
37-11Permittivity Measurement
where
f z
e
r
e
r
e
r
j r j r j r
( ) cos( )= + −
− − −
β β β
β
d d d
d
1 2
1 2
2 ⋅
(37.37)
r z a
1
2 2
= − +( )
(37.38)
r z a
2
2 2
= + +( )
(3
7
.39
)
r z a= +
2 2
(3
7
.40
)
ωµ
β
µ
ε
η
0
d
0
Intrinsic impedance of the medium= = =
*
(37.41)
ε ε ε
σ
ωε
* = −
0
0
r
j
(37.42)
β ω µ ε
d 0
2 2
= *
(37.43)
Since
th
e
in
put
im
pedance
Z
in
is known precisely aer measurement, Equation 37.36 can be solved
nu
merically
fo
r
co
mplex
β
d
using a root-nding routine. e material characteristics are then deter-
mined
f
rom
E
quations
3
7
.42 a
nd
3
7
.43.
37.3.4 Nondestructive Method for Measuring
theComplex Permittivity of Materials
Most of the techniques described thus fa ...