Environmental Engineering Reference
In-Depth Information
As already mentioned, the reflected waveform usually includes the so-called mul-
tiple reflections due to the signal traveling back and forth between the measurement
instrument and the device under test. Multiple reflections contain information on
the spectral behavior of the whole system, including those contributions that in-
trinsically 'belong' to the device. Therefore, as a general rule, a time window long
enough to include all the multiple reflections occurring before the steady-state con-
dition is achieved, should be set. In this way, the subsequent FD-transformation
would provide a complete spectral picture.
Additionally, longer time windows guarantee a better frequency resolution,
Δ
f ,
of the FD-transformed data, according to the following equation:
1
T w
Δ
f
=
(6.1)
where T w is the duration of the time window.
However, when characterizing antennas, other issues come along. In fact, when
the electromagnetic signal generated by the TDR unit enters the antenna connected
to it, part of the signal is reflected back due to the impedance mismatch of the phys-
ical device (i.e., at the antenna port); nevertheless, another portion of the signal is
radiated according to the radiation pattern of the antenna. As soon as the radiated
signal reaches an object, it is reflected and the antenna receives the signal that is
bounced back. As a consequence, the measured TDR waveform might include un-
wanted contributions due to some spurious reflections. Such effects can be excluded
by choosing an appropriate time window that leaves them out. This is a relevant
advantage of TD-based measurements over the direct FD-measurements, and can
be considered as the practical way for avoiding the use of the anechoic chamber.
Fig. 6.2(a) shows a typical schematization of a TDR antenna waveform: in par-
ticular, the grey-colored area corresponds to the portion of the signal that should
be included in the acquisition window. Fig. 6.2(b) shows a schematization of the
measurement setup in which an antenna is connected to the TDR unit through an
L c -long cable and the nearest reflecting object is placed at a distance d from the an-
tenna. Therefore, the time window that excludes possible unwanted reflections can
be calculated through the following equation:
2 d
L
v
T w =
c +
(6.2)
where c =
10 8 ms 1 is the speed of light in vacuum, L is the fraction of L c that
corresponds to the portion of the cable included in the time window 1 ,and v is ve-
locity of the signal propagated in the cable. The incident signal portion is windowed
out, as required for the successive FD-processing [16].
3
×
1
In practice, the L -long cable portion inclusion is necessary for effectively performing the
subsequent FD-transformation, as reported in [4, 14].
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