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  • 8/3/2019 System VSWR

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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