Practical_Antenna_Handbook_0071639586

C h a p t e r 4 : T r a n s m i s s i o n L i n e s a n d I m p e d a n c e M a t c h i n g 129
0.3 s
Figure 4.8B TDR pulse with tiny “blip”. (Z L = Z 0 .)
0.9 s
The trace in Fig. 4.8B corresponds to a
load matched to the line (Z L = Z 0 ). A slight
discontinuity, representing a small reflected
wave, can be seen on the high side
of the pulse. Even though the load and line
Figure 4.8A Idealized TDR pulse. Small “pip” on top is are matched, any connector or other dimensional
change may present a slight im-
reflected signal interfering with forward pulse.
pedance discontinuity or bump that shows
up on the ’scope. In general, any discontinuity in the line, any damage to the line, any
too-sharp bend or other anomaly, can cause a slight impedance variation and, hence, a
reflection.
Observe that the anomaly occurs approximately one-third of the 0.9-μs duration (or
0.3 μs) after the onset of the pulse. This tells us that the reflected wave arrives back at
the source 0.3 μs after the incident wave leaves. Because this time period represents a
round-trip, you can conclude that the wave required 0.3 μs/2, or 0.15 μs, to propagate
the length of the line. Since we know the velocity factor, let’s calculate the approximate
length of the cable:
Length = cv T
F
8
–7
= (3 × 10 m/s) × (0.66) × (1.5×
10 s)
= 29.7 m
(4.27)
which agrees “within experimental accuracy” with the 30 m actual length prepared for
the experiment ahead of time. Thus, the simulated TDR setup (or an actual TDR instrument
or VNA) can be used to measure the length of a transmission line. A general equation
is
cvFTd L (meters) =
(4.28)
2
where L = length of transmission line, in meters
c = velocity of light (3 × 10 8 m/s)
v F = velocity factor of transmission line
T d = round-trip time between onset of pulse and first reflection