Environmental Engineering Reference
In-Depth Information
and 50
-load calibration measurements. The SOL-calibrated frequency response
of the sample under test can be extracted from the signal flow graph according to
Ω
S
11
,
M
−
a
S
11
,
SOL
=
(3.22)
bS
11
,
M
−
ab
+
c
where
a
,
b
,and
c
include the contribution of
S
11
,
MO
,
S
11
,
MS
,and
S
11
,
ML
, which are
the reflection scattering parameters when an open, a short and a matched loads are
connected:
a
=
S
11
,
ML
,
(3.23)
S
11
,
MO
+
S
11
,
MS
−
2
S
11
,
ML
b
=
,
(3.24)
S
11
,
MO
−
S
11
,
MS
(
−
)(
−
)
2
S
11
,
ML
S
11
,
MO
S
11
,
MS
2
S
11
,
ML
c
=
.
(3.25)
S
11
,
MO
−
S
11
,
MS
The aforementioned error-compensation model is solved directly in FD; neverthe-
less, it can implemented in the TD/FD transformation algorithm described in [15],
thus extracting the calibrated
S
11
(
from TDR measurements [17]. The aforemen-
tioned calibration procedures were implemented in the transformation algorithm
used for transforming TD data into FD data. An additional advantage of this strat-
egy is that it overcomes the need of acquiring the input function,
v
0
.
However, calibration standards are often not readily available for many commercial
probes. In these cases, it is necessary to fabricate appropriate calibration fixtures or
custom-made calibration standards.
An innovative calibration procedure, namely triple short calibration (TSC), has
been presented in [35]: this procedure, which will be described in detail in Chap. 5,
relies on three short-circuit applied at three different sections along the probe. The
major advantage is that realizing a short-circuit condition is easier than achieving
an open-circuit condition or a matched condition, especially for probes as the one
represented in Fig. 3.4.
f
)
3.6.3
Time-gated Frequency Domain Approach
Time gating is a calibration strategy that can be adopted for excluding systematic
errors in the TD/FD combined approach [5]. Time gating implies the individuation
and the removal of those portions of the waveform that are considered undesired
effects (e.g., reflections caused by connection transitions): once these effects are
removed from the TD data (via software), the data are transformed into the FD. As
a result of the process, the gated frequency response will resemble more closely the
response of the sole SUT. As a matter of fact, the time-gating option is often directly
integrated within VNAs: in this case, the FD response is transformed in TD; then
gating is applied, and, finally, the data are transformed back into the FD.
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