CHAPTER 2 - Conveying Power at Radio Frequency
120
The solutions of (2.14-12) for voltage (2.14-13) and current (2.14-14) are also simplified as shown
below
( )
( )
Figure 2.14-3 show a transmission line of length terminated with a load impedance
. To simplify
the calculations, the origin of the z-axis, along which the signal propagates, is chosen to be at the
load end.
Figure 2.14-3 Transmission line terminated with a load impedance Z
L
The impedance at the load end, i.e. at position , may therefore be expressed by means of
equations (2.14-13) and (2.14-14) as shown below
( )
( )
With a bit of mathematical manipulation we may solve (2.14-15) for
.
We can then define the load reflection coefficient
as the ratio of reflected and incident voltages
as measured at the load terminals and also express it as a function of
and , as shown by
(2.14-16)
As we will see in section 3.5 this value is very useful and along with the value of for the line, it
allows us to calculate the reflection coefficient at an arbitrary distance from the load.
( )
-l
) ( , ) ( z I z V
,
0
Z
+
-
L
V
(2.14-15)
(2.14-16)
(2.14-13)
(2.14-14)
Conquer Radio Frequency
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