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    by

    Lotis P. Patunob, M.Eng., ECE

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    Microwaves

    An electromagnetic waves with frequencies that ranges

    from approximately 500 MHz to 300 GHz or more. And

    its wavelengths fall between 1cm and 60 cm.

    Wavelength

    The distance between

    repeating units of apropagating wave of a

    given frequency.

    Designated by lambda

    ().

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    Categories of Microwave Systems:

    A. Short haul used to carry information for relatively

    short distances, e.i. between cities within the same state.

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    Categories of Microwave Systems:

    A. Long haul used to carry information for relatively

    long distances, such as interstate.

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    Advantages of Microwave Radio:

    1. Radio systems do not require a right-of-way

    acquisition between stations.

    2. Each station requires the purchase or lease of only asmall area of land.

    3. Because of their high operating frequencies,

    microwave radio systems can carry large quantities of

    information.

    4. Short wavelengths, require relatively small antennas.

    5. Radio signals are more easily propagated around

    physical obstacles, such as high mountains

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    Disadvantages of Microwave Radio:

    1. It is more difficult to analyze and design circuits at

    microwave frequencies.

    2. Measuring techniques are more difficult to perfectand implement at microwave frequencies.

    3. It is difficult to implement conventional circuit

    components at microwave frequencies.

    4. Transient time is more critical at microwave

    frequencies.

    5. Microwave frequencies propagate in a straight line,

    which limits their use to line-of-sight applications.

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    Applications of Microwave:

    1. Telephone communications.

    2. Radar

    3. Space Communications

    4. Heating

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    Microwave Parameters:

    It is the loss that would be obtained between two

    isotropic antennas in free space, where there are noground influences or obstructions.

    A. Free Space Path Loss, LFS

    It is defined as a loss incurred by an electromagnetic

    wave as it propagates in a straight line through a

    vacuum with no absorption or reflection of energy fromnearby objects.

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    Note: signal strength is 1/

    distance; & antenna gain

    aperture.

    24

    dFSL

    )(10)(10 log20log204.32 kmMHz dfFSL

    )(10)(10 log20log204.92 kmGHz dfFSL

    )(10)(10 log20log206.36 miMHz dfFSL

    )(10)(10 log20log206.96 miGHz dfFSL

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    Microwave Parameters:

    General Equation:

    B. Parabolic Antenna Gain, G

    where: D = antenna diameter in m

    = signal wavelength in m

    = efficiency

    2

    DG

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    Microwave Parameters:

    Antenna Gain for Typical Values of (0.55 to 0.75):

    Parabolic Antenna Gain for Typical Values of (0.55

    to 0.75) in Metric system:

    2

    6

    D

    G

    )(10)(10 log20log204.42 mMHz DfG

    )(10)(10 log20log208.17 mGHz DfG

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    Microwave Parameters:

    Parabolic Antenna Gain for Typical Values of (0.55

    to 0.75) in English system:

    )(10)(10 log20log206.52 ftMHz DfG

    )(10)(10log20log205.7

    ftGHzDfG

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    Microwave Parameters:

    C. Fade Margin, FM

    It is an attenuation allowance so that anticipated

    fading will still keep the signal above specified

    minimum RF input.

    It considers the nonideal and less predictable

    characteristics of a radio wave propagation such as

    multipath propagation and terrain sensitivity.

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    Microwave Parameters:

    Fade Margin in Metric system:

    )1(log10)6(log10log3013010)(10)(10

    RabfdFMMHzkm

    )1(log10)6(log10log307010)(10)(10

    RabfdFMGHzkm

    Fade Margin in English system:

    )1(log10)6(log10log308.123 10)(10)(10 RabfdFM MHzmi

    )1(log10)6(log10log308.6310)(10)(10

    RabfdFMGHzmi

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    Microwave Parameters:

    where: R = propagation reliability

    Values for a Description

    4.0 for very smooth terrain,

    over water, flat desert

    1.0 for average terrain with

    some roughness

    0.25 for mountainous, very

    rough, or very dry terrain

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    Microwave Parameters:

    Values for b Description

    0.50 for hot, humid coastal areas

    0.25 for normal, interior

    temperate or sub-arctic area

    0.125 for mountainous, very drybut non-reflective areas

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    Microwave Parameters:

    D. System Reliability Estimates

    D.1. Propagation Reliability for Non-diversity Systems:

    %1001 xUndpR where: Undp = the path unavailability or

    fade probability

    10/635.1 10)1025.1( FMxxdabfUndp

    where: d = path length in mi

    f = frequency in GHz

    FM = fade margin in dB

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    Diversity

    It suggests that there is more than one transmission path

    or method of transmission available bet. a transmitter

    and a receiver. Its purpose is to increase the reliability of

    the system by increasing its availability

    Frequency diversity

    It simply modulates two different RF carrier frequencies

    with the same information. At the destination, both aredemodulated but the one yields the better quality is

    selected.

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    Space diversity

    The output of a transmitter is fed to two or more

    antennas that are physically separated by anappreciable number of wavelengths.

    Diversity

    Receiver diversity

    It is using more than one receiver for a single RFchannel.

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    Microwave Parameters:

    D. System Reliability Estimates

    D.2. Propagation Reliability for Diversity Systems:

    where: Udiv = the path unavailability or

    fade probability

    where: Idiv = the diversity improvement factor

    %100)1( xUdivR

    di v

    ndp

    di v I

    UU

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    Microwave Parameters:

    D. System Reliability Estimates

    D.3. Equipment Reliability:

    where: U = unavailability or probability of outage

    where: MTTR = mean time to repair

    MTBF = mean time before failure

    %100)1( xUR

    MTBFMTTRU

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    Microwave Parameters:

    E. Received Signal Level, RSL

    RXRFSTTXLGLGLPRSL dBmo )(

    It is the difference from the nominal transmitter

    output, antenna transmit and receive gain, from thatof the fixed losses of transmit and receive side and its

    path loss.

    where: LTX and LRX = transmitter and receiver

    total insertion losses in dB

    GT and GR = transmit and receive antenna

    gains in dB

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    Microwave Parameters:

    RSL = FM + Threshold (receiver)

    where:

    FM = Fade Margin in dB

    Threshold (receiver) = receiver minimum RF

    input in dBm; Cmin

    where: LFS = Free Space Loss in dB

    Po(dBm) = Transmitter Output Power in dBm

    KTBN;min NN

    CC

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    Microwave Parameters:

    F. System Gain, Gs (dB)

    It is the difference between the nominal output power

    of a transmitter and the minimum rf input power to areceiver.

    )()()( .min dBmdBmodBS inputRFPG

    gainslossesPdBmo

    (dBm))(

    inputRF.min

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    Microwave Parameters:

    )()()()()()( dBRdBTdBbdBfdBFSdBdBs GGLLLFMG

    where: Lf(dB) = transmission line loss bet. thedistribution network and

    its respective antenna (dB)

    Lb(dB) = total coupling or branching loss

    in the distribution network bet.the output of a transmitter or

    receiver and the transmission line

    (dB)

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    G. Fresnel Zone and Fresnel Radius

    Fresnel zone the area where the interference is

    constructive.

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    If a reflected signal is bounced within an odd-

    numbered Fresnel zone, it would arrive at the receiver

    in phaseaddition with the direct signal.

    G. Fresnel Zone and Fresnel Radius

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    Fresnel zones are a series of concentric ellipsoids that

    surround the path from the transmitter to the receiver.

    )()(

    )(2)(1)(1 1.547

    kmMHz

    kmkmm

    Df

    ddF

    Fresnel zone radius, (F1)

    in Metric System:

    )()(

    )(2)(1

    )(1 3.17kmMHz

    kmkmm

    Df

    ddF

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    )()(

    )(2)(1

    )(1 2280

    miMHz

    mimi

    ft

    Df

    ddF

    Fresnel zone radius, (F1) in English System:

    )()(

    )(2)(1)(1 1.72

    miGHz

    mimift

    Df

    ddF

    nFFn 1nth Fresnel zone radius (Fn):

    Fresnel zone clearance (Fc)- it takes into account the

    unusual conditions that

    occur in the atmosphere.

    16.0 FFc

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    H. Passive Repeater

    Gain of a Passive Repeater

    2)(cos4

    log20

    A

    G dBp

    where: A = the actual area of the passive repeater in (ft2 )

    = wavelength = c/f in (ft)

    = alpha, the angle bet. the incident wave and the

    reflected wave in ()

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    I. Net Path Loss, NPL:

    It is the total loss of the system.

    RFSpFSTdB GLGLGNPL 21)(

    Example:

    A plane passive reflector 10x16 ft is erected

    21 miles from one active site and only 1 mile from

    the other and = 50. The operating frequency is2000 MHz. Determine the net path loss of the

    system.

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    Example:

    In a microwave communication system with a

    normal temperate and average terrain has the

    following parameters:

    a. Operating frequency = 4 GHzb. Path length = 25 mi

    c. Tx/Rx antenna diameter = 3 ft.

    d. Transmitter Output Power = 1 W

    e. Threshold(receiver) = - 80 dBmf. Tx total insertion loss = 5 dB

    g. Rx total insertion loss = 4 dB

    Deermine: LFS(dB) , FM(dB) & % Reliability

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    Waveguides

    It is a conducting tube through which the energy is

    transmitted, in the form of electromagnetic waves.

    It is an alternative to cable for frequency of 1 Ghz andabove.

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    Electromagnetic Wave

    It is made up of magnetic and electric fields that are at

    right angles to each other and at right angles to the

    direction of propagation. It travels in a straight line at

    approximately the speed of light.

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    Modes of Propagation - the possible direction of

    distribution of energy

    1. Transverse Electric (TE) has the electric field

    transverse the direction of propagation, while the

    magnetic field is along the propagation direction

    2. Transverse Magnetic (TM0) has the magnetic field atright angles to the direction of propagation along the

    guide, and the electric field in the direction of

    propagation.

    Classification of Modes of Propagation:

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    Format: TEm,n

    where: n = indicates the no. of half wave variation

    of the electric field along the y or b

    (height) dimension.

    m = indicates the no. of half wave variation

    of the electric field along the x or a

    (width) dimension.

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    where: arrows = represent the E field perpendicular to

    the sides of the guide.

    xs = represent the H field that is going into

    the waveguide.

    dots = represent the H field that is coming out

    of the waveguide.

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    Types of Waveguides:

    A. Rectangular used when energy must be coupled

    from the source to a load and both are fixed in place

    since they are smaller than circular waveguides for a

    given wavelength.

    General formula for

    cut off wavelength, c:

    22

    2

    y

    n

    x

    m

    c

    Cut off wavelength for

    TEm,0:

    m

    x

    c

    2

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    Cut off wavelength for TE1,0:

    xc

    2

    where: TE1,0 = called the dominant mode, the mode for

    the lowest frequency that can be

    propagated in a waveguide

    x = the width of the waveguide

    y = the height of the waveguide

    Note: x /2 for dominant mode means no propagation

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    B. Circular used for rotating systems such as radar

    antenna

    K

    r

    c

    2

    where: K = 1.84 for dominant mode

    Example:

    What is the cut off wavelength that a 2.5 cm widewaveguide will support the dominant mode (m = 1)?

    How about for the next mode (m = 2)?

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    Key wavelength formula for rectangular/circularwaveguide:

    Rectangular Circular

    Cut off wavelength 2x 3.41r

    Longest transmitted

    with little attenuation

    1.6x 3.2r

    Shortest before next

    mode is possible

    1.1x 2.8r

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    Group Velocity, Vg

    The actual speed at which

    a signal travels down the

    guide.

    2

    1

    ccg VV

    Phase Velocity, Vp

    The rate at which the

    wave appears to move

    along the wall of theguide.

    2

    1

    c

    cp

    VV

    Note: VgVp = Vc2

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    Waveguide Characteristic Impedance:

    TE mode:

    20

    1

    377

    c

    Z

    TM mode:

    20

    1

    377

    c

    Z

    Example:

    A 6 GHz signal is to be propagated in a waveguidewhose width is 7.5 cm. Calculate the characteristic

    impedance for TE1,0 mode and TM1,1 mode if the

    thickness is 3.75 cm.

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    Example:

    A 6 GHz signal is to be propagated in the dominant

    mode in a rectangular waveguide if its group velocity

    is to be 90% of the speed of light, what must be width

    of the guide?

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