Quantitative and Qualitative Characterization of Liquid Materials - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 65

parameter derived directly from VNA measurements ( S vna
11 MEAS ) and to the scattering ,

parameter derived from the FFT of TDR data ( S fft
11 MEAS ).

In this way, it was demonstrated that the measurement accuracy in the evalua-
tion of levels and dielectric permittivity is substantially improved with respect to
the simple time-domain approach. Additionally, it was also shown that the TD/FD
combined approach can provide as much accuracy as direct VNA measurements.
Finally, it is important to highlight that, for all the TDR and VNA measurements,
the SOL calibration procedure (with the calibration structure connected at the end of
the feeding coaxial cable) was performed, according to the calibration error model
reported in subsection 3.6.2 [5]. Additionally, also the TDR measurements were cal-
ibrated, according to the time-domain calibration procedure described in subsection
4.2.2.

,

4.3.3.1 Time-Domain Approach

As mentioned in the previous section, the apparent dielectric permittivity of fuel,
ε app , f , was extrapolated from the amplitude of the first reflection in the TDR wave-
form, caused by the air-to-fuel impedance change. As an example, Fig. 4.8 shows
the TDR waveform (together with its derivative), when the probe was immersed in
sample #1. As highlighted in the figure, the significant reflection points are asso-
ciated to the level estimation derived from the distance difference between peaks
of the derivative curve. Based on the ε app , f evaluation and measuring the apparent

distance associated to the fuel, the fuel level ( H t f ) was determined from (4.2). 1
The water level, H t w , was therefore simply derived from the difference between
the overall probe length and the estimated actual fuel level. Table 4.3 summarizes the
results obtained solely from the TDR waveforms analysis described in the previous
section [6, 7]. The deviation between reference values and the TDR-estimated values
is also reported.

Ta b l e 4 . 3 Summarized results, obtained through the TD-based approach, for the three con-
sidered samples. The apparent permittivity of fuel (ε app , f ), the estimated level of fuel ( H t f ),
and the estimated level of tap water ( H t w ) are reported. Deviations of estimated levels from
reference levels are also reported

H td
f

H t w ε app , f deviation

(mm) (mm) (mm)

Sample #1 2.23 281 152 ± 2

Sample #2 2.22 219 214 0

±

Sample #3 2.23 331 102 4

1

The apex td indicates that results were obtained from time-domain measurements only.