Environmental Engineering Reference
In-Depth Information
shows that, due to the limited measurement bandwidth (from 10 MHz to 700 MHz),
the evaluation of
ε
∞
and of
f
r
is somewhat less accurate. On the other hand, both
the
s
and, most importantly, the liquid levels are estimated with high accuracy.
This demonstrates that the proposed setup is definitely suitable to estimate the static
permittivity and level of fuel.
When
ε
ε
∞
and
f
r
are of interest, the probe design should be modified, and a coaxial
probe with smaller radius should be adopted in order to achieve larger working
bandwidths, without any modification in the optimization procedure (this case will
be considered in Sect. 4.4).
After the proposed optimization technique was tested on the idealized data,
demonstrating its reliability and accuracy, it was applied to 'real' measurements
performed on the same samples. In particular, the procedure was implemented con-
sidering as input first the scattering parameter directly measured by the VNA, and
successively, the one obtained through the FFT-based algorithm of TD data (i.e.,
the TD/FD combined approach) [5]. The obtained results are reported in Table 4.5
and Table 4.6 for VNA and FFT data, respectively. Analysis of the two tables
demonstrates that the optimization procedure can suitably estimate fuel and wa-
ter levels with a maximum deviation within the uncertainty in the evaluation of the
reference levels. In particular, it is important to point out that the TD/FD combined
approach does not cause substantial accuracy decrease with respect to the VNA
measurements. This confirms that a low-cost TDR system, associated to the
Ta b l e 4 . 5
Fuel static permittivity, fuel level, and water level extrapolated for the three sam-
ples using frequency-domain minimization routine, applied on VNA measurements. Devia-
tions from reference levels are also reported
vna
s
H
vna
f
H
vna
w
ε
deviation
,
f
(mm)
(mm)
(mm)
±
.
Sample #1
2.37
283.5
149.5
0
5
Sample #2
2.24
219.5
213.5
±
0
.
5
Sample #3
2.17
335.1
97.9
±
0
.
1
f
), fuel level (
H
ff
f
), and water level (
H
ff
w
) extrapolated
for the three samples using frequency-domain minimization routine, applied on FFT of TDR
measurements. Deviations from reference levels are also reported
fft
s
Ta b l e 4 . 6
Fuel static permittivity (
ε
,
fft
s
H
fft
f
H
fft
w
ε
deviation
,
f
(mm)
(mm)
(mm)
Sample #1
2.21
282.7
150.3
±
0
.
3
Sample #2
2.18
219.3
213.7
±
0
.
3
Sample #3
2.16
334.7
98.3
±
0
.
3
Search WWH ::
Custom Search