Qualitative Characterization of Granular Materials and Moisture Measurements - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 109

TDR-based conductivity measurements rely on the Giese-Tiemann (G-T) method,
which is based on the linear relation between σ 0 and the static conductance of the

load, G s [22]:

σ 0 = K p G s (5.20)

where K p is the probe constant. The value of G s is evaluated from measurements
of the reflection coefficient at longer times (i.e., when the TDR has achieved the
steady state, approximately corresponding to the zero-frequency response), of the
probe inserted in the MUT, ρ ∞ :

1
Z TDR

1 − ρ ∞

G s , G − T = (5.21)

1 + ρ ∞

where Z TDR is the output impedance of the used TDR instrument. The value of the
probe constant can be estimated from the probe geometry:

= ε

0 cZ p
L

K p (5.22)

where L is the length of the used probe, Z p is the characteristic impedance of the
probe, c is the velocity of light in vacuum, and

ε 0 is the permittivity of vacuum. In
(5.22), the evaluation of Z p is not always an easy task. For this reason, to obtain
more accurate estimation of the electrical conductivity, the proportionality constant
K p is usually determined empirically, through multiple preliminary calibration mea-
surements on electrolyte solutions of known conductivity.
The G-T approach neglects the series resistance of the cable, connectors, and ca-
ble tester; as a result, for higher electrical conductivity values (i.e., 2Sm − 1 ), σ 0 > 0 .

this method underestimates σ 0 . For this reason, in [28], the series resistor model

was introduced, thus considering the coaxial cable and the sample as two resistors
in series. The G-T method was modified as follows:

K p

σ 0 = (5.23)

( 1 / G s ) − R cable

where R cable is the resistance due to the cable. Castiglione-Shouse (C-S) proposed an
alternative approach for taking into account cable resistance; their method required
the correction of the measured reflection coefficient by scaling it with respect to the
reflection coefficients measured with the probe in air,

ρ ∞ , air , and short-circuited at

the distal end, ρ ∞ , sc , respectively [8]:

ρ − ρ ∞ , air
ρ ∞ , air

ρ ∞ , scaled = 2

− ρ ∞ , sc +

1 . (5.24)

However, Lin et al. argued that, despite providing accurate results, the C-S method
is theoretically incorrect and that the series resistor model is indeed accurate [41].
In particular, Lin et al. suggested that the C-S scaling method actually accounts for