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 123
Figure 4.5 Standing waves.
A
B
C
Now let’s look at a transmission line with characteristic impedance Z 0 connected to
a load impedance Z L , as shown in Fig. 4.2. The generator at the input of the line consists
of a voltage source V with source impedance Z S in series
V
with a switch S 1 . Assume for the present that both the
source and the load impedances are pure resistances
V/ 2
T 0
(i.e., R + j0) equal to Z 0 , the characteristic impedance of
the transmission line.
V
When the switch is closed at time T 0 (Fig. 4.6A), the
voltage at the input of the line (V IN ) jumps to V/2. In
Fig. 4.2, you may have noticed that the L′C′ circuit resembles
a delay line. As might be expected, therefore,
0
V
L/ 2 L the voltage wavefront propagates along the line at a velocity
v:
V/ 2
1
T 0
v =
(4.17)
V
L'C'
V/ 2
0
V
T 0
T 1
L/ 2
T 1
L
T d
where v = velocity, in meters per second
L′ = inductance, in henrys per meter
C′ = capacitance, in farads per meter
At time T 1 (Fig. 4.6B), the wavefront has propagated
one-half the distance L, and by T d it has propagated the
entire length of the cable (Fig. 4.6C).
If the load is perfectly matched to the line (i.e.,
Z L = Z 0 ), the load absorbs the wave and no component is
0
L/ 2
L
Figure 4.6 Step-function propagation along transmission line at
three points.