Qualitative Characterization of Granular Materials and Moisture Measurements - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 112

The first step of the TLM method involves a couple of TDR measurements, which
are performed on the probe in air and immersed in de-ionized water at a known tem-
perature, respectively. Secondly, the same experimental conditions are simulated
through the TL model described in Fig. 5.11. Therefore, by employing the sim-
plex optimization procedure (available within MWO), the optimal values of probe
length, characteristic impedance, and each parasitic element are evaluated, through
the minimization between measured and simulated TDR waveforms.
In these simulations, the frequency dependent dielectric parameters of water are
obtained through the well-known Debye modeling [35]. The optimized waveforms
(together with the corresponding measured waveforms) are reported in Fig. 5.12(a)
for probe in air, and in Fig. 5.12(b) for probe in water, respectively. An excellent
fitting quality is observed. The optimized values obtained for Z p and L are 172 and

15.2 cm, respectively. It is worth noting that the nominal probe length is 15 cm and
that the approximate characteristic impedance is 180

Ω

: this value was calculated
from the nominal geometrical parameters. The slightly larger length obtained from
simulations is attributed to the aforementioned fringing effect of the open-ended
termination. As for the optimized value obtained for the characteristic impedance,
in the simulation, the non-uniform geometry of the probe is appropriately considered
[5]. The obtained values of Z p and L led to a value of the probe constant, K p , equal
to 3.1 m − 1 .
Once K p is estimated,

Ω

σ 0 can be evaluated through (5.25), measuring the static
conductance G s of the probe immersed in the MUT. In turn, G s is related to the
measured static reflection coefficient: in the TLM method, the ohmic losses of the
connecting cable are compensated for through the series resistor-model [28]. Fi-
nally, non-idealities in the TDR instrument are corrected by dividing all the values
of the measured static reflection coefficients by the one obtained with the output
connector left open, whose corresponding ideal value is +1. The overall adopted
procedure can be summarized in the following steps:
1. the static reflection coefficient,

ρ

oc , with the TDR instrument output connector

left open is measured.
2. The parasitic resistance, R p , of the connecting cable is evaluated from the static
reflection coefficient, ρ sc (appropriately corrected through ρ oc ) measured with the

probe in air short-circuited at its distal end, i.e.:

+ ρ oc
ρ oc

1

R p = Z 0

ρ oc .

(5.26)

− ρ sc 1

The resistance of the probe rods does not appear in (5.26) since it is negligible
compared to the resistance of the cable.
3. The static reflection coefficient with the probe inserted in the MUT (

ρ sample ), is

measured, and the corrected reflection coefficient ρ corr , TLM is derived, i.e.:

ρ corr , TLM = ρ sample
ρ

. (5.27)

oc