Quantitative and Qualitative Characterization of Liquid Materials - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 57

cables and to the material under investigation itself. The related error contribution
basically affects the dielectric constant estimation described by (4.1). However, a
separate calibration procedure can help discriminating the attenuations due to the
sample under investigation from that due to the measurement setup. In fact, the
coaxial cable loss attenuation constant, A , can be found through the following pro-
cedure [4]: measuring the reflection coefficient when the distal end of the probe is
open-circuited and short-circuited (i.e.,

o meas and s meas ), and comparing the results

ρ ρ

oc
ideal

sc
ideal

with the theoretical values (i.e., ρ =+ 1and ρ = − 1), the reflection coeffi-

cient amplitudes can be corrected, according to

A = ex p ( 2 α L cable ) (4.3)

ρ corr = A ρ meas (4.4)

m − 1 where is the attenuation coefficient of the coaxial cable, and L cable [m] is the

length of the coaxial cable. The constant A accounts for signal losses over a path of
length 2 L cable , and equals 1 for ideal cables. For the specific 3 m-long coaxial cable
used in the measurements reported in this section, the evaluated A is 1.06.

α [ ]

4.2.2.3 Intrinsic Limitation of the Proposed Method

Finally, the implications of points 4) and 5) can be considered as intrinsic limi-
tations of the proposed method itself and of the considered measurement setup,
respectively.
Generally, the presence of a steady curve portion in the TDR waveform indicates
that the liquid can be considered as a lossless dielectric. Conversely, when dissipa-
tive liquids are considered (such as electrolyte solutions or water-like liquids), the
ohmic and polarization losses cause a strong variation of the reflection coefficient at
the probe-portion filled with liquid. This problem can be circumvented through the
estimation of the static electrical conductivity, or through the consideration of the
FD approach (as detailed in the following section).
As for the parasitic effects of multiple reflections described in point 5), they can
be caused, for instance, by the connection between the TDR unit and the cable, by
the cable-to-probe connection, and by the plastic ring insertion in the probe head.
They cause a periodical presence of parasitic multiple reflections of TDR wave-
forms. For example, in Fig. 4.3, it can be noticed that the effects of parasitic mul-
tiple reflections are clearly detectable at longer distance after the probe-end point
(approximately 4.9 m). Considering the distance where it occurs, this effect is at-
tributable to the repetition of the reflection occurring at the probe head section;
however, this does not play a dominant role in terms of error contribution for the
considered application.