Environmental Engineering Reference
In-Depth Information
It is important to emphasize that the proposed TLM method can virtually take into
account every single parasitic contribution associated to a specific experimental
setup. As a result, the influence of systematic error contributions is dramatically
reduced.
5.5.2.2
ICM Method
Considering a TEM mode propagating through the three-rod probe, the characteris-
tic impedance of the probe in air may be written as follows:
1
cC
0
Z
p
=
(5.29)
where
C
0
is the capacitance per unit length of the probe in air. Combining (5.25)
and (5.29), the following expression is obtained:
G
s
ε
0
C
s0
=
σ
0
=
G
s
K
p
(5.30)
where
C
s0
=
C
0
L
is the capacitance of the probe in air.
When the probe is inserted in a sample material, the quasi-static capacitance of
the probe will include two contributions: 1) a parasitic capacitance,
C
p
, that is due to
the connecting coaxial cable and to the probe-head; 2) the static capacitance of the
probe filled with the MUT,
C
s
. Therefore, the total capacitance measured through an
LCR meter,
C
m
, will be given by the following expression:
C
m
=
C
p
+
C
s
=
C
p
+
C
s0
ε
s
(5.31)
where
ε
s
is the static permittivity of the material filling the probe.
Consequently, from ICMs on two materials with well-known static dielectric per-
mittivity (
ε
s2
, respectively), it is possible to retrieve the value of
C
p
and, most
importantly, of
C
s0
, according to
ε
s1
and
C
m2
C
m1
ε
s2
−
ε
s1
−
C
s0
=
(5.32)
where
C
m1
and
C
m2
are the LCR-measured capacitances in the two reference mate-
rials, respectively. Finally, from (5.30), it is possible to estimate
K
p
.
For the ICM method, the Agilent 4263B LCR meter was used directly connected
to the TDR probe; and air [66] and pure water [24] were chosen as reference materi-
als. LCR measurements were performed at a frequency of 100 kHz, with a measure-
ment average of 256 and temperature kept constant at 25
◦
C. LCR measurements
showed that, at this frequency, the probe behaves just like a capacitor; in fact, the
phase angle of the corresponding impedance resulted approximately -90
◦
, thus con-
firming the validity of the approximations introduced using (5.31)
8
.
8
It is worth mentioning that, at 100 kHz, the dielectric behavior of air and water is practi-
cally static, thus dissipative and dispersive effects are avoided.
Search WWH ::
Custom Search