power flow and return loss
TRANSCRIPT
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Power Flow and
Return LossWe have discovered that two waves propagate along a
transmission line, one in each direction ( 0 0andj z j zV e V e ++ ).
The result is that electromagnetic energy flows along the
transmission line at a given rate (i.e., power).
Q: How much power flows along a transmission line, and
where does that power go?
A: We can answer that question by determining the
power absorbed by the load!
0
0
( ) j z j zV
I z e e
Z
+
+ =
+
( ) 0j z j zV z V e e ++ = +
-
+
VL
-
A
ZL
IL
z = A 0z =
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The time average power absorbed by an impedance ZL is:
{ }
{ }
( ) ( ){ }
( ){ }
( )
Re
Re
Re
Re
0 0 0 00 0
0
2
20
0
2
20
0
1
2
1 ( 0) ( 0)2
1
2
12
12
abs L L
j j j j
P V I
V z I z
V e e V e e Z
V
Z
VZ
+ ++ +
+
+
=
= = =
= +
=
=
The significance of this result can be seen by rewriting the
expression as:
( )
2
20
0
2 2
0 0
0 0
2 2
0 0
0 0
12
2 2
2 2
abs VP Z
V V
Z Z
V V
Z Z
+
+ +
+
=
=
=
The two terms in above expression have a very definite physical
meaning. The first term is the time-averaged powerof the
wave propagating along the transmission line toward the load.
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We say that this wave is incident on the load:
2
0
0
inc
VP P
Z
+
+= =
Likewise, the second term of the Pabsequation describes the
power of the wave moving in the other direction (away from
the load). We refer to this as the wave reflected from the
load:
2 22
20 0
0 02 2incref
V VP P PZ Z
+
= = = =
Thus, the power absorbed by the load is simply:
abs inc refP P P=
or, rearranging, we find:
inc abs refP P P= +
This equation is simply an expression of the conservation of
energy !
It says that power flowing toward the load (Pinc) is either
absorbed by the load (Pabs) or reflected back from the load
(Pref).
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Note that if2
1 = , then Pinc= Pref, and therefore no power is
absorbed by the load.
This of course makes sense !
The magnitude of the reflection coefficient ( ) is equal to one
only when the load impedance is purely reactive (i.e., purely
imaginary).
Of course, a purely reactive element (e.g., capacitor or inductor)
cannot absorb any powerall the power must be reflected!
Return Loss
The ratio of the reflected power to the incident power is known
as return loss. Typically, return loss is expressed in dB:
2
10 1010 10. . log log ref
inc
PR L
P
= =
ZL
Pabs
Pinc Pref
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For example, if the return loss is 10dB, then 10% of the
incident power is reflected at the load, with the remaining 90%
being absorbed by the loadwe lose 10% of the incident
power
Likewise, if the return loss is 30dB, then 0.1 % of the incident
power is reflected at the load, with the remaining 99.9% being
absorbed by the loadwe lose 0.1% of the incident power.
Thus, a larger numeric value for return loss actually indicates
less lost power. An ideal return loss would be dB, whereas a
return loss of 0 dB indicates that 1 = --the load is reactive!