3.2 Reflection Coefficient
129
Figure 3.2-7 Reflection coefficient when transmission line's physical length , electrical length =45ι, =100Ω
Also note that must be different from to get a reflection! If it isn't, from (2.14-16)
shown below, we get a modulus of zero for the reflection coefficient.
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We are still rotating around the polar plot, but along of circle with a radius of zero! The rotation will
therefore be imperceptible and we will remain right in the centre of the plot.
There is another important point to make. In the cases illustrated above, our mismatch was
determined by a load impedance
=100Ω which was greater than the characteristic impedance of
the line
=50Ω This ensures that the ratio of B and A in equation (3.2-6), is positive.
Ignoring losses in eq. (3.2-4), the reflection coefficient for
=100Ω can be expressed as
( )
However if we had chosen a termination
, the ratio of A and B would have been
negative. For instance if
we get
Now if you recall our treatment of complex exponentials (section 1.5.4), you will recall that we may
write
( ) ( )
0
15
30
45
60
75
90
105
120
135
150
165
-180
-165
-150
-135
-120
-105
-90
-75
-60
-45
-30
-15
Graph 1
Swp Max
1000 MHz
Swp Min
1000 MHz
Mag Max
1
0.2
Per Div
1000 MHz
Mag 0.3333
Ang -90 Deg
S(1,1)
Schematic 1
(3.2-6)
(3.2-8)
(3.2-9)
(3.2-7)
Conquer Radio Frequency
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