3.2 Reflection Coefficient
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3.2 Reflection Coefficient
Referring to Figure 3.1-2, and using equations (3.1-5), (3.1-6), (3.1-8) and (3.1-9), at point z=0,
we may write
( ) ( )
( ) ( )
Notice how the ratio of the total voltage and total current for the impedance
is fixed by itself!
The reflection coefficient measured at the load terminals,
, which is just the ratio of reflected and
incident voltages at z=0, may be expressed as
( )
( )
( )
You may say, "This is all well and good but how can I perform a measurement right at the terminals
of
?". You would be right, most of the time you can't do that and there will be a length of line,
albeit short, between your measurement point and your load impedance. So the question is, "If I
don't measure my
and right at the terminals of the load how is the reflection coefficient
affected?"
Well the answer is quite simple. Your reflection coefficient is a complex quantity which has
magnitude and phase. The magnitude will be fixed once you have picked
but the phase will
change depending on where you measure. Let us remember that, at any point along the line, is the
ratio of
and and hence
( )
may be expressed as
( )
You can see that the modulus of the complex number which represents depends solely on A and B
which are fixed for a specific termination. Its phase however depends on the point along your
transmission line where you are measuring your !
Now using (3.1-3) we can rewrite (3.2-3) as
( )
The
part represents an exponential decay which accounts for resistive losses whereas the
accounts for phase shifts as mentioned in section 2.14.2.2 and in section 1.5.3.
(3.2-1)
(3.2-2)
(3.2-3)
(3.2-4)
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