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System VSWR / Return Loss
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Fundamentals
Wireless Infrastructure System
Power Transfer
Transmission Lines
Reflections
Coaxial Cables
Examples
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Wireless Infrastructure System
Antenna
Jumper Cable
Feeder Cable
Surge Arrestor
Jumper Cable
Radio
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Maximum Power Transfer
From a.c. circuit theory, maximum power delivered toa load (termination) occurs when ZL is set equal to thecomplex conjugate of the source (generator)impedance, i.e.
For transmission line systems ZL = RS = Zo
ZLVS
ZS
ZL = Z*S = RS - jXS
ZS = RS + jXS
ZL = RL + jXL
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Load Mismatch
When ZL Z*S then power is reflected back to thesource (generator).
At high frequencies the incident and reflectedpowers travel as waves.
The reflected wave interferes (adds and subtracts)with the incident wave.
This interference causes voltage maxima andminima to occur.
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Transmission Line Theory
The voltage at any point along a transmission line is:
+
VL
-
ZL
ZS
VS
+
Vin-
Zo,
Iin ILl
z
z = 0 z = l
V(z) = Vo+
e-z
+ Vo-
e+z
= V+
+ V-
where V+ is the forward traveling wave
V- is the reverse traveling wave
Zo transmission lines Characteristic Impedance
transmission lines Propagation Constant = + j
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Measuring Reflections
At any point on a transmission line the voltage isthe vector addition of an incident (forward) wave
and a reflected (reverse) wave.
The magnitude and phase relationships betweenthe incident and reflected waves is determined bythe load terminating the transmission line, ZL.
Reflected Voltage vector
Incident Voltage vector
Total Voltage vector
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Reflection Coefficient
Define the Reflection Coefficient, , as:
this is a complex number Its relationship with ZL is:
=Reflected Voltage (or current) at z
Forward Voltage (or current) at z
V-
V+=
I-
I+=
ZL - ZoZL + Zo =
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A Perfect Load
For a lossless, perfectly matched transmission line:
f = 300 MHz
= 100 mmV o
+ = 1.0 V
Zo = 50 = jZL = Zo
Total Voltage
Voltage(V)
0.2
0.40.6
0.8
1.0
1.2
1.4
1.61.8
2.0
ZLZo
, z = l - 1m z = l
To source
NOTE: Total Voltage = Incident Voltage
Reflected Voltage = 0
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An Imperfect Load
For a lossless, imperfectly matched transmission line:
f = 300 MHz
= 100 mm
V o+ = 1.0 V
Zo = 50 = jZL Zo
ZLZo
, z = l - 1m z = l
To source
Incident Voltage
Reflected Voltage
Total Voltage
Voltage(V)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.61.8
2.0
Vmax = 1.5
Vmin = 0.5
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VSWR and Return Loss
Voltage Standing Wave Ratio, VSWR
Return Loss, R.L.
1 + | |
1 - | |VSWR =VmaxVmin
=
R.L. = -20 log | | = -20 logVSWR 1
VSWR + 1[ ]
1.5
0.5For the previous slide VSWR = = 3.0
3.0 1
3.0 + 1[ ]R.L. = -20 log = -6.0 dB => || = 0.5
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A Real Transmission Line
f = 1700 MHz
V o+ = 1.0 V
Zo = 50 = 6.0 dB/100m = 40.45 nepers/mZL = 75 = 0.2 VSWR = 1.5
Incident Voltage
Reflected Voltage
VSWR
ZLZo, = + j
zz = 0 z = 50m
Vmax = |V+| + |V-|
Vmin = |V+
| - |V-
|
VSWR
0.2
0.4
0.6
0.8
1.0
1.2
1.41.6
1.8
2.0
Voltage(V)
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0Max. Total
Voltage, Vmax
Min. TotalVoltage, Vmin
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Power Relationships
Reflected Power,
Transmitted Power,
where PI = Incident Power
PR = PI | |2 = PI
VSWR 1
VSWR + 1[ ]2
PT = PI (1 - | |2) = PI
4 VSWR
( VSWR + 1)2
VSWR
Reflection
Coefficient
Return Loss
(dB)
Transmission
Loss (dB)
Reflected
Power
Transmitted
Power
1.20 0.09 20.8 0.04 1% 99%
1.30 0.13 17.7 0.07 2% 98%1.40 0.17 15.6 0.12 3% 97%
1.50 0.20 14.0 0.18 4% 96%
2.00 0.33 9.5 0.51 11% 89%
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System Reflection Coefficient
Each component in the WirelessInfrastructure has a reflection
coefficient, . Each component then causes a
reflected wave.
Loss in the cables attenuate thereflected waves.
Cable length changes the phases ofthe reflected waves.
The reflected voltage wave at thesystem input, V-sys, is a vectoraddition of all the reflected waves. V-sys
ant
bj
tj
f
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System Reflection Coefficient
The reflected voltage waves at thesystem input are:
antenna:
top jumper cable:
main feeder cable:
bottom jumper cable:
where V+o is the forward voltage wave at the input
and the as are voltage attenuation coefficients
ant
bjV-sys
abj
atj
tj
f
af
V-bj = V+
o bj
V-
f = V+
o abj f abj
V-tj = V+
o abj af tj af abj
V-ant = V+
o abj af atj ant atj af abj
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System Reflection Coefficient
The reflected voltage wave at the systeminput, V-sys, is:
These terms are vectors and can be viewed
as:
Note: the blue vectors rotate due to reflection coefficientphase and cable lengths
V-sys = V-bj + V
-f + V
-tj + V
-ant
Vbj Vf
Vtj
Vant
V-sys
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System Reflection Coefficient
V-sys is a maximum when all the reflections are inphase:
A more typical value is determined by the square
root of the sum of the reflections squared:
max. V-sys = |V-bj| + |V
-f| + |V
-tj| + |V
-ant|
typical V-sys = |V-bj|
2 + |V-f|2 + |V-tj|
2 + |V-ant|2
=> typical | sys |
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Summary
The system input VSWR / Return Loss at a singlefrequency is dependent upon the following:
VSWR / Return Loss of individual components
Cable losses
Cable lengths
VSWR / Return Loss is also dependent on
frequency.
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Summary---continue
The closer the component to the test port thebigger the impact to the test result. This is due to
the loss in the cable
The difference between VSWR 1.2 and VSWR1.5 is only very small. About 0.15dB in terms of
lost power
It is common the system VSWR alarm value to beset at up to 1.5
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