
694 Microwave Engineering
Relations Required
Surface resistance R
s
= √(
ωμ
/2
σ
)
ω
= 2
π
f = 2
π
× 10
10
(
ωμ
/2
σ
) = (2
π
× 10
10
× 4
π
× 10
−7
)/(2 × 5.8 × 10
7
)
= (8
π
2
× 10
3
)/(11.6 × 10
7
) = 0.6896
π
2
× 10
−4
R
s
= √(0.6896
π
2
× 10
−4
) = 0.0261 Ω
A
w
b t
b t
b t
b t
t
= +
−
+
+
−
−
= +
×
−
+
+
−
× −
1
2 1 2
1
2 10
8 2
1 8 2
8 2
2 8 2
2π π
ln ln == 4 7813.
B
b
w t
t
w
w
t
= +
+
+ +
= +
× + ×
1
0 5 0 7
0 5
0 414 1
2
4
1
8
0 5 10 0 7
( . . )
.
.
ln
. .
π
π
22
0 5
0 414 2
10
1
2
4 10
2
1 3577.
.
ln .+
×
+
×
=
π
π
a. √
ε
r
Z
0
= 50 × √5.23 = 114.346 < 120
α
c
s
R
Z b
B= =
×
×
× = ×
−
0 16 0 16 0 0261
50 8
1 3577
0
. . .
. 1.4175 10 Nep/m
5
b. √
ε
r
Z
0
= 50 × √6.25 = 125 > 120
α
ε
π
π
c
s r
R Z
b t
A=
×
−
=
× × × ×
−
−
−
2 7 10
30
2 7 10 0 0261 6