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In-Depth Information
Z
xx
+
H
+
Z
yx
+
H
2
2
Z
xy
tan
Z
yy
tan
=
tan
2
1
+
H
k
1
tan
2
(1
.
89)
+
k
2
tan
+
k
3
H
H
=
+
tan
2
1
H
k
1
sin
2
=
+
k
2
sin
H
cos
+
k
3
cos
2
,
H
H
H
where
k
1
=
Z
xy
+
Z
yy
2Re
Z
xx
Z
xy
+
Z
yx
Z
yy
,
+
Z
yx
2
2
2
2
,
k
2
=
k
3
= |
Z
xx
|
.
The scalar indicator
Z
H
can be naturally called a
H
-polarized impedance. It is
a function of the angle
H
defining the direction of the magnetic field polarization
axis.
Determine
H
,atwhichthe
H-
polarized impedance has a maximum and mini-
mum. The condition
dZ
H
d
H
=
0
gives the equation
k
2
k
3
−
tan 2
H
=
k
1
,
(1
.
90)
max
H
mi
H
, differing by
which has two solutions,
2.
Similar to the
H-
polarized impedance
Z
H
, we introduce a scalar indicator
Z
E
defined as the ratio between the Euclidean norms
and
/
E
and
H
of electric and
magnetic fields
E
(
E
x
,
E
y
) and
H
(
H
x
,
H
y
),the electric field being linearly polar-
ized at an angle
E
to the original
x
axis:
|
E
·
E
x
+
E
y
2
E
x
+
E
y
2
E
x
|
E
E
E
y
Z
E
(
E
)
=
H
=
=
H
y
=
H
y
H
x
+
2
H
·
H
H
x
H
y
2
|
H
x
|
+
+
E
y
2
2
|
E
x
|
(1
.
91)
=
Y
xx
E
x
+
Y
xy
E
y
Y
yx
E
x
+
Y
yy
E
y
2
2
+
1
+
tan
2
E
=
2
,
Y
xx
+
E
+
Y
yx
+
E
2
Y
xy
tan
Y
yy
tan
