Antenna and Wave Propagation

Antenna and Wave Propagation

MirMuhammad Lodro, M.Res., M.E. Assistant Professor, Department of Electrical Engineering, Sukkur IBA

Jan 01, 2016

List of Figures 2.1 2.2 2.3 2.4 3.1 3.2

3.3 3.4 3.5

4.1 4.2 4.3

Loss tangent (conduction current density and displacement current density vectors are orthogonal to eachother) . . . . . . . . . . . . Skin Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of EM wave polarization . . . . . . . . . . . . . . . . . . . Circularly polarized EM wave with right hand sense of rotation[1] Half-wave dipole antenna . . . . . . . . . . . . . . . . . . . . . . . Radiation Pattern of Vertical Dipole (a)normalised E-plane or vertical pattern (φ = 0) (b) normalised H-plane or horizontal pattern (φ = π/2) (c) three-dimensional plane . . . . . . . . . . . . . . . . The monopole antenna . . . . . . . . . . . . . . . . . . . . . . . . Two-element antenna array diagram . . . . . . . . . . . . . . . . Radiation patterns of broadside array, intermediate array and end fire array [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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30 34 37 38

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Rhombic antenna geometrical structure and its radiation pattern[2] 86 Helical antenna operating modes . . . . . . . . . . . . . . . . . . . 88 Whip Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

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Contents 1 Introduction and Mathematical Preliminaries 1.1 Fundamentals of Scalars and Vector . . . . . . . 1.1.1 Dot Product . . . . . . . . . . . . . . . . 1.1.2 Cross Product . . . . . . . . . . . . . . . 1.2 Coordinate System . . . . . . . . . . . . . . . . 1.2.1 Cartesian Coordinate System . . . . . . 1.2.2 Properties of Unit Vectors . . . . . . . . 1.2.3 Cylindrical Coordinate System . . . . . . 1.2.4 Spherical Coordinate System . . . . . . . 1.3 DEL ∇ Operator . . . . . . . . . . . . . . . . . 1.3.1 Gradient of Scalar V . . . . . . . . . . .

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2 Propagation of EM Waves 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Maxwell’s Field Equations . . . . . . . . . . . . . . . . . . . . . 2.3 Maxwell’s Field Equations in Free Space . . . . . . . . . . . . . 2.4 Maxwell’s Equations for Harmonically Varying Fields . . . . . . 2.5 EM Wave in Homogeneous Medium . . . . . . . . . . . . . . . . 2.6 Wave Equations for Lossless Medium . . . . . . . . . . . . . . . 2.7 Uniform Plane Wave in Free Space . . . . . . . . . . . . . . . . 2.8 Solution of Maxwell’s Equation for Uniform Plane Wave . . . . 2.9 EM Wave Equation for Conducting Media . . . . . . . . . . . . 2.10 Propagation of EM Wave in Perfect Dielectrics . . . . . . . . . . 2.11 Propagation of Uniform Plane EM Wave in Conducting Medium

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2.12 Conductor and Dielectrics . . . . . . . . . . . . . . . . . . . . 2.13 Propagation of Plane EM Waves in Good Dielectrics . . . . . 2.14 Propagation of Plane EM Waves in Good Conductors . . . . . 2.14.1 Skin Depth . . . . . . . . . . . . . . . . . . . . . . . . 2.15 Impedance of Homogenous Isotropic Perfect Dielectric Medium 2.16 Electromagnetic Wave Polarization . . . . . . . . . . . . . . . 2.16.1 Linear Polarization . . . . . . . . . . . . . . . . . . . . 2.16.2 Elliptical Polarization . . . . . . . . . . . . . . . . . . . 2.16.3 Circular Polarization . . . . . . . . . . . . . . . . . . . 2.17 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 EM 3.1 3.2 3.3 3.4 3.5 3.6

Radiation and Antennas Introduction . . . . . . . . . . . . . . . . . Short Electric Dipole or Hertzian Antenna Retarded Vector Potential . . . . . . . . . Antenna Functions . . . . . . . . . . . . . Antenna Properties . . . . . . . . . . . . . Antenna Parameters . . . . . . . . . . . . 3.6.1 Antenna Impedance . . . . . . . . 3.6.2 Radiation Resistance . . . . . . . . 3.6.3 Directional Characteristics . . . . . 3.6.4 Effective Length of Antenna . . . . 3.6.5 Radiation Intensity . . . . . . . . . 3.6.6 Directive Gain . . . . . . . . . . . . 3.6.7 Directivity . . . . . . . . . . . . . . 3.6.8 Power Gain . . . . . . . . . . . . . 3.6.9 Antenna Efficiency . . . . . . . . . 3.6.10 Effective Area . . . . . . . . . . . . 3.6.11 Antenna Equivalent Circuit . . . . 3.6.12 Antenna Bandwidth . . . . . . . . 3.6.13 Front-to-Back Ratio (FBR) . . . . 3.6.14 Polarization . . . . . . . . . . . . . 3.7 Basic Antenna Elements . . . . . . . . . . 3

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3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17

3.18

Directivity of Electric Current Element . . . . . . . . . . . . . . . Gain of Half-wavelength Antenna . . . . . . . . . . . . . . . . . . Radiation Pattern of Alternating Current Element . . . . . . . . . Radiation Pattern Expression of Center-fed Vertical Dipole of Finite Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Pattern of Center-fed Vertical Dipole . . . . . . . . . . Radiation Pattern of Center-fed Horizontal Dipole . . . . . . . . . Radiation Pattern of Vertical Monopole . . . . . . . . . . . . . . . Two-element Uniform Array . . . . . . . . . . . . . . . . . . . . . Field Strength of Uniform Linear Array . . . . . . . . . . . . . . . 3.16.1 First Side-lobe Ratio (FSR) . . . . . . . . . . . . . . . . . Broadside Array and End-fire Array . . . . . . . . . . . . . . . . . 3.17.1 Broadside Array . . . . . . . . . . . . . . . . . . . . . . . . 3.17.2 End-fire Array . . . . . . . . . . . . . . . . . . . . . . . . . Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Antennas for HF, VHF 4.1 Introduction . . . . . 4.2 Yagi-Uda Antenna . 4.3 Folded Dipole . . . . 4.4 V-antenna . . . . . . 4.5 Inverted V-antenna . 4.6 Rhombic Antenna . . 4.7 Helical Antenna . . . 4.8 Whip Antenna . . .

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5 Radio Wave Propagation 5.1 Factors Involved in Propagation of Radio Waves . 5.2 Factors that Influence the Propagation . . . . . . 5.3 Ground Wave Field Strength . . . . . . . . . . . . 5.4 Reflection of Radio Waves by the Surface of Earth 5.4.1 Roughness of Earth . . . . . . . . . . . . . 5.4.2 Reflection Factors of Earth . . . . . . . . .

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5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13

5.14 5.15 5.16 5.17 5.18

5.19 5.20

Space Wave or Tropospheric Wave Propagation . . . . Field Strength Due to Space Wave . . . . . . . . . . . Duct Propagation . . . . . . . . . . . . . . . . . . . . . Duct Propagation . . . . . . . . . . . . . . . . . . . . . Troposcatter . . . . . . . . . . . . . . . . . . . . . . . . Fading of EM Waves in Troposphere . . . . . . . . . . Line of Sight (LOS) . . . . . . . . . . . . . . . . . . . . Ionospheric Wave Propagation . . . . . . . . . . . . . . Characteristics of Ionosphere . . . . . . . . . . . . . . . 5.13.1 Characteristics of D-Layer . . . . . . . . . . . . 5.13.2 Characteristics of E-Layer . . . . . . . . . . . . 5.13.3 Characteristics of Es -Layer . . . . . . . . . . . . 5.13.4 Characteristics of F1 -Layer . . . . . . . . . . . . 5.13.5 Characteristics of F2 Layer . . . . . . . . . . . . Refractive Index of Ionosphere . . . . . . . . . . . . . . 5.14.1 Critical Frequency . . . . . . . . . . . . . . . . Mechanism of Ionospheric Propagation—Reflection and Characteristics Parameters of Ionospheric Propagation Faraday Rotation . . . . . . . . . . . . . . . . . . . . . Ionospheric Abnormalities . . . . . . . . . . . . . . . . 5.18.1 Normal . . . . . . . . . . . . . . . . . . . . . . 5.18.2 Abnormal . . . . . . . . . . . . . . . . . . . . . Ionospheric Storms . . . . . . . . . . . . . . . . . . . . Sudden Ionospheric Disturbance (SID) . . . . . . . . .

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Chapter 1 Introduction and Mathematical Preliminaries 1.1

Fundamentals of Scalars and Vector

A scalar has magnitude and an algebraic sign. For example temperature, mass, charge, work, and so on. Whereas a vector has both magnitude and direction. For example velocity, force, electric field, magnetic field and so on. A vector A is expressed in two forms A = Ax , Ay , Az and A = Ax ax + Ay ay + Az az , where Ax , Ay , Az and ax , ay + az are known as components of vector A and unit vectors along the coordinate axes. The magnitude of A is written as A = |A|. The unit vector of A is a and is given by a=

A A

The sum and difference of two vectors are given by A + B = (Ax + Bx )ax + (Ay + By )ay + (Az + Bz )az A − B = (Ax − Bx )ax + (Ay − By )ay + (Az − Bz )az

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1.1.1

Dot Product

The dot product of two vectors is given by A · B orB · A A · B = B · A = AB cos θ A · B = Ax Bx + Ay By + Az Bz

Where θ is the angle between vectors A and B. The dot product of two vectors is scalar.

1.1.2

Cross Product

The cross product of two vectors is denoted by A × B as follows: A × B = AB sin θan Where an is unit vector perpendicular to A and B. Moreover

ax ay az A × B = Ax Ay Az Bx By Bz = ax [Ay Bz − Az By ] + ay [Az Bx − Ax Bz ] + az [Ax By − Ay Bx ] Cross product of two vectors is a vector.

1.2

Coordinate System

Coordinate system is defined as a system used to represent a point in space. Basically coordinate systems are of three types namely cartesian coordinate system, cylindrical coordinate system and spherical coordinate system. 7

1.2.1

Cartesian Coordinate System

In this system a point P is represented by P (x, y, z). The variables are x, y, z. A point is obtained by intersection of three planes given by x = k1 , y = k2 , z = k3 . The unit of x,y and z is meter. The three axes x,y, z are mutually perpendicular. These are said to be orthogonal to each other.

1.2.2

Properties of Unit Vectors

Following are the possible combinations of the dot and cross multiplication of the unit vectors. ax · ax = 1

ay · az = 0

ay · ay = 1

az × ay = az

az · az = 1

ay × az = ax

ax × ax = 0

az × ax = ay

ay × ay = 0

ay × ax = −az

az × az = 0

az × ay = −ax

ax · ay = 0

ax × az = −ay

ax · az = 0

1.2.3

Cylindrical Coordinate System

In this system a point P is represented by P (ρ, φ, z) where ρ represents radius of cylinder, φ is called azimuthal angle and z is same as in Cartesian coordinate system. The unit of ρ is meter,φ is measured in degree or radian and z is given in meters. In Cylindrical coordinate system, appoint is obtained by intersection of three surface namely:

A cylindrical surface

ρ = k1 meter

A plane

φ = α radian

Another plane

z = k2 meter

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All the three surface are mutually perpendicular. These are said to be mutually orthogonal. A point in Cylindrical coordinate system is shown as P (ρ, φ, z). The coordinate ρ is radius of the cylinder, φ is measured from x−axis and z is measured the same way as for cartesian system. Here aρ , aφ , az represents unit vectors along the coordinates ρ,φ and z. Their magnitude is unity and they are in the increasing directions of ρ,φ, z respectively. It is obvious that increase in ρ results in cylinders of greater radius, φ increases in anti-clockwise direction, z is same as in cartesian system. The relations between x, y, z and ρ,φ, z: x = ρ cos φ y = ρ sin φ z=z and p

x2 + y 2 0 ≤ ρ < ∞ y φ = tan−1 , 0 ≤ φ < 2π x z=z 0≤z θc and it will be reflected when θ < θc . It depends on thickness of the layer, height and frequency of the wave.

5.17

Faraday Rotation

Rotation of the plane of polarisation is defined as Faraday Rotation. The process occurs in the ionospheric regions when a plane wave enters the ionosphere. It’s variable effect and leads to loss of signal power at the receiving antenna due to polarisation mismatch.

5.18

Ionospheric Abnormalities

Electrical characteristics of the ionosphere depend on solar radiation and hence they vary continuously. the variations of ionosphere are classified as follows:

5.18.1

Normal

Normal variation in the characteristics of the ionosphere occur due to the following: • Diurnal • Seasonal • Thickness • Height variations of the ionosphere layer

5.18.2

Abnormal

The abnormal variations in the characteristics of the ionosphere occur mainly due to changes in solar activity. The common abnormal variations are: 104

• Ionospheric storms • Sunspot cycle • Fading • Whistlers • Tides and Winds

5.19

Ionospheric Storms

These are due to high absorption of sky waves and abnormal changes at critical frequencies of E and F2 layers.These storms usually persist for few days.

5.20

Sudden Ionospheric Disturbance (SID)

The sudden appearance of solar flares causes SIDs. The solar flares occur suddenly and sporadically. These occur during solar peak activity. SIDs block out signals completely. They persists for few minutes to an hour. SIDs do not occur at layer of low air density and hence it’s not found in E, F1 and F2 layer.

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Bibliography [1] William Hart Hayt and John A Buck. Engineering electromagnetics, volume 7. McGraw-Hill New York, 2001. [2] Warren L Stutzman and Gary A Thiele. Antenna theory and design. John Wiley & Sons, 2012.

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