006
-25 -20 -15 -10 -5 0 5 10 15 20
25
y [cm]
6.7:
6 cm)
84

6.5 2
2
2 1:4
2
200 y 0 z
3
2 11.5 mm 2 11.5 mm
3.11(b) y 0 z
6 7 m4 m2.4 m 6.2
2 30 mm
10 mm
S 3
(Anritsu MS4623B)
S
4.5
6.8 6.9 480MHz 1+j0
V1+j0V
6.8 3cm 6.9
6cm (6.12)
5 1 M= 51,N= 11
w 3cm-25 cm z 25 cm
6.8 6.9
0
85

0.014
0.012
On the Emitter
Estimated
Theoretical
Current [A]
0.01
0.008
0.006
0.004
Real
part
0.002
0
Imaginary part
-0.002
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
0.002
On the Director
Real part
Estimated
Theoretical
0
Current [A]
-0.002
-0.004
Imaginary part
-0.006
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
6.8: 3cm
86

0.016
0.014
On the Emitter
Estimated
Theoretical
0.012
Current [A]
0.01
0.008
0.006
Real
part
0.004
0.002
0
Imaginary part
-0.002
-25 -20 -15 -10 -5 0 5 10 15 20
y [cm]
25
0.002
On the Director
Estimated
Theoretical
0
Real part
Current [A]
-0.002
-0.004
Imaginary part
-0.006
-25 -20 -15 -10 -5 0 5 10 15 20
25
y [cm]
6.9: 6cm
87

3cm6 cm
0
6.9 6.10
2
88

0.016
0.014
On the Emitter
Estimated
Theoretical
0.012
0.01
Current [A]
0.008
0.006
0.004
Real
part
0.002
0
Imaginary part
-0.002
-25 -20 -15 -10 -5 0 5 10 15 20
25
y [cm]
0.002
0
On the Director
Real part
Estimated
Theoretical
Current [A]
-0.002
-0.004
Imaginary part
-0.006
-25 -20 -15 -10 -5 0 5 10 15 20
25
y [cm]
6.10:
6cm
89

6.6
2 2
2
2
2
2
3
2
4
2 2
y
6.1 x
y x y
y x
2
90

7
2
3
2
3
4
3 2
2
91

5
0
6 1
2 2
2 1
2 2
2
6
92

A
2 (2.1)
[33]
A.1
Maxwell
r2H = J + " @E
@t
r2E = 0 @H @t
r1E = "
(A.1)
(A.2)
(A.3)
r1H = 0 (A.4)
(A.4)
A
B = H = r2A
(A.5)
(A.5) (A.2)
r2E = 0 @ (r2A) (A.6)
@t
93

2
r2E + @ (r2A) =0
@t !
r2 E + @A =0 (A.7)
@t
(A.7) r2 0 1 r
(A.7)
E + @A
@t = 0r
(A.8)
0r
E = 0r 0 @A
@t
(A.9)
A (A.5)
H
A.2
(A.9) A
(A.5) (A.9) (A.1)
r2(r 2A) =J 0 "r
@
@t
!
0 " @2
@t 2
2
r(r 1A) 0r 2 A = J 0 "r
@
@t
!
0 " @2
@t 2
(A.10)
(A.11)
r 2 A 0 " @2
@
= 0J + "r
2
@t @t
!
+ r(r 1A) (A.12)
A r2A r1A
r1A (
r1A = 0"r @
@t
(A.13)
1
r2r =0
2
r2(r 2A) =rr 1 A 0r 2 A
94

(A.13) (A.12) A
r 2 A 0 "r @2 A
= 0J (A.14)
2
@t
A A(r)e j!t 2 e j!t 0! 2
(A.14)
r 2 A(r)+! 2 "A(r) =0J(r)
(A.15)
A(r) = 4
ZZZ J(r
0
)e
0jkR
R
dx 0 xy 0 xz 0
(A.16)
r = xa x + ya y + za z (A.17)
r 0 = x 0 a x + y 0 a y + z 0 a z (A.18)
R = jr 0 r 0 j (A.19)
k 2 = ! 2 " (A.20)
A.3
A.1 y J r
(A.16)
I 1l 1l
y (A.16) J;A y
r 0 0 A
A = A y a y = 4 r
I1le 0jkr
a y
(A.21)
A r = A y cos
A = 0A y sin (A.22)
A ' = 0
95

x
ϕ
∆l
I
θ
r
P
z
y
H x
H x = H ϕ
H ϕ
sin ϕ
A.1:
96

(A.5) (A.22) H
H r = 1 (r2A) r
" #
1 @
=
r sin @ (sin A ') 0 @A
@'
= 0 (A.23)
H = 1 (r2A)
= 1 "
1 @A 1 #
r
r sin @' 0 @
r @r (rA ')
= 0 (A.24)
H ' = 1 (r2A) '
"
@
@r (rA ) 0 @A r
#
= 1
A y (A.21)
"
@
= 1 0 sin @(rA y) @ cos
0 A y
r @ @
= sin #
"0 @ r @r (rA y)+A z
= sin 0 @A y
@r
I1l sin
H ' = 0
4
= I1le0jkr
4
@
@r
e 0jkr
!
r
jk
r + 1 !
sin
r 2
#
(A.25)
(A.26)
(2.1) H ' (A.23) (A.24)
0
97

B
(Coecient Matrix)
1
Gauss-Jordan (LU
Gauss-Seidel
(Conjugate Gradient method; CG
H = I 1 b=Ax
x
Gauss-Seidel
1
Ax = b
(B.1)
b x (2.4)
A A H (B.1)
A H Ax = A H b
(B.2)
A R x = A H Ax (B.3)
b 0 = A H b (B.4)
98

M x N A M 2 N
A H A A R A R N 2 N
(B.3) (B.4) 1
A R x = b 0
(B.5)
x
x x 0 (B.5) r i
r 0 = b 0 0 A R x 0 (B.6)
p 0 = r 0 (B.7)
r i i x 0 0
kr i k > 10 010
(B.8)
kr i k > 10 08
x i
= (p i 1 r i )
(p i 1 A R p i )
x i+1 = x i + p i
r i+1 = r i 0 A R p i (B.9)
= kr i+1k 2
kr i k 2
p i+1 = r i+1 + p i
i = i +1
(p i 1 r i ) p i r i kr i k r i
(B.9)
[16][17]
99

C
3
3 (3.19)
C.1 6dB
C.1(a)
V 0 m V 0 m = 1 2 V open (C.1)
V open 6dB
V m C.1
V m = 1 4 V open
(C.2)
C.1(b) i 0
a
i 0 = V open
(C.3)
a
Z 0 + Z in
Z in
V open
i a = 1 2 1
Z 0 + Z in
C.2C.4
i a = 2 1 V open
Z 0 + Z in
(C.4)
(C.5)
(3.19) C.5
100

Transmission
line
Transmission
line
v open (t)
Z 0
Z 6 dB
0 Z 0 Z 0 v m (t)
Attenuator
1
vm ( t)
= vopen
( t)
4
(a)
i a (t)
v open (t)
Z 0
Z 6 dB
0 Z
Attenuator 0 Z in
I
a
{ i ( )}
( ω ) = t
F
a
(b)
C.1: i a (!)
101

D
D.1
1 (Condition number)
[17] (ill-posed)
1
A 1 cond(A)
cond(A) =kAkkA 01 k
(D.1)
kAk a ij (i=1,2,..m, j=1,2,...n)
kAk =
vu
u
t m X
nX
i=1 j=1
a
ij a ij
(D.2)
(D.1) Ax = b x A b
1
D.2
102

H = I
(2.3)
30 cm d =
3cm1cm
(2.2) (M = N =51)
1.6107E3 (2.4)
M =51;N =111l =5cm5.8946
(D.2)
103

D.3
4.3
I n (y) I 0 (y)
n
Error(y)
Error(y) =
I 0 (y) 0 I n n(y)
I n (y)
2 100 [%] (D.3)
D.1
015cm < = y < = 15cm y =0cm
01 1
0.1 0.5 1
2 5 10
104

Error (y) [%]
1200
1000
800
600
Given random error 0.1%
0.5%
1%
2%
5%
10%
400
200
0
-15 -10 -5 0 5 10 15
y [cm]
(a) Real part
Error (y) [%]
600
500
400
300
200
Given random error 0.1%
0.5%
1%
2%
5%
10%
100
0
-15 -10 -5 0 5 10 15
y [cm]
(b) Imaginary part
D.1:
105

D.2 5 1
D.1 D.2
10
106

Error (y) [%]
4
3.5
3
2.5
2
1.5
Given random error 0.1%
0.5%
1%
2%
5%
10%
1
0.5
0
-15 -10 -5 0 5 10 15
y [cm]
(a) Real part
Error (y) [%]
16
14
12
10
8
6
Given random error 0.1%
0.5%
1%
2%
5%
10%
4
2
0
-15 -10 -5 0 5 10 15
y [cm]
(b) Imaginary part
D.2: 5 1
107

D.4
I n (y) I 0 (y)
n
Error(y)
Error(y) =
I 0 (y) n 0 I n(y)
I n (y)
2 100 [%] (D.4)
D.3 x,y,z
01 1
(1cm) 1
015cm < = y < = 15cm y =0cm
D.3 x; y z
108

50
45
40
X axis
Y axis
Z axis
Error (y) [%]
35
30
25
20
15
10
5
0
-15 -10 -5 0 5 10 15
y [cm]
(a) Real part
100
80
X axis
Y axis
Z axis
Error (y) [%]
60
40
20
0
-15 -10 -5 0 5 10 15
y [cm]
(b) Imaginary part
D.3:
109

E
-25 cm < = y < = 25 cm 1cm
51 -25 cm < = y < = 25 cm
1l,
-25 cm < = y < = 25 cm
4 ( 30
cm 4.3
1l 0 1l E 4
a) (2.2)
b) 4 6
E.1 E.3 E a) b)
c)d)
-25 < = y < = -15 cm 15 cm < = y < = 25 cm
0 E
a) cond(A) 3
cond(A H A)
110

E.1:
(1l 0 ) (1l)
a) 51 (10 mm) 51 (10 mm) 50 cm 1.6107E3
b) 51 (10 mm) 11 (50 mm) 50 cm 5.8946
c) 51 (10 mm) 31 (10 mm) 30 cm 2.2642E6
d) 51 (10 mm) 51 (6 mm) 30 cm 4.9598E18
0.015
a) 51p -> 51p
b) 51p -> 11p
0.01
Current [A]
0.005
0
-0.005
-0.01
-25 -20 -15 -10 -5 0 5 10 15 20 25
y [cm]
E.1: b) (1l 0 > 1l)
111

0.015
a) 51p -> 51p
c) 51p -> 31p (∆ keep)
0.01
Current [A]
0.005
0
-0.005
-0.01
-25 -20 -15 -10 -5 0 5 10 15 20 25
y [cm]
E.2: c) (1l 0
=1l)
0.015
0.01
a) ∆ l :10mm -> ∆ l’ :10mm
d) ∆ l :10mm -> ∆ l’ :6mm
(51points)
Current [A]
0.005
0
-0.005
-0.01
-25 -20 -15 -10 -5 0 5 10 15 20 25
y [cm]
E.3: d) (1l 0 > 1l)
112

E.1 E.3
y
d)
3 0
c) d) E.2 E.3
c) d)
113

F
1+j0V
5 5.4
1+j0V
(4.16)
H =
V 1
Z 0 1 (1 + S 11 ) 1 (S 31 0 S 21 ) 1 F M
2
(F.1)
V 1
S
F.1
F.1 l Z d
a g
a i (i=1, 4)b j (j=1, 4)
a 1 = a g (F.2)
a 4 = 0 d b 4 (F.3)
b 1 = S 12 S 21 a g 0 d (F.4)
b 4 = A 21 a g (F.5)
114

Port 1 Port 4
b 1 a 1
a 4 b 4
Z 0
Z 0
a g
Z 0
− jβl
e
0
e
− jβl
0
Z d
V 1 Vd
Antenna
Γ d
l
Test cable
Connector
Semi-Rigid cable
element
F.1:
V 1 ;V d
q
V 1 = (a 1 + b 1 ) Z 0
= (1 + S 12 S 21 0 d )a g
qZ 0 (F.6)
V d = (a 4 + b 4 )
q
Z 0
= (0 d +1)S 21 a g
qZ 0 (F.7)
(F.6) (F.7) a g
V 1 = 1+S 12S 21 0 d
(0 d +1)S 21
1 V d (F.8)
S S 11 =0, S 22 =0,
S 21 = S 12 = e 0jl
V d =1+j0V
V 1 = 1+0 d 1 e 02jl
(0 d +1)e 0jl (F.9)
115

(F.9) (F.1) 1+j0V
116

G
2
5 1
6
2
4 2
1 1
6.4
2
G.1
G.1 2
y x 6.4
y
x 1 4
x =0cm
1 (1line)x = 03cm
2 (2lines)x =0cm, 06cm
3 (3lines)x =0cm, 03cm, 06cm
117

Two-Element
Yagi-Uda antenna
3cm
3cm
Emitter
30cm
3cm
6cm
x
Director
24cm
Loop
probe
y
z
G.1: 3
4 (4lines)x =0cm, 03cm, 06cm, 09cm
z =3cm
G.2
025cm < = y < = 25cm
1cm 51 1 2
025cm < = y < = 25cm
1cm 1 (1line)
5mm 101
G.2 x 2
x
( G.3)
G.4 3 3
3
30cm 24cm 2
118

Current [mA]
Current [mA]
16
14
12
10
8
6
4
2
0
-2
-4
8
6
4
2
0
Emitter(30cm)
Real
Director(24cm)
Theoretical
1 line H data
2 lines
3 lines
4 lines
Imaginary
-2
Imaginary
-4
-15 -10 -5 0 5 10 15
y [cm]
G.2: x 2
Real
3cm 1mm
119

Current[mA]
16
14
12
10
8
6
4
Emitter (30cm)
Theoretical
Simulation
(x= 0cm,-3cm)
(x=-1cm,-4cm)
2
0
-2
Current[mA]
-4
2
0
-2
-4
Director (24cm)
-6-15 -10 -5 0 5 10
y [cm]
G.3: 2 (2
120

16
14
12
10
Emitter (30cm)
Theoretical
H data 1line
2lines
3lines
4lines
5lines
Current [mA]
8
6
4
2
0
-2
-4
-15 -10 -5 0 5 10 15
y [cm]
6
4
Director1(24cm)
Current [mA]
2
0
-2
Current [mA]
-4
-6
6
4
2
0
-2
-4
Director2(24cm)
-6
-15 -10 -5 0 5 10 15
y [cm]
G.4: x (3
121

Current [mA]
Current [mA]
16
14
12
10
8
6
4
2
0
-2
4
2
0
-2
Emitter(30cm)
Real
Director(24cm)
Imaginary
Imaginary
Real
Estimated
Theoretical
-4
-15 -10 -5 0
y [cm]
5 10 15
G.5: (x ) 2
G.2
2 x
2
z
G.5 x = 03cm, z =2cm, 3cm
2
G.1 x 1
z 2 2
2
122

Bernard Huyart Xavier Begaud Radiofrequency Research
Group
123

[1] 38 "
" June ,1990
[2] 89 "
" April ,1997
[3] 13 2005
[4] 2006 7 25 "
"
[5] T. Hondou et al."Passive Exposure to Mobile Phones: Enhancement of Intensity
by Reection"Journal of the Physical Society of Japan Vol. 75 No.
8, pp.084801-087805, August, 2006
[6] ""
1993
[7] K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving
Maxwell's Equations in Isotripic Media," IEEE Transaction on Antennas and
Propagations, Vil.14, No.4, 1966
[8] E. Hankui, T. Harada, and T. Kuriyama, Estimation of Current Distribution
on Cellular Telephone Antennas Aected by Human Body Interaction,
IEICE Trans. on Electron. Vol. E84-C, No. 9, Sept 2001, pp. 1260-1263
[9] T. Harada, N. Masuda, and M. Yamaguchi, Near-Field Magnetic Measurements
and Their Application to EMC of Digital Equipment, IEICE Trans.
Electron., Vol. E89-C, No. 1, Jan 2006
124

[10]
Vol.J87-C No.3pp.335-342Mar. 2004
[11] S. Hayashi, K. Masuda, and K. Hatakeyama,Radiated emission estimation
of a metallic enclosure model source by inverse-forward analysis, IEICE
Trans. Commun., Vol. E78-B, No. 2, pp. 173-180, Feb. 1995
[12] 2002
B-4-60pp.411Mar. 2002
[13]
Vol.J88-C No.12pp.1159-1166Dec. 2005
[14] W. L. Stutzman, G. A. Thiele, Antenna Theory and Design Second Edition,
John Willey & Sons, Inc., 1998
[15] A
Vol. 117-ANo. 5pp. 450-455May 1997
[16] T. K. Sarkar, Application of Conjugate Gradient Method to Electromagnetics
and Signal Analysis, Elsevier Science Publishing Co., Inc, 1991
[17] 1993
[18] S.Ishigami, H.Iida, and T.Iwasaki, "Measurements of complex antenna factor
by the near-eld 3-antenna method," IEEE Trans. on Electromagn. Compat.,
Vol.38, No3, pp.424-432, Aug. 1996
[19] T. Iwasaki and K. Tomizawa: Systematic uncertainties of the complex
antenna factor of a dipole antenna as determined by two methods, IEEE
Trans. Electromagn. Compat., Vol.46, No.2, pp.234-245, 2004.
[20]
Vol.J-80B-II, No.12, pp.1091-1098, December 1997
125

[21] M. Ishii, T. Iwasaki, "A method for nding the direction of arrival of a single
short pulse by the waveform reconstruction, IEICE Trans. on Communications,
Vol.E83-B, No.3, pp.453-459, 2000
[22] M. Takashima, K. Fujii and T. Iwasaki,Measurement of magnetic complex
antenna factor of a double-gapped shielded loop antenna,IEICE Trans. On
Commun. vol. J84-B, No.11, pp. 2066-2070, Nov. 2001.
[23] I. Yokoshima: Absolute measurements for small loop antenna for RF magnetic
eld standards,IEEE Trans. Instrum. and Meas., Vol.IM-23, No.3, pp.
217-221, Sept. 1974.
[24] 1999
[25] L. Hamada, G. Nakanishi, T. Iwasaki, "Waveform Reconstruction of Electromagnetic
Fields by Using Log-Periodic Dipole Array Antenna," EMC EU-
ROPE 2002, September, 2002
[26] L. Hamada, N. Otonari and T. Iwasaki: Measurement of electromagnetic
elds near a monopole antenna excited by a pulse, IEEE Trans. Electromagn.
Compat., Vol. 44, No.1, pp.72-78, 2002.
[27] Pocklington H. E., "Electrical oscillation in wires," Camblidge Phil. Soc.
Peoc., 9. pp.324-332. 1987
[28] T. Harada, N. Masuda, and M. Yamaguchi, Near-Field Magnetic Measurements
and Their Application to EMC of Digital Equipment, IEICE Trans.
Electron., Vol. E89-C, No. 1, Jan 2006
[29]
1992
[30] K. Fujii and T. Iwasaki,Evaluation of Sites for Measuring Complex Antenna
Factors: Comparison of Theoretical Calculation and TRL-Based Experiment,
IEICE Trans. on Commun., Vol. E83-B, No. 10, pp. 2419-2426, Oct. 2000
126

[31] TRL
S B, vol. J86-B, no.7 pp.1050-
1061, July 2003
[32] 2001
[33] 1995
127

1.
(1) Akiko KOHMURA, Takashi IWASAKI
"Determination of Magnetic Complex Antenna Factor of Double-
Output Shielded Loop Antenna Using an Equivalent Circuit,"
IEEJ, Transaction on Fundamentals and Materials, Vol.126, No.6, pp.414-
419, June 2006
( 3 )
(2) ,
" 2
,"
B, Vol.J89-B, No.12, pp.2237-2244, December 2006
( 2 4 5 )
128

2.
(6 )
(1) ,
","
B, Vol.J87-B, No.7, pp.1033-1038 , July 2004
()
(2) Akiko KOHMURA, Tomonori HASEGAWA, Takashi IWASAKI
"A Method for Measuring Reection Distribution of The Electromagnetic
Absorber by A Scalar Inverse Scattering,"
EMC'04 Sendai, 2B3-1, pp.321-324, June, 2004
(3) Akiko KOHMURA and Takashi IWASAKI
"Estimation of Current Distribution on Dipole Antenna Elements
Using a Double-Output Shielded Loop Probe,"
EMC Europe 2006, ABS-37, pp. 750-755, September 2006
129

(4) ,
,
, IM-01-23, pp.33-38, June 2001
(5) ,
,
13 , pp.27, March 2002
(6) ,
,
15 , 1-156, pp.193, March 2003
(7) ,
,
, IM-03-31, pp.11-15, June 2003
(8) ,
,
15 , pp.246, August 2003
(9) ,
,
, EMT-03-45, pp.47-51, November 2003
(10) ,
,
, EMCJ-14-8, pp.9-12, April 2004
130

(11) ,
,
, pp.19-28, June 2004
(12) , ,
,
, IM-04-16, pp.23-28, June 2004
(13) , ,
,
, IM-04-19, pp.41-46, June 2004
(14) ,
2 ,"
2005 , B-4-64, pp.38September
2005
(15) ,
,
, IM-06-18, pp.13-18, June 2006
(16) ,
,
, IM-06-19, pp.19-24, June 2006
(17) ,
2 2
,
, IM-06-51, pp.37-42, November 2006
131

(18) ,
2
,
2007 , B-4-63March 2007
(19) ,
2
,
2007 , B-4-62, March 2007
3.
(1) 15 (7))
(2) 16 9 17 5 (ENST)
JASSO
132

( )
1978 8 8
1997 3
1997 4
2001 3
2001 4
2003 3
2003 4
2004 9 2005 5
(Ecole Nationale Superieure
des Telecommunications)
2007 3
133