Lecture Notes Antenna & Wave Propagation

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Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Lecture Notes On Antenna & Wave Propagation B.TECH ECE III YEAR I SEMESTER (JNTUA-R13) by Dr.V.Thrimurthulu Professor & Head Department of Electronics & Communication Engineering Chadalawada Ramanamma Engineering College Chadalawada Nagar, Renigunta Road Tirupathi CREC Dept. of ECE P a g e 1 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR B.Tech. III - I Sem (13A04501) ANTENNAS & WAVE PROPAGATION Course Objective: 1. To introduce the fundamental principles of antenna theory and various types of antennas. 2. Applying the principles of antennas to the analysis, design, and measurements of antennas. 3. To know the applications of some basic and practical configurations such as dipoles, loops, 4. and broadband, aperture type and horn antennas. Learning Outcome: Through lecture, and out-of-class assignments, students are provided learning experiences that enable them to: a) Understand the basic principles of all types of antennas and b) Analyze different types of antennas designed for various frequency ranges. c) Become proficient with analytical skills for understanding practical antennas. d) Design some practical antennas such as dipole, Yagi - uda, and horn antennas. e) Determine the radiation patterns (in principal planes) of antennas through measurement setups. f) Develop technical & writing skills important for effective communication. g) Acquire team-work skills for working effectively in groups. UNIT I : Antenna Basics & Dipole antennas: Introduction, Basic antenna parameters- patterns, Beam Area, Radiation Intensity, Beam Efficiency, Directivity-Gain-Resolution, Antenna Apertures, Effective height, Fields from oscillating dipole, Field Zones, Shape-Impedance considerations, Polarization – Linear, Elliptical, & Circular polarizations, Antenna temperature, Antenna impedance, Front–to-back ratio, Antenna theorems, Radiation – Basic Maxwell‘s equations, Retarded potential-Helmholtz Theorem, Radiation from Small Electric Dipole, Quarter wave Monopole and Half wave Dipole – Current Distributions, Field Components, Radiated power, Radiation Resistance, Beam width, Natural current distributions, far fields and patterns of Thin Linear Center-fed Antennas of different lengths, Illustrative problems. UNIT II : VHF, UHF and Microwave Antennas - I: Loop Antennas - Introduction, Small Loop, Comparison of far fields of small loop and short dipole, Radiation Resistances and Directives of small and large loops (Qualitative Treatment), Arrays with Parasitic Elements - Yagi - Uda Arrays, Folded Dipoles & their characteristics. Helical Antennas-Helical Geometry, Helix modes, Practical Design considerations for Monofilar Helical Antenna in Axial and Normal Modes. Horn Antennas- Types, Fermat‘s Principle, Optimum Horns, Design considerations of Pyramidal Horns, Illustrative Problems. UNIT III :VHF, UHF and Microwave Antennas - II: Micro strip Antennas- Introduction, features, advantages and limitations, Rectangular patch antennas- Geometry and parameters, characteristics of Micro strip antennas, Impact of different parameters on characteristics, reflector antennas - Introduction, Flat sheet and corner reflectors, parabola reflectors- geometry, pattern characteristics, Feed Methods, Reflector Types - Related Features, Lens Antennas - Geometry of Non-metallic Dielectric Lenses, Zoning , Tolerances, Applications, Illustrative Problems. UNIT IV : Antenna Arrays & Measurements: Point sources - Definition, Patterns, arrays of 2 Isotropic sources- Different cases, Principle of Pattern Multiplication, Uniform Linear Arrays – Broadside Arrays, Endfire Arrays, EFA with Increased Directivity, Derivation of their characteristics and comparison, BSAa CREC Dept. of ECE P a g e 2 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation with Non-uniform Amplitude Distributions - General considerations and Bionomial Arrays, Illustrative problems. Antenna Measurements: Introduction, Concepts- Reciprocity, Near and Far Fields, Coordination system, sources of errors, Patterns to be Measured, Pattern Measurement Arrangement, Directivity Measurement , Gain Measurements (by comparison, Absolute and 3-Antenna Methods). UNIT V : Wave Propagation: Introduction, Definitions, Characterizations and general classifications, different modes of wave propagation, Ray/Mode concepts, Ground wave propagation (Qualitative treatment) - Introduction, Plane earth reflections, Space and surface waves, wave tilt, curved earth reflections, Space wave propagation - Introduction, field strength variation with distance and height, effect of earth‘s curvature, absorption, Super refraction, M-curves and duct propagation, scattering phenomena, tropospheric propagation, fading and path loss calculations, Sky wave propagation - Introduction, structure of Ionosphere, refraction and reflection of sky waves by Ionosphere, Ray path, Critical frequency, MUF, LUF, OF, Virtual height and Skip distance, Relation between MUF and Skip distance, Multi-HOP propagation, Energy loss in Ionosphere, Summary of Wave Characteristics in different frequency ranges, Illustrative problems. Text Books: 1. John D. Kraus and Ronald J. Marhefka and Ahmad S.Khan, ―Antennas and wave propagation,‖ TMH, New Delhi, 4th Ed., (special Indian Edition), 2010. 2. E.C. Jordan and K.G. Balmain, ―Electromagnetic Waves and Radiating Systems,‖ PHI, nd 2 Edn, 2000. Reference Books: 1. C.A. Balanis, ―Antenna Theory- Analysis and Design,‖ John Wiley & Sons, 2nd Edn., 2001. 2. K.D. Prasad, Satya Prakashan, ―Antennas and Wave Propagation,‖ Tech. India Publications, New Delhi, 2001. 3. E.V.D. Glazier and H.R.L. Lamont, ―Transmission and Propagation - The Services Text Book of Radio,‖ vol. 5, Standard Publishers Distributors, Delhi. 4. F.E. Terman, ―Electronic and Radio Engineering,‖ McGraw-Hill, 4th edition, 1955. 5. John D. Kraus, ―Antennas,‖ McGraw-Hill (International Edition), 2nd Edn., 1988. CREC Dept. of ECE P a g e 3 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation UNIT I Antenna Basics & Dipole antennas CREC Dept. of ECE P a g e 4 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation 1. Fundamental Concept 1.1 Introduction:  An antenna (or aerial) is an electrical device which converts electric power into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver. In transmission, a radio transmitter supplies an oscillating radio frequency electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts some of the power of an electromagnetic wave in order to produce a tiny voltage at its terminals, that is applied to a receiver to be amplified.  Antennas are essential components of all equipment that uses radio. They are used in systems such as radio broadcasting, broadcast television, two-way radio, communications receivers, radar, cell phones, and satellite communications, as well as other devices such as garage door openers, wireless microphones, bluetooth enabled devices, wireless computer networks, baby monitors, and RFID tags on merchandise.  Typically an antenna consists of an arrangement of metallic conductors ("elements"), electrically connected (often through a transmission line) to the receiver or transmitter.  Antennas act as transformers between conducted waves and electromagnetic waves propagating freely in space.  Their name is borrowed from zoology, in which the Latin word antennae is used to describe the long, thin feelers possessed by many insects.  In wireless communication systems, signals are radiated in space as an electromagnetic wave by using a receiving transmitting antenna and a fraction of this radiated power is intercepted by using a receiving antenna.  An antenna is a device used for radiating or receiver radio waves. An antenna can also be thought of as a transitional structure between free space and a guiding device (such as transmission line or waveguide). Usually antennas are metallic structures, but dielectric antennas are also used now a day.  a rigid metallic structure is called an "antenna" while the wire form is called an "aerial" With this introduction, in this first lecture let us see some common types of antennas that are in use: 1.2 Types of Antennas: Wire antennas: (Fig. 1, 2 and Fig. 9 single element) o dipole, monopole, loop antenna, helix o Usually used in personal applications, automobiles, buildings, ships, aircrafts and spacecrafts. Aperture antennas: (Fig. 3, 4) o horn antennas, waveguide opening o Usually used in aircrafts and space crafts, because these antennas can be flush- CREC Dept. of ECE P a g e 5 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation mounted. Reflector antennas: (Fig. 5) o parabolic reflectors, corner reflectors o These are high gain antennas usually used in radio astronomy, microwave communication and satellite tracking. Lens antennas: o convex-plane, co vex-convex , convex-concave and concave-plane lenses o These antennas are usually used for very high frequency applications. Microstrip antennas: (Fig. 6) o rectan gular, circular etc. shaped metallic patch above a ground plane o Used in aircraft, spacecraft, s atellites, mis siles, cars, mobile phones etc. Array antennas: (Fig. 7, and 8) o Yagi-Uda antenn a, microstrip patch array, aperture array, slotted waveguide array. o Used for very high gain applications with added advantage, such as, controllable radiation pattern. Fig. 1 Fig. 2 Fig. 3 Fig. 4 CREC Dept. of ECE P a g e 6 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Fig. 5 Fig. 6 Fig. 7 Fig. 8 1.3 Radiation Mechanism: When electric charges undergo acceleration or deceleration, electromagnetic radiation will be produced. Hence it is the motion of charges, that is currents, is the source of radiation. Here it may be highlighted that, not all current distributions will produce a strong enough radiation for communication. To give a mathematical flavor to it, as we know 1.1 And 1.2 So -1.3  As shown in these equations, to creat radiation (electric field), there must be a time- varying current dI/dt or an acceleration (or deceleration) a of a charge q.    If the charge is not moving, a current is not created and there is no radiation.    If a charge is moving with an uniform velocity,   there is no radiation if the wire is straight, and infinite in extent  there is radiation if the wire is curved, bent, discontinuous, terminated, or truncated  If the charge is oscillating in a time-motion, it radiates even if the wire is straight.  These situations are shown in Fig. 9. CREC Dept. of ECE P a g e 7 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Fig. 9: Conditions for radiation So, it is the current distribution on the antennas that produce the radiation. Usually these current distributions are excited by transmission lines and waveguides ( Fig. 10) Fig. 10: Antenna radiation mechanism Principle- Under time varying conditions , Maxwell‗s equations predict the radiation of EM energy from current source(or accelerated charge). This happens at all frequencies , but is insignificant as long as the size of the source region is not comparable to the wavelength. While transmission.lines are designed to minimize this radiation loss, radiation into free space becomes main purpose in case of Antennas . For steady state harmonic variation, usually we focus on time changing current For transients or pulses ,we focus on accelerated charge The radiation is perpendicular to the acceleration. The radiated power is proportional to the square of . I L or Q V Where I = Time changing current in Amps/sec L = Length of the current element in meters Q= Charge in Coulombs V= Time changing velocity Transmission line opened out in a Tapered fashion as Antenna: CREC Dept. of ECE P a g e 8 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation a) As Transmitting Antenna: –Here the Transmission Line is connected to source or generator at one end. Along the uniform part of the line energy is guided as Plane TEM wave with little loss. Spacing between line is a small fraction of λ. As the line is opened out and the separation b/n the two lines becomes comparable to λ, it acts like an antenna and launches a free space wave since currents on the transmission Line flow out on the antenna but fields associated with them keep on going. From the circuit point of view the antennas appear to the tr. lines As a resistance R , called Radiation resistance r b) As Receiving Antenna –Active radiation by other Antenna or Passive radiation from distant objects raises the apparent temperature of R This has nothing to do with the physical r . temperature of the antenna itself but is related to the temperature of distant objects that the antenna is looking at. R may be thought of as virtual resistance that does not exist physically but r is a quantity coupling the antenna to distant regions of space via a virtual transmission .line Figure11:Antenna as a a) Transmission Mode b) Receiving Mode Reciprocity-An antenna exhibits identical impedance during Transmission or Reception, same directional patterns during Transmission or Reception, same effective height while transmitting or receiving . Transmission and reception antennas can be used interchangeably. Medium must be linear, passive and isotropic(physical properties are the same in different directions.) Antennas are usually optimised for reception or transmission, not both. CREC Dept. of ECE P a g e 9 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Current and voltage distribution. a) A current flowing in a wire of a length related to the RF produces an electromagnetic field. This field radiates from the wire and is set free in space. The principles of radiation of electromagnetic energy are based on two laws. (1) A moving electric field creates a magnetic (H) field. (2) A moving magnetic field creates an electric (E) field. b) In space, these two fields will be in-phase and perpendicular to each other at any given moment. Although a conductor is usually considered to be present when a moving electric or magnetic field is mentioned, the laws governing these fields do not say anything about a conductor. Thus, these laws hold true whether a conductor is present or not. c) The current and voltage distribution on a half-wave Hertz antenna is shown in Figure 1-1. In view A, a piece of wire is cut in half and attached to the terminals of a high frequency (HF), alternating current (AC) generator. The frequency of the generator is set so each half of the wire is one-quarter wavelength of the output. The symbol for wavelength is the Greek letter lambda (D). The result is the common dipole antenna. d) At a given moment, the generator's right side is positive and its left side is negative. A law of physics states that like charges repel each other. Consequently, electrons will flow away from the negative terminal as far as possible while the positive terminal will attract electrons. View B of Figure 1-1 shows the direction and distribution of electron flow. The distribution curve shows that most current flows in the center and none flows at the ends. The current distribution over the antenna is always the same, regardless of how much or how little current is flowing. However, current at any given point on the antenna will vary directly with the amount of voltage that the generator develops. e) One-quarter cycle after the electrons begin to flow, the generator develops it; minimum voltage and the current decreases to zero. At that moment, the condition shown in view C of Figure 1-1 will exist. Although no current is flowing, a minimum number of electrons are at the left end of the line and a minimum number are at the right end. The charge distribution along the wire varies as the voltage of the generator varies (view C). f) Figure 12. Current and voltage distribution on an antenna 1. A current flows in the antenna with an amplitude that varies with the generator voltage. 2. A sine wave distribution of charge exists on the antenna. The charges reverse polarity every half cycle. 3. The sine wave variation in charge magnitude lags the sine wave variation in current by one-quarter cycle. CREC Dept. of ECE P a g e 10 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation 1.4 Antenna Parameters: Figure 13 :Schematic diagram of basic parameters Dual Characteristics of an Antenna The duality of an antenna specifies a circuit device on one band and a space device on the other hand. Figure 13 shows the schematic diagram of basic antenna parameters, illustrating dual characteristics of an antenna. Most practical transmitting antennas are divided into two basic classifications, HERTZ ANTENNAS (half-wave) and MARCONI (quarter-wave) ANTENNAS. Hertz antennas are generally installed some distance above the ground and are positioned to radiate either vertically or horizontally. Marconi antennas operate with one end grounded and are mounted perpendicular to the earth or a surface acting as a ground. The Hertz antenna, also referred to as a dipole, is the basis for some of the more complex antenna systems used today. Hertz antennas are generally used for operating frequencies of 2 MHz and above, while Marconi antennas are used for operating frequencies below 2 MHz.All antennas, regardless of their shape or size, have four basic characteristics: reciprocity, directivity, gain, and polarization. Isotropic Radiator:An antenna does not radiate uniformly in all directions. For the sake of a reference, we consider a hypothetical antenna called an isotropic radiator having equal radiation in all directions. Directional Antenna: A directional antenna is one which can radiate or receive electromagnetic waves more effectively in some directions than in others. Radiation Pattern: The relative distribution of radiated power as a function of direction in space (i.e., as function of and ) is called the radiation pattern of the antenna. Instead of 3D surface, it is common practice to show planar cross section radiation pattern. E-plane and H-plane patterns give two most important views. The E-plane pattern is a view obtained from a section containing maximum value of the radiated field and electric field lies in the plane of the section. Similarly when such a section is taken such that the plane of the section contains H field and the direction of maximum radiation.A typical radiation patter plot is shown in figure 14. The main lobe contains the direction of maximum radiation. However in some antennas, more than one major lobe may exist. Lobe other than major lobe are called minor lobes. Minor lobes can be further represent radiation in the considered direction and require to be minimized. CREC Dept. of ECE P a g e 11 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation HPBW or half power beam width refers to the angular width between the points at which the radiated power per unit area is one half of the maximum. Figure 14: Radiation Pattern Similarly FNBW (First null beam width) refers to the angular width between the first two nulls as shown in Figure 14. By the term beam width we usually refer to 3 dB beam width or HPBW. RECIPROCITY is the ability to use the same antenna for both transmitting and receiving. The electrical characteristics of an antenna apply equally, regardless of whether you use the antenna for transmitting or receiving. The more efficient an antenna is for transmitting a certain frequency, the more efficient it will be as a receiving antenna for the same frequency. This is illustrated by figure 2-1, view A. When the antenna is used for transmitting, maximum radiation occurs at right angles to its axis. When the same antenna is used for receiving (view B), its best reception is along the same path; that is, at right angles to the axis of the antenna. Figure 13. Reciprocity of Antenna CREC Dept. of ECE P a g e 12 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Polarization of an electromagnetic wave refers to the orientation of the electric field component of the wave. For a linearly polarized wave, the orientation stays the same as the wave moves through space. If we choose our axis system such that the electric field is vertical, we say that the wave is vertically polarized. If our transmitting antenna is vertically oriented, the electromagnetic wave radiated is vertically polarized since, as we saw before, the electric field is in the direction of the current in the antenna. The convention is to refer to polarization with reference to the surface of the earth. Precise orientation is less problematic than one might think, since waves bounce of the ground and other objects so do not maintain their original orientation anyway. In space, horizontal and vertical lose their meaning, so alignment of linearly polarized sending and receiving antennas is more difficult to achieve. These difficulties are somewhat circumvented by circular polarization of waves. With circular polarization, the tip of the electric field vector traces out a circle when viewed in the direction of propagation. Figure 15. Polarisation Polarization categories Vertical and horizontal are the simplest forms of polarization and they both fall into a category known as linear polarization. However it is also possible to use circular polarization. This has a number of benefits for areas such as satellite applications where it helps overcome the effects of propagation anomalies, ground reflections and the effects of the spin that occur on many satellites. Circular polarization is a little more difficult to visualize than linear polarization. However it can be imagined by visualizing a signal propagating from an antenna that is rotating. The tip of the electric field vector will then be seen to trace out a helix or corkscrew as it travels away from the antenna. Circular polarization can be seen to be either right or left handed dependent upon the direction of rotation as seen from the transmitter. Another form of polarization is known as elliptical polarization. It occurs when there is a mix of linear and circular polarization. This can be visualized as before by the tip of the electric field vector tracing out an elliptically shaped corkscrew. However it is possible for linearly polarized antennas to receive circularly polarized signals and vice versa. The strength will be equal whether the linearly polarized antenna is mounted vertically, horizontally or in any other plane but directed towards the arriving signal. There will be some degradation because the signal level will be 3 dB less than if a circularly polarized CREC Dept. of ECE P a g e 13 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation antenna of the same sense was used. The same situation exists when a circularly polarized antenna receives a linearly polarized signal. Figure: ( a) Linear polarization (b) Circular polarization (c) Elliptical polarization DIRECTIVITY The DIRECTIVITY of an antenna or array is a measure of the antenna‘s ability to focus the energy in one or more specific directions. You can determine an antenna‘s directivity by looking at its radiation pattern. In an array propagating a given amount of energy, more radiation takes place in certain directions than in others. The elements in the array can be arranged so they change the pattern and distribute the energy more evenly in all directions. The opposite is also possible. The elements can be arranged so the radiated energy is focused in one direction. The elements can be considered as a group of antennas fed from a common source. It is defined as the ratio of maximum radiation intensity of subject or test antenna to the radiation intensity of an isotropic antenna. (or) Directivity is defined as the ratio of maximum radiation intensity to the average radiation intensity. Directivity (D) in terms of total power radiated is, D = 4π x Maximum radiation intensity/ Total power radiated Gain: Gain is a parameter which measures the degree of directivity of the antenna's radiation pattern. A high-gain antenna will preferentially radiate in a particular direction. Specifically, the antenna gain, or power gain of an antenna is defined as the ratio of the intensity (power per unit surface) radiated by the antenna in the direction of its maximum output, at an arbitrary distance, divided by the intensity radiated at the same distance by a hypothetical isotropic antenna. As we mentioned earlier, some antennas are highly directional. That is, they propagate more energy in certain directions than in others. The ratio between the amount of energy propagated in these directions and the energy that would be propagated if the antenna were not directional is known as antenna GAIN. The gain of an antenna is constant. whether the antenna is used for transmitting or receiving. Directivity function D  , describes the variation of the radiation intensity. The directivity  function D  , is defined by  Power radiated per unit solid angle D  , = - (1)  Average power radiated per unit solid an gle CREC Dept. of ECE P a g e 14 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation dP r If P is the radiated power, the gives the amount of power radiated per unit solid angle. Had r d this power beam uniformly radiated in all directions then average power radiated per unit solid P r angle is . 4 dP dP rr dd  ............................. (2) D,4 P P r r 4 The maximum of directivity function is called the directivity. In defining directivity function total radiated power is taken as the reference. Another parameter called the gain of an antenna is defined in the similar manner which takes into account the total input power rather than the total radiated power is used as the reference. The amount of power given as input to the antenna is not fully radiated. PP …………………………………… (3) r in where  is the radiation efficiency of the antenna. The gain of the antenna is defined as Radiated power per unit solid angle G,4 - (4)  input power GD,, (5)  The maximum gain function is termed as gain of the antenna. Another parameter which incorporates the gain is effective isotropic radiated power or EIRP which is defined as the product of the input power and maximum gain or simply the gain. An antenna with a gain of 100 and input power of 1 W is equally effective as an antenna having a gain of 50 and input power 2 W. Radiation resistance: The radiation resistance of an antenna is defined as the equivalent resistance that would dissipate the same amount power as is radiated by the antenna. For the elementary current element we have discussed so far. From equation (3.26) we find that radiated power density 2 2 22  I dl k sin  00 Pa (1) r av 22 32 r Radiated power CREC Dept. of ECE P a g e 15 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation 2 2 22 22  2 22  I dl k I dl k 00 22 00 3 P sin r sin d d  dd sin (2) r 22 2   32 r 32   00   00 2 2 I k dl  00  P ................................... (3) 12  2 2 Further, dP P .r sin d d ar P .ar r d r av av 2 2 2 I k dl sin dP 00 r  ……………… (4) 2 d 32 From (3) and (4) 2 D,1.5sin  Directivity DD  , which occurs at  .  max 2 If R is the radiation resistance of the elementary dipole antenna, then r 1 2 I R P rr 2 Substituting P from (3) we get r 2   dl 0 R 2 . - (5)  r 6  0 Substituting  120 0 2 3  480 dl R - (6)  r 6  0 2  dl 2 R 80 ………………….. (7)  r   0 For such an elementary dipole antenna the principal E and H plane pattern are shown in Fig 16(a) and (b). Fig ure16(b) Principal H plane pattern Figure16 (a) Principal E plane pattern eelemenrelementary 0 Dipole. The bandwidth (3 dB beam width) can be found to be 90 in the E plane. Dipole. CREC Dept. of ECE P a g e 16 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Effective Area of an Antenna: An antenna operating as a receiving antenna extracts power from an incident electromagnetic wave. The incident wave on a receiving antenna may be assumed to be a uniform plane wave being intercepted by the antenna. This is illustrated in Fig 3.5. The incident electric field sets up currents in the antenna and delivers power to any load connected to the antenna. The induced current also re-radiates fields known as scattered field. The total electric field outside the antenna will be sum of the incident and scattered fields and for perfectly conducing antenna the total tangential electric field component must vanish on the antenna surface. Fig 17: Plane wave intercepted by an antenna Let P represents the power density of the incident wave at the location of the receiving antenna inc and P represents the maximum average power delivered to the load under matched conditions L with the receiving antenna properly oriented with respect to the polarization of the incident wave. We can write, P A P ................................ (9) L em inc 2 E where P and the term A is called the maximum effective aperture of the antenna. A em em inc 2 0 is related to the directivity of the antenna D as, 4 DA - (10) em 2  If the antenna is lossy then some amount of the power intercepted by the antenna will be dissipated in the antenna. From eqn. (2) we find that GD Therefore, from (5), 44  G A A ....................................................(11)  em e 22  2 AA is called the effective aperture of the antenna ( in m ). e em CREC Dept. of ECE P a g e 17 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation So effective area or aperture A of an antenna is defined as that equivalent area which when e intercepted by the incident power density P gives the same amount of received power P which in R is available at the antenna output terminals. A e If the antenna has a physical aperture A then aperture efficiency  a A  Effective length/height of the antenna: When a receiving antenna intercepts incident electromagnetic waves, a voltage is induced across the antenna terminals. The effective length he of a receiving antenna is defined as the ratio of the open circuit terminal voltage to the incident electric field strength in the direction of antennas polarization. V oc hm ……………………………….. (12) e E where V = open circuit voltage oc E = electric field strength Effective length he is also referred to as effective height. Radian and Steradian: Radian is plane angle with it‗s vertex a the centre of a circle of radius r and is subtended by an arc whose length is equal to r. Circumference of the circle is 2πr Therefore total angle of the circle is 2π radians. Steradian is solid angle with it‗s vertex at the centre of a sphere of radius r, which is subtended by a spherical surface area equal to the area of a square with side length r Area of the 2 sphere is 4πr . Therefore the total solid angle of the sphere is 4π steradians  Beam Area In polar two-dimensional coordinates an incremental area dA on the surface of sphere is the product of the length r dθ in the θ direction and r sin θ dΦ in the Φ direction as shown in figure Figure 18: radian and steradian CREC Dept. of ECE P a g e 18 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation Thus 2 dA = (rdθ) (r sinθ dΦ) = r dΩ Where, dΩ = solid angle expressed in steradians. The area of the strip of width r dθ extending around the sphere at a constant angle θ is given by (2πr sin θ) (r dθ). Integrating this for θ values from 0 to π yields the area of the sphere. Thus, Area of sphere = 2πr2 2 = 2πr -cosθ0 2 π = 4πr Where, 4π = Solid angle subtended by a sphere The beam area or beam solid angle or ΩA of an antenna is given by the integral of the normalized power pattern over a sphere Beam area, ΩA = Ω (sr) Where, dΩ = sinθ dθ dΦ  Radiation Intensity The power radiated from an antenna per unit solid angle is called the radiation intensity U (watts per steradian or per square degree). The normalized power pattern of the previous section can also be expressed in terms of this parameter as the ratio of the radiation intensity U (θ , Φ ), as a function of angle, to its maximum value. Thus, Pn(θ,Φ) = U(θ,Φ)/U(θ,Φ)max = S(θ,Φ)/S(θ,Φ)max Whereas the Poynting vector S depends on the distance from the antenna (varying inversely as the square of the distance), the radiation intensity U is independent of the distance, assuming in both cases that we are in the far field of the antenna  Beam Efficiency The beam area QA (or beam solid angle) consists of the main beam area (or solid angle) ΩM plus the minor-lobe area (or solid angle) Ω m . Thus, ΩA = ΩM + Ω m The ratio of the main beam area to the (total) beam area is called the (main) beam efficiency εM. Thus, Beam Efficiency = εM = ΩM/ ΩA (dimensionless) The ratio of the minor-lobe area ( Ω m ) to the (total) beam area is called the stray factor. Thus, εm = Ω m / ΩA = stray factor.  Bandwidth Note that the system is designed for specific frequency; i.e. at any other frequency it will not be one-half wavelength. The bandwidth of an antenna is the range of frequencies over which the antenna gives reasonable performance. One definition of reasonable performance is that the standing wave ratio is 2:1 or less at the bounds of the range of frequencies over which the antenna is to be used. CREC Dept. of ECE P a g e 19 Dr.V.Thrimurthulu Lecture Notes Antenna & Wave Propagation  Antenna Equivalent Circuit: To a generator feeding a transmitting antenna, the antenna appears as a lead. In the same manner, the receiver circuitry connected to a receiving antenna's output terminal will appear as load impedance. Both transmitting and receiving antennas can be represented by equivalent circuits as shown by figure 18(a) and figure 18(b). Fig 18 (a): Equivalent circuit of a T antenna x V = open circuit voltage of the generator g Z = antenna impedance g Z = Characteristics impedance of the transmission line connecting generator to the antenna. 0 P = Incident power to the antenna terminal inc P = Power reflected from the antenna terminal. refl P = Input power to the antenna in X = Antenna reactance A R = Loss resistance of the antenna l R = Radiation resistance r Z R R jX R jX antenna impedance.  A l r A A A Fig 18 (b): Equivalent circuit of receiving antenna h = effective length e E = incident field strength V = h0 E open circuit voltage oc Z = Input impedance of the receiver. load R , R and X as defined earlier. e r A CREC Dept. of ECE P a g e 20

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