Environmental Engineering Reference
In-Depth Information
η
−
Z
ANT
|
S
11
|
=
(5.36)
η
+
Z
ANT
η
=
μ
0
/
ε
m
and
Z
ANT
is the antenna impedance. Equation (5.36) shows that
where
S
11
(
ε
m
.
It is important to underline that in the previous equations the thickness of the
material sample (
d
) in front of the antenna is assumed as semi-infinite. This as-
sumption remains valid as long as the power fed into the antenna is sufficiently
low. In this way, the antenna is not affected by what is beyond the back of the
MUT (i.e., only the reflections at the front-face of the MUT have to be considered)
[see Fig. 5.15].
It is worth pointing out that Eqs. (5.33) - (5.35) represent a simplified model
for describing the dependence of the resonant frequency on the relative dielectric
permittivity. Indeed, a more accurate model should also take into account the effect
of dielectric losses (by considering the complex relative permittivity of the material
in which the antenna radiates) and the thickness of the MUT [6]. Nevertheless, as
confirmed by the experiments reported in the following subsection, (5.33) - (5.35)
provide sound qualitative information on the dependence of
f
res
on
f
)
of the antenna is intrinsically associated to
ε
m
.
5.6.2
Experimental Validation of the Method: Measurements on
Moistened Sand Samples
The used antenna is a simple and inexpensive
2-resonant microstrip antenna re-
alized on an RF35 substrate with a coaxial/transmission-line excitation [see Fig.
5.16]; its working frequency (in air) is approximately 2 GHz.
The antenna was fed through an SMA connector, thus allowing performing the
SOL calibration measurements as required by the TD/FD combined approach [11].
λ
/
5.6.2.1
Validation of the Method on Reference Materials
Preliminary measurements with the antenna used as probe were performed on seven
well-referenced materials: air, butan-1-ol, n-hexane, chlorobenzene, 2-heptanol, 2-
propanol, and iso-propoxyethanol. This was done for validating the theoretical
model described by Eqs. (5.33)-(5.35), thus verifying the direct relation between
ε
m
and the corresponding
f
res
.
The reference liquids were placed inside the box; the antenna was placed in con-
tact with each of them, and the corresponding resonant frequency (
f
res
−
ref
) was mea-
sured. The frequency-dependent permittivities of the reference liquids were mea-
sured according to the procedure described in Chapt. 3 and compared with reference
values reported in [7] and [24]. A good agreement between measured and theoretical
data was observed [12].
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