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    AntennaNot in Scope: Electromagnetic Waves & Transmission Line Theories

    Erwinio Rene DC Bagoyo

    De La Salle University / Intel Technology Phils, Inc

    Course: MEP-ECE, 10689532

    Email: [email protected]

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    Table of Contents

    Overview

    Antenna parameters Resonant frequency,

    Gain

    Bandwidth

    Impedance

    Radiation pattern

    Polarization

    Efficiency

    Transmission and reception

    Basic antenna models

    Antennas in reception Effect of ground

    References

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    Overview - I

    There are two fundamental types of antennas:

    Omni-directional (radiates equally in all directions) or Directional (radiates more in one direction than in the other)

    An antenna is a circuit element the provides a transition froma guided wave on a transmission line to a free space waveand it provides for the collection of electromagnetic energy.

    In a transmission system, a radio-frequency is developed,amplified, modulated, and applied to the antenna. The RFcurrents flowing through the antenna produce electromagneticwaves that radiate into the atmosphere.

    In receiving system, electromagnetic waves cutting through theantenna induce alternating current for use by the receiver.

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    Overview - II

    Receiving antenna transfer energy from the atmosphere to its

    terminal with the same efficiency with which it transfersenergy from the transmitter into the atmosphere.

    This property of interchangeabilty for transmitting and receivingoperations is known as antenna reciprocity.

    Antenna characteristics are essentially the same during sendingand receiving electromagnetic energy.

    Efficient operation requires that the receiving antenna be ofthe same polarization as the transmitting antenna.

    Polarization is the direction of the electric field and is, therefore,the same the as the antennas physical configuration.

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    Antenna Parameters - I

    Resonant Frequency:

    The "resonant frequency" and "electrical resonance" is related to theelectrical length of the antenna. The electrical length is usually thephysical length of the wire divided by its velocity factor (the ratio of thespeed of wave propagation in the wire to c, the speed of light in avacuum):

    f = c/P or P = c/f

    Where:c = Speed of propagation (mi/s)

    P = wavelength (mi)

    f = frequency (Hz)

    Sample Problem

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    Antenna Parameters -II

    Gain:

    "Gain" as a parameter measures the directionality of a given antenna.

    Gain, Directive gain or Power gain of an antenna is defined as the ratio of theintensity (power per unit surface) radiated by the antenna in a given direction at anarbitrary distance divided by the intensity radiated at the same distance by anhypothetical isotropic antenna:

    Antenna gain with respect to an isotropic antenna is expressed in dBi. Half wavedipole antennas gain can be expressed as 2.15 dBi.

    Antenna gain with respect to dipole, it is expressed in dBd.

    Gain can also be expressed in the formula below:

    A(dB) = 10 log10 (P2/P1)

    Where:A(dB) = Antenna gain in dB

    P1 = Power of actual antenna,

    P2 = Power of reference antenna

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    Antenna Parameters - III

    Since transmitting antenna can also be a receiving antenna (reciprocity) they havealso gain:

    A(dB) = 20 log10 (V2/V1)

    Where:A(dB) = Power in dBV1 = Voltage of actual antenna,V2 = Voltage of reference antenna

    Amount of power by an antenna through free space can be predicted by thefollowing:

    Pr = (Pt GtGrP2) / (16T2d2)

    Where:Pr = Power received (W),Pt = Power transmitted (W)Gt = Transmitting Antenna Gain (ratio, not dB) compared to isotropic

    radiator

    Gr = Receiving Antenna Gain (ratio, not dB) compared to isotropicradiatorP = wavelength (m),d = distance between antennas (m)

    Sample Problem

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    Antenna Parameters - IV

    Bandwidth: The "bandwidth" of an antenna is the range of frequencies over which it is effective,

    usually centered around the resonant frequency. The bandwidth of an antenna may be increased by several techniques, including

    using thicker wires, replacing wires with cages to simulate a thicker wire, taperingantenna components (like in a feed horn), and combining multiple antennas into asingle assembly and allowing the natural impedance to select the correct antenna.

    Impedance As an electro-magnetic wave travels through the different parts of the antenna

    system (radio, feed line, antenna, free space) it may encounter differences inimpedance

    The ratio of maximum power to minimum power in the wave can be measured and iscalled the standing wave ratio (SWR).

    Reducing SWR maximizing power transfer through each part of the antennasystem.

    SWR = Z0:ZLWhere:

    SWR = Standing Wave RatioZ0 = Characteristic impedance of the line

    ZL = Impedance of the load

    Sample Problem

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    Antenna Parameters - V

    Radiation Pattern:

    The radiation pattern is a graphical depiction of the relative field strengthtransmitted from or received by the antenna.

    Radiation pattern of an antenna can be defined as the locus of all pointswhere the emitted power per unit surface is the same.

    As the radiated power per unit surface is proportional to the squaredelectrical field of the electromagnetic wave. The radiation pattern is thelocus of points with the same electrical field

    Radiation pattern of a half-wave dipole antenna.Linear scale.

    Gain of a half-wave dipole. The scale is in dBi.

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    Antenna Parameters - VI

    Gain of a half-wave dipole. Cartesianrepresentation.

    3D Radiation pattern of a half-wave dipole antenna.

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    Antenna Parameters - VII

    Polarization:

    The "polarization" of an antenna is the orientation of the electric field (E-plane) of the radio wave with respect to the Earth's surface and isdetermined by the physical structure of the antenna and by itsorientation.

    Reflections generally affect polarization. For radio waves the mostimportant reflector is the ionosphere - signals which reflect from it willhave their polarization changed unpredictably

    Polarization is largely predictable from antenna construction, butespecially in directional antennas, the polarization of side lobes can bequite different from that of the main propagation lobe.

    Polarization is the sum of the E-plane orientations over time projectedonto an imaginary plane perpendicular to the direction of motion of theradio wave.

    Two special cases Linear polarization (the ellipse collapses into a line);

    and Circular polarization (in which the ellipse varies maximally).

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    Antenna Parameters - VIII

    Polarization (cont): In practice, regardless of confusing terminology, it is important that linearly

    polarized antennas be matched, lest the received signal strength be greatly reduced.So horizontal should be used with horizontal and vertical with vertical. Intermediatematchings will lose some signal strength, but not as much as a complete mismatch

    Efficiency "Efficiency" is the ratio of power actually radiated to the power put into the antenna

    terminals. A dummy load may have a SWR of 1:1 but an efficiency of 0, as it absorbs all power

    and radiates heat but not RF energy, showing that SWR alone is not an effectivemeasure of an antenna's efficiency.

    Radiation in an antenna is caused by radiation resistance which can only bemeasured as part of total resistance including loss resistance. Radiation resistancecan be expressed:

    Rr = P/I2

    Where:

    Rr = radiation resistance (ohm)I = effective rms value of antenna current at the feed point (A)P = total power radiated from the antenna

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    Antenna Parameters - IX

    Transmission and Reception:

    All of these parameters are expressed in terms of a transmissionantenna, but are identically applicable to a receiving antenna, dueto reciprocity.

    For a transmitting antenna, this is the antenna itself. For areceiving antenna, this is at the (radio) receiver rather than at theantenna. Tuning is done by adjusting the length of an electrically

    long linear antenna to alter the electrical resonance of theantenna.

    Antenna tuning is done by adjusting an inductance or capacitancecombined with the active antenna (but distinct and separate fromthe active antenna).

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    Antenna Parameters - X

    Transmission and Reception (cont):

    Antennas used for transmission have a maximum power rating,beyond which heating, arcing or sparking may occur in thecomponents, which may cause them to be damaged or destroyed.

    Antennas designed specifically for reception might be optimizedfor noise rejection capabilities.

    An "antenna shield" is a conductive or low reluctance structure

    (such as a wire, plate or grid) which is adapted to be placed inthe vicinity of an antenna to reduce, undesired electromagneticradiation, or electric or magnetic fields, which are directedtoward the active antenna from an external source or whichemanate from the active antenna.

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    Basic Antenna Models - I

    Isotropic Radiator - purely theoretical antenna that radiates equally in alldirections. It is considered to be a point in space with no dimensions and no

    mass. This antenna cannot physically exist, but is useful as a theoreticalmodel for comparison with all other antennas.

    Dipole Antenna - simply two wires pointed in opposite directions arrangedeither horizontally or vertically, Simplest practical antenna, it is also used as reference model for other antennas;

    gain with respect to a dipole is labeled as dBd.

    Generally, is considered to be omnidirectional.

    Yagi-Uda Antenna - is a directional variation of the dipole with parasiticelements added with functionality similar to adding a reflector and lenses(directors) to focus a filament lightbulb.

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    Basic Antenna Models - II

    Parabolic Antenna - is a special antenna where a reflector dish is used to focus the signalfrom a directional antenna feeder. Antennas of this type are commonly found as Satellite

    television antennas, Wi-fi / WLAN, radio astronomy, radio-links, mobile phone backhauland military tactical radio link -antennas. They are characterized by high directionalityand gain.

    Quad Antenna - is an array of square loops that vary in size. The quad is related to theloop in exactly the same way the yagi is related to the dipole. Typically, the quad needsfewer elements to get the same gain as a yagi.

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    Antennas in Reception - II

    Where:

    Va

    is the Thvenin equivalent circuit tension.

    Za is the Thvenin equivalent circuit impedance and is the same as the antennaimpedance.

    Ra is the series resistive part of the antenna impedance .

    Ga is the directive gain of the antenna (the same as in emission) in the direction ofarrival of electromagnetic waves.

    P is the wavelength.

    EB is the electrical field of the incoming electromagnetic wave.

    ] is the angle of misalignment of the electrical field of the incoming wave with theantenna. For a dipole antenna, the maximum induced voltage is obtained whenthe electrical field is parallel to the dipole. If this is not the case and they are

    misaligned by an angle , the induced voltage will be multiplied by cos ].

    is an universal constant called vacuum impedance.

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    Antennas in Reception - III

    From this formula, it is easy to prove the following definitions:

    Antenna effective length

    is the length which, multiplied by the electrical field of the received wave,give the voltage of the Thvenin equivalent antenna circuit.

    Maximum available power

    is the maximum power that an antenna can extract from the incomingelectromagnetic wave.

    Cross section or effective capture surface

    is the surface which multiplied by the power per unit surface of theincoming wave, gives the maximum available power

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    Effect of Ground - I

    At frequencies used in antennas, the ground behaves mainly as a dielectric.The conductivity of ground at these frequencies is negligible.

    When the object is a dielectric, the fraction reflected depends (among othersthings) on the angle of incidence. When the angle of incidence is small (thatis, the wave arrives almost perpendicularly) most of the energy traverses thesurface and very little is reflected. When the angle of incidence is near 90(grazing incidence) almost all the wave is reflected.

    Most of the electromagnetic waves emitted by an antenna to the ground

    below the antenna at moderate (say < 60) angles of incidence enter theearth and are absorbed (lost).

    The wave reflected by earth can be considered asemitted by the image antenna.

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    Effect of Ground - II

    For a vertical polarized emission antenna the far electric field of theelectromagnetic wave produced by the direct ray plus the reflected ray is:

    .

    The sign inversion for the parallel field case just changes a cosine to a sinus:

    In these two equations:

    is the electrical field radiated by the antenna if there were no ground.

    is the wave number.

    is the wave length.

    is the distance between antenna and its image (twice the height of thecenter of the antenna).

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    References

    1. Modern Electronic Communication by Jeffrey S Beasley and Garry

    Miller, 8

    th

    Edition, 2005. Pages: 648-6882. Electronic Communication by Adamson Thomas, 2nd Edition, 1992.

    Pages: 313-364

    3. Web Wikipedia (www.wikipedia.org) - Topic: Antenna

    http://en.wikipedia.org/wiki/Antenna_%28radio%29

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    END

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    BACKUP

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    Sample Problems - I

    Problem: What frequency is the shorted with length of 25cm. (A)one-quarter wavelength; (B) one-half wavelength.

    Solution:(A) First find the frequency where four times the length of the given

    transmission line will equal the wavelength

    P = 4 x 25 cm = 100cm = 1m, thus

    f = c/P

    = 3 x108 m/s /1 m

    f = 3 x108 Hz = 300 Mhz

    (B) First find the frequency where two times the length of the giventransmission line will equal the wavelength

    P = 2 x 25 cm = 50cm = 0.5m, thusf = c/P

    = 3 x108 m/s /0.5 m

    f = 6 x108 Hz = 600 Mhz

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    Sample Problems - II

    Problem: An antenna is radiating 500W and has a 6-dB gain over areference antenna. How much power must the reference antennain order to be equally effective in the most preferred direction?

    Solution:

    A(dB) = 10 log10 (P2/P1)

    6 = 10 log10 (P2/500)

    0.6 = log10 (P2/500)

    Antilog (0.6) = P2/500

    4 = P2/500

    P2= 4 x 500W = 2000W (2 KW)

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    Sample Problems - III

    Problem: Determine the dB gain of receiving antenna that deliversa 60-uV signal to a transmission line over that of an antenna thatdelivers a 20-uV signal under identical conditions?

    Solution:

    A(dB) = 20 log10 (V2/V1)

    A(dB) = 20 log10 (60 x 10-6/20 x 10-6)

    A(dB) = 20 log10 (3) = 200 (0.477)

    A(dB) = 9.54 dB

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    Sample Problems - IV

    Problem: Two P/2 dipoles are separated by 50km. They arealigned for optimum reception. The transmitter feeds its antennawith 10 W at 144 Mhz. Calculate the power received.

    Solution:

    The two dipoles have a gain of 2.15 dB. That translate into a gain ratio oflog-1 2.15, dB = 1.64

    Pr = (Pt GtGrP2) / (16T2d2)

    = (10 W x 1.64 x 1.64 x ( 3 x108/ 144 x 10 6) 2 ) / 16 T2 X(50 x 103M)2

    Pr = 2.96 x 10-10 W

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    Sample Problems - V

    Problem: Two P/2 dipoles are separated by 50km. They arealigned for optimum reception. The transmitter feeds its antennawith 10 W at 144 Mhz. Calculate the power received.

    Solution:

    The two dipoles have a gain of 2.15 dB. That translate into a gain ratio oflog-1 2.15, dB = 1.64

    Pr = (Pt GtGrP2) / (16T2d2)

    = (10 W x 1.64 x 1.64 x ( 3 x108/ 144 x 10 6) 2 ) / 16 T2 X(50 x 103M)2

    Pr = 2.96 x 10-10 W

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    Sample Problems - VI

    Problem: A transmission line with a characteristic impedance of50-ohm is delivering power to 150-ohm load. Calculate the SWR.

    Solution:

    SWR = Z0:ZL= 150-ohm/50-ohm

    SWR = 3:1