Environmental Engineering Reference
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0.2
0.0
-0.2
probe end
-0.4
air/diesel oil
interface
diesel o il/water
interface
-0.6
-0.8
reflection co e fficient
first derivati v e
-1.0
4
5
6
7
apparent distance (m)
Fig. 4.5 TDR waveform and derivative of data for a diesel oil-tap water layered sample
(short-circuited probe-termination)
apparent height for tap water, H water
app , was 81.1 cm, and the corrected reflection
coefficient was -0.8, corresponding to the expected value of dielectric constant
(
ε water =
80). Also the third reflection related to diesel oil-water interface could be
directly evaluated as difference between the total coaxial probe length, the coaxial
probe in air portion and the diesel oil distance.
4.3
Estimation of Levels and Permittivities of Industrial
Liquids Using the TD/FD Approach
The simple TD approach described in the previous section provides adequately ac-
curate results as long as the investigated liquids can be considered non-dispersive
and lossless. Conversely, when the dependence of permittivity on frequency or the
effect of losses cannot be neglected, to enhance the measurement accuracy, specific
dielectric models (such as the Cole-Cole formula) have to be adopted for describing
permittivity.
This can be achieved adopting a frequency-domain approach, thus considering
the reflection scattering parameter, S 11 (
. As mentioned in Sect. 3.4, this parameter
can be obtained either through direct frequency-domain measurements with a VNA
or through an appropriate fast Fourier transform (FFT)-based processing of TDR
data [5, 15, 17, 26].
On such bases, the approach proposed herein for the simultaneous estimation
of liquid levels and of permittivity (in terms of Cole-Cole parameters), relies on
FD data and on the transmission line (TL) modeling of the measurement cell (i.e.,
probe + LUT). In particular, the measurement cell is modeled as a function of the
f
)
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