Environmental Engineering Reference
In-Depth Information
Fig. 3.15
Signal flow graph
describing the error model
for the SOL calibration
procedure [15]
locate exactly where the beginning and the end of the probe are. This is not a trivial
task especially when unmatched probes are used. For example, for the widely-used
three-rod probe schematized in Fig. 3.4, the actual beginning of the sensing element
is section
k
1 and this point has to be individuated in the corresponding TDR
waveform. In fact, when the probe is inserted in a material with specific dielectric
characteristics, only
L
app
will change. The offset length (
L
0
) has to be individuated:
L
0
corresponds to the electric distance between the cable end and the section
k
=
1.
The individuation of the point that, in the TDR waveform, corresponds to section
k
=
1 may be complicated because of the masking effect caused by the transition
coaxial cable/rods and the portion of the rods included in the rigid support (i.e.,
probe-head).
On such bases, to discriminate the electric distance of the rods inserted in the
SUT,
L
app
, from the electric distance of the probe-head,
L
0
, a simple but effective
procedure has to be performed. To evaluate
L
0
, it is necessary to perform preliminary
TDR measurements on materials with well-known dielectric characteristics, such as
air and de-ionized water [16]. Considering Fig. 3.4, this can be simply summarized
in the following equations:
=
L
0
+
ε
app
,
water
L
L
p
.
water
=
(3.20)
L
0
+
√
ε
air
L
L
p
,
air
=
(3.21)
ε
app
,
water
=
where
L
is the physical length of the sensitive portion of the probe in air;
ε
air
=
80 is the apparent permittivity of water; and
1 is the dielectric constant of air.
Once
L
0
is individuated, it can be compensated for in successive measurements.
3.6.2
Calibration Procedure in Frequency Domain
Frequency domain reflectometry can rely on well-established calibration proce-
dures. For single-port measurements, such as microwave reflectometry measure-
ments, the short-open-load (SOL) calibration is largely used [14]. The error model
can be identified using a signal flow graph as shown in Fig. 3.15:
S
11
,
SOL
is the re-
sponse of the sample under test;
S
11
,
M
is the measured response (which includes the
parasitic effects); and
a
,
b
and
c
are the parameters calculated from the open, short
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