3.5 Reflection Coefficient VS Impedance
139
3.5 Reflection Coefficient VS Impedance
Figure 3.5-1 Transmission line segment of length l
We have seen how, in the case of a lossless transmission line, the reflection coefficient may
be expressed as shown by eq. (3.2-4)
( )
We
can use eq. (3.2-4) to rewrite equation (3.1-4) as shown below
( )
( )
and equation (3.1-7) as shown below
( )
( )
Now using (3.5-1) and (3.5-2) we may work out the impedance at distance from the load
( )
( )
( )
( )
( )
This shows a direct correspondence between
( )
and
( )
! In section 3.6 and 4.4 we will
see how this correspondence can be extremely useful and how it allows a "conversion chart" to be
superimposed on the polar plot of the reflection coefficient to convert its value to the corresponding
impedance. This "conversion chart" is called Smith chart and we will be using it extensively
throughout this treatment.
We should also point out two important and useful relationships expressed by eq (3.5-4) and (3.5-5).
( )
(3.5-1)
(3.5-2)
(3.5-3)
(3.5-4)
(3.5-5)
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