Antenna Fundamentals Lecture - 1 PDF

Lecture - 1- Antenna Fundamentals What is an Antenna? An Antenna is a transducer, which converts electrical power into electromagnetic waves and vice versa. An Antenna can be used either as a transmitting antenna or a receiving antenna.  Their name is borrowed from zoology, i...

Lecture - 1- Antenna Fundamentals What is an Antenna? An Antenna is a transducer, which converts electrical power into electromagnetic waves and vice versa. An Antenna can be used either as a transmitting antenna or a receiving antenna.  Their name is borrowed from zoology, in which the Latin word antennae is used to describe the long, thin feelers possessed by many insects. A metallic conductor's structure is called an "antenna" while the wire form is called an “aerial”.  Just as in humans the ears are the transducers that convert acoustic waves into electrochemical impulses.  The antenna is the transition between a guiding device (transmission line, waveguide) and free space (or another usually unbounded medium). Its main purpose is to convert the energy of a guided wave into the energy of a free space wave (or vice versa) as efficiently as possible, while at the same time the radiated power has a certain desired pattern of distribution in space.  An antenna intercepts some of the power of an electromagnetic wave to produce a tiny voltage at its terminals, which is applied to a receiver to be amplified.  Typically an antenna consists of an arrangement of metallic conductors ("elements"), electrically connected (often through a transmission line) to the receiver or transmitter. Radiation Mechanism   To create radiation, there must be a time-varying current or an acceleration (or deceleration) of charge.  For a transmission line, to become a waveguide or to radiate power, has to be processed as such: 1. If a charge is not moving, current is not created and there is no radiation. 2. If charge is moving with a 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, as shown in Figure 1.1 3. If charge is oscillating in a time-motion, it radiates even if the wire is straight  The radiation from an antenna can be explained with the help of Figure 1.2 which shows a voltage source connected to a two conductor transmission line. When a sinusoidal voltage is applied across the transmission line, an electric field is created and these results in the creation of electric lines of force which are tangential to the electric field.  The free electrons on the conductors are forcibly displaced by the electric lines of force and the movement of these charges causes the flow of current which in turn leads to the creation of a magnetic field.  Due to the time varying electric and magnetic fields, electromagnetic waves are created and these travel between the conductors.  As these waves approach open space, free space waves are formed by connecting the open ends of the electric lines.  Inside the transmission line and the antenna, the electromagnetic waves are sustained due to the charges, but as soon as they enter the free space, they form closed loops and are radiated. Figure 1.1   Maxwell's equations describe how electric charges and electric currents create electric and magnetic fields. Further, they describe how an electric field can generate a magnetic field, and vice versa E: electric field [volt/m] H: magnetic field intensities [ampere/m] D: electric flux densities also called the electric displacement [coulomb/m2] B: magnetic flux densities or magnetic induction [weber/m2] or [tesla]. ρ: free electric charge density [coulomb/m3] J: electric current density (charge flux) of any external charges (that is, not including any induced polarization charges or magnetization currents in a material [ampere/m2] ∇× is the curl operator ∇· is the divergence operator The charge and current densities ρ, J may be thought of as the sources of the electromagnetic fields. For wave propagation problems, these densities are localized in space; for example, they are restricted to flow on an antenna. The generated electric and magnetic fields are radiated away from these sources and can propagate to large distances to the receiving antennas. , Basic Types of Antennas Antennas may be divided into various types depending upon:  The physical structure of the antenna.  The frequency ranges of operation.  The mode of applications. Physical structure: Following are the types of antennas according to the physical structure.  Wire antennas  Aperture antennas  Reflector antennas  Lens antennas  Micro strip antennas  Array antennas Frequency of operation: Following are the types of antennas according to the frequency of operation.  Very Low Frequency (VLF) ,Low Frequency (LF)  Medium Frequency (MF)  High Frequency (HF) , Very High Frequency (VHF)  Ultra High Frequency (UHF), Super High Frequency (SHF)  Micro wave  Radio wave Mode of Applications: Following are the types of antennas according to the modes of applications-  Point-to-point communications  Broadcasting applications  Radar communications  Satellite communications The physical structure of the antenna. 1. Wire antennas (single-element) Simple to make but their dimensions are commensurable with the wavelength. This limits the frequency range of their applicability (at most 1-2 GHz). At low frequencies, these antennas become increasingly large. -Usually used in personal applications, automobiles, buildings, ships, aircrafts and spacecraft 2. Aperture antennas (single element) - Horn antennas, waveguide opening - Waveguide transmission lines were primarily developed to transfer high power microwave EM signals (centimeter wavelengths). These types of antennas are preferable in the frequency range from 1 to 20 GHz. 3. Microstrip antennas : -The patch antennas consist of a metallic patch etched on a dielectric substrate, which has a grounded metallic plane at the opposite side. - Used in aircraft, spacecraft, satellites, missiles, cars, mobile phones etc. 4. Reflector antennas - A reflector is used to concentrate the EM energy in a focal point where the receiver/feed is located, Reflector antennas have very high gain and directivity. - Typical applications: radio telescopes, satellite communications, microwave communication. 5. Lens antennas -Lenses play a similar role to that of reflectors in reflector antennas, usually used for very high frequency applications (f > 100 GHz). -They are classified according to their shape and the material they are made of. 6. Antenna arrays Antenna arrays consist of multiple (usually identical) radiating elements. Arranging to achieve very high gain applications with added advantage, such as, controllable radiation pattern, which cannot be obtained through a single element. (Yagi-Uda antenna, microstrip patch array, aperture array, slotted waveguide array)  Elementary antennas 21 X/2 Dipole Vertical polar Horizontal polar pattern pattern Fig. 2.7 2.5 Half-wave dipole A very well-known and efficient radiator is the half-wave dipole antenna, consisting of two X14 lengthsand centre fed. Such a radiator has an input impedance of about 75 Q and a sinusoidal current distribution. At VHF frequencies and beyond, the dimensions are of convenient length and so the dipole is a popular TV antenna. The expression for the vertical polar pattern is derived by considering the antenna as composed of a number of small dipolés placed end to end and is given in Appendix E. PlotS of the vertical and horizontal patterns are shown in Fig. 2.7. dipoles, the patterns are similar but interchanged. Example 2.6 Draw a diagram showing the approximate current distribution along a half-wave dipole which is centre-fed with a current of 2 A (r.m.s.). The magnitude of the electric field strength (E) at a distance (r) metres from a radiating current element (I d/) ampere-metres in the plane perpendicular to and bisecting the length of the element is given by 6071 d/ volts/m Use this relationship to calculate the electric field at a point in this plane at a distance 10 km from the half-wave dipole.  22 If the radiation resistance of the dipole is 74 Q, calculate the gain in dB of the dipole, compared with that of an aerial which radiates uniformly the same total power. (U.L.) Solution The expression for E can be applied to a dipole by subscituting the value of the effective length le of a dipole where le = 211T X X/2 = Å/T. Hence, the expression A n ten nas for E becomes 607/X 601 where I is the r.m.s. antenna current. Hence 60 x 2 Er.m.s.= 12 mV/m lo x 103 The power density at the distant point due to an isotrope radiating uniformly a power P = | 2 Rt is 12Rr 4 x 74 (10ß)2 The power density at the same point due to the dipole radiating a total power E2/120T Hence Power gain G — 1 20T 4 x 74 or 2.6 Helical antenna7-s A convenient element for providing circular polarization is the wirec. helix. (The helical antenna shown in Fig. 2.8a consists of a metal conductor wound in the form of a helix and backed at one end by a metal ground plane. It is conveniently fed from a coaxial cable with the centre conductor connected to the helix and the outer sheath connected to a circular ground plane of radius X/2 approximately. '  Elementary (a) (b) (c) (d ) Fig. 2.8 amennas 23 The helical geometry is characterised by its diameter D, turn spacing S, pitch angle V, uncoiled length of turn -L, and number of turns N. If a single turn of the helix is uncoiled as shown in Fig. 2.8b, we have tan. and When the diameter D of the helix is small compared to ? wgve!cngth, the helix radiates normal to its axis in the 'normal mode? as shown in Fig. 2.8cyHowever, if the diameter D is of the order of a wavelength, the helix radiates along its axis in the 'axial mode' ,as shown in Fig. 2.8d. in the latter case, the radiation is approximately circularly polarized and is clockwise for a clockwise helical winding or vice versa. The helical antenna is simple to construct and convenient in size. It can provide high gain and operates over a bandwidth ratio of about 2 : 1. Hence, it is often used in space applications for transmitting and receiving telemetry signals from satellites or missiles. It can be shown that the gain G and input impedance Zi are given by 15NST2D2/X3 and Z = 140TDIX where X is the wavelength of operation. Typically, 13 dB and 154 Q. , 2.7 Frequency-independent antennas9—10  24 An antenna which supports a standing wave pattern like the dipole. usually operates satisfactorily over a narrow bandwidth of about 1.1 : I. However, there are certain antennas which can operate over a very wide bandwidth of about 10: 1 and are called frequency-independent antennas. These antennas have physical structures which are either self-scaling as the frequency varies or depend mainly on angles rather than physical lengths. Typical examples of these are the spiral antenna and the log- periodic dipole array. Spiral antenna The spiral antenna shown in Fig. 2. is based on the equiangular spiral illustrated in Fig. 2.9a. The equation of the equiangular curve in the x—y plane is of the form r = roe where r is the radius vector, a is a constant which determines the flare rate and is the angular variation. Thus, the curve is defined essentially by angles and the equiangular propercy arises because the angle 25 Antennas ( a) ( b) Fig. 2.9 Spiral Feed input metal strip D ielectric cone (a ) ( b) Fig. 2.10 between the radius vector and the tangent to the curve, has the same value for all positions on the curve. Furthermore, if the initial value go = 0 or T, we obtain the two spirals shown in Fig. 2.9b. The equiangular spiral antenna shown in Fig. 2. IOa consists of two equiangular arms constructed from metal sheet. If it is fed at the centre with infinite arms, the antenna would be self-scaling and frequencyindependent. In practice, it is found that the radiation is strongest in a region around r = X/2 and so the infinite structure can be truncated at a position corresponding to r = X to yield an antenna of finite dimensions. 26 The antenna radiates broadside to the x—y plane along the z-axis and the pattern varies as cos 9, where 9 is the angle from the z-axis in the vertical y—z plane. The half-power beamwidth of the radiation is circular over its frequency range. However, to maintain its symmetry, the antenna may be fed at its centre by a coaxial cable along one arm and with a similar dummy cable placed along the other arm which is left  Elementary antennas 23 unconnected. Furthermore, if the spiral antenna has the conical gecmetry shown in Fig. 2.10b, unidirectional radiation is emitted in the apex direction. Log-periodic array11 An antenna structure which cannot be defined solely by angles, but has self-scaling properties is the log-periodic antenna. if its dimensions are scaled in some ratio T, the antenna will have similar properties at frequencies f, Tf, 72f etc. where T is called the geometric ratio. It is also found that the antenna characteristics such as impedance or directivity, vary periodically with the logarithm of the frequency and this accounts for its name. Furthermore, if the periodic variations are small over a broad band of frequencies, the antenna behaviour is effectively frequency-independent. Various planar structures in sheet metal or wire construction have been designed on this basis using trapezoidal or triangular toothed structures, but the best known example which yields higher gain than the smaller toothed structures, is the log-periodic array shown in Fig. 2.11. The antenna structure shown in Fig. 2.11 consists of an array of parallel dipoles with lengths In and distances dn increasing in a defined manner such that and d2 ¯ d3 dn+l where T is the geometric ratio. Furthermore, the spacing between adjacent elements is given by a factor where 212 213 21n+l 28 Fig. 2. u Antennas &' The edges of the dipoles lie along two straight lines which converge at one end with an apex angle and from the geometry of the array we obtain the relationship tan 0/2 = 2Sl 40 where typically, T varies between to 0 95 and varies between 10 0 to 45 0. The highest operating frequency is attained when the shortest dipole length is about X/2 and the lowest operating frequency is attained when the longest dipole is about X/ 2. The array is conveniently fed at the apex end by a balanced line, with connections crisscrossed to adjacent elements, to give the correct phasing of the elements as shown in Fig. 2.11. An end-fire radiati.01i1 pattern is produced in the apex direction by this arrangement and it is linearly polarised in the plane of the dipoles. Typical values of directivity:obtained are about 8 to 12'dB and the input impedance may vary between 70 to 100 Q. The log-periodic array is liked for HF communications and in the UHF range for TV.  3.4 Rhombic antenna 13 The results of the previous section can be used in the design of a horizontal rhombic antenna, which consists of four lengths of horizontal wire laid out in the form of a rhombus as illustrated in Fig. 3.8. Energy is fed in at one end from a balanced transmission line and travelling waves along the rhombic structure are absorbed at the far end in a terminating matched load. The properties of the antenna are described in terms of its leg length L, the tilt angle and its height h above ground level. Each wire or leg is equal to 4k at least and the tilt angle is then largely responsible for the resultant gain of the antenna. Hence, it is also related to the angle 9 of the rhombus since 6 (90 — p ). 7}  Fig. 3.8 Each leg length radiates two main lobes which are 180 0 out of phase since the magnetic field above and below a current conductor is in opposite phase. The lobes a, b, c, d are arranged to be either horizontal or nearly so by the proper choice of tilt angle cp. In order that the radiation from lobes a and b or c and d may reinforce one another at a distant point in the horizontal plane, the phase difference of current along the wire from centre point A to centre point B must be such that it is greater than the direct path in space from A to B by nT, where n is an odd integer. Hence, we must have (ß x AOB) - x AB) = (for n = 1) where ß is the phase-change coefficient along the wire conductor, 130 = 27/X is the phase-change coefficient in free space and X is the wavelength. In practice, the tilt angle for lobes a, b, c, d to be horizontal is slightly different from that which gives a maximum field at the distant point, but the value of p is not critical for leg lengths around 4X to 6k. The rhombic antenna gives a highly directional pattern in the horizontal plane as is shown in Fig. 3.8 but its performance also depends upon the height h above ground level. The presence of the ground tends to push the radiation upwards and it determines the angle of elevation a of the lowest lobe as shown in Fig. 3.8. The optimum values of L, and h must be chosen for best results using the following relationships: and Typically, if h = X, L = 6k, a = 14 5 0 and so the antenna is often used 34 Anten nas for directing low-angle radiation towards the ionosphere in long distance HF communication. Furthermore, as the tilt angle is not critical for leg lengths between 4X to 6k, the antenna has a broad bandwidth as the frequency of operation can be varied over a 2 : 1 range. In addition, some structures gan be varied in height h to allow for a variation in the angle of elevation a when ionospheric conditions change. The rhombic antenna can be used for transmitting or receiving radiation. Its characteristic impedance is of the order of 600—800 ohms and to ensure that it remains fairly constant over the operating range of frequencies, each leg of the rhombus is often constructed using three separated conductors instead of a single conductor. The antenna gain Is about 15 dB with a bandwidth of several MHz in the HF band; However, about half the input power is dissipated in the matched termination and ascounts for its low efficiency. Other disadvantages of the antenna include the presence of high sidelobes due to radiation which does not combine to form the main beam and at longer wavelengths, the antenna though simple to construct at relatively lowcost, requires a large ground area for its erection. A rhombic aerial used for HF communications is shown in Fig. 3.8. The aerial performance depends on the leg lepgth L, the tilt angle and on the height h. All three parameters determine the performance in a fairly complicated manner. Typical horizontal and vertical polar diagrams are shown in Fig. 3.8. The vertical polar diagram shows a single main lobe directed at a low angle a and its value depends upon the aerial height h. The horizontal polar diagram consists of a high gain central lobe and a number of sidelobes on either side. The rhombic aerial has: (a) wide bandwidth compared to a X/2 dipole. (b) low efficiency compared to resonant aerials such as the Yagi array. (c) high sidelobes compared to a X/2 dipole array. (d) low cost construction compared to other large arrays.  Turnstile Antenna The Turnstile antenna is another type of array antenna. The shape of this array symbolizes the turnstile, which is used at the entrances of few places. This antenna has a wide variety of military applications. Frequency range The frequency range in which the turnstile antennas operate is around 30 MHz to 3GHz which belong to the VHF and UHF bands. Modes of Operation The following are the modes of operation of a Turnstile antenna. Normal mode In Normal mode of operation, the antenna radiates horizontally polarized waves which are perpendicular to its axis. Axial mode In Axial mode of operation, the antenna radiates circularly polarized waves along its axis i.e. parallel to its axis. For circular polarization, the transmitter radiating with right-circular polarization should have a receiver with same right-circular polarization and vice versa. If it is left-circular polarized one, unlike the transmitter, there will be a severe loss of gain. Super Turnstile Antenna For a turnstile antenna, the radiation power is 3dB below the maximum radiation of a half-wave dipole radiating the same power. Therefore, to overcome this disadvantage, the Super- turnstile antenna is built. The simple dipole elements in turnstile are replaced by four flat sheets in Super-turnstile. The design of Super-turnstile array is such that 1 to 8 bays can be constructed on a single mast. The other name for Super-turnstile antenna is the Batwing Antenna. The above images show super-turnstile antenna. Figure 1 shows the arrangement of super-turnstile array with the red dots being the feed points. Figure 2 shows the stacked turnstile array used in satellite communications. Radiation Pattern The radiation pattern will be similar to the radiation pattern of two super imposed dipoles. Though it is close to omni-directional pattern, it leaves a cloverleaf shaped pattern. The above figure shows the radiational pattern of a turnstile array. The typical figure-of eight patterns were combined to produce a nearly circular pattern.   Figure A shows the individual patterns being combined.  Figure B shows the vertical pattern of single bay and also the combined pattern of four bays.  Figure C shows the resultant combined pattern of four bays showing better directivity. Advantages The following are the advantages of Turnstile antennas −  High-gain is achieved by stacking  Super-turnstile produces high-gain output  Better directivity is achieved Disadvantage The following is the disadvantage of Turnstile antennas −  The radiation power is 3dB below the maximum radiation of a half wave dipole radiating the same power. Applications The following are the applications of Turnstile antennas −  Used for VHF communications  Used for FM and TV broadcasting  Used in military communications  Used in satellite communications Radiation is the term used to represent the emission or reception of wave front at the antenna, specifying its strength. In any illustration, the sketch drawn to represent the radiation of an antenna is its radiation pattern. One can simply understand the function and directivity of an antenna by having a look at its radiation pattern. The power when radiated from the antenna has its effect in the near and far field regions.  Graphically, radiation can be plotted as a function of angular position and radial distance from the antenna.  This is a mathematical function of radiation properties of the antenna represented as a function of spherical co-ordinates, E (θ, Ø) and H (θ, Ø). Radiation Pattern The energy radiated by an antenna is represented by the Radiation pattern of the antenna. Radiation Patterns are diagrammatical representations of the distribution of radiated energy into space, as a function of direction. Let us look at the pattern of energy radiation. The figure given above shows radiation pattern of a dipole antenna. The energy being radiated is represented by the patterns drawn in a particular direction. The arrows represent directions of radiation. The radiation patterns can be field patterns or power patterns.  The field patterns are plotted as a function of electric and magnetic fields. They are plotted on logarithmic scale.  The power patterns are plotted as a function of square of the magnitude of electric and magnetic fields. They are plotted on logarithmic or commonly on dB scale. Radiation Pattern in 3D The radiation pattern is a three-dimensional figure and represented in spherical coordinates (r, θ, Φ) assuming its origin at the center of spherical coordinate system. It looks like the following figure − The given figure is a three dimensional radiation pattern for an Omni directional pattern. This clearly indicates the three co-ordinates (x, y, z). Radiation Pattern in 2D Two-dimensional pattern can be obtained from three-dimensional pattern by dividing it into horizontal and vertical planes. These resultant patterns are known as Horizontal pattern and Vertical pattern respectively. The figures show the Omni directional radiation pattern in H and V planes as explained above. H-plane represents the Horizontal pattern, whereas V-plane represents the Vertical pattern. Lobe Formation In the representation of radiation pattern, we often come across different shapes, which indicate the major and minor radiation areas, by which the radiation efficiency of the antenna is known. To have a better understanding, consider the following figure, which represents the radiation pattern of a dipole antenna. Here, the radiation pattern has main lobe, side lobes and back lobe.  The major part of the radiated field, which covers a larger area, is the main lobe or major lobe. This is the portion where maximum radiated energy exists. The direction of this lobe indicates the directivity of the antenna.   The other parts of the pattern where the radiation is distributed side wards are known as side lobes or minor lobes. These are the areas where the power is wasted.  There is other lobe, which is exactly opposite to the direction of main lobe. It is known as back lobe, which is also a minor lobe. A considerable amount of energy is wasted even here. Types of Radiation Pattern: 1. Isotropic pattern: is the pattern of an antenna having equal radiation in all directions. This is an ideal (not physically achievable) concept. However, it is used to define other antenna parameters. It is represented simply by a sphere whose center coincides with the location of the isotropic radiator. 2. Directional antenna is an antenna, which radiates (receives) much more efficiently in some directions than in others. Usually, this term is applied to antennas whose directivity is much higher than that of a half-wavelength dipole. 3. Omnidirectional antenna is an antenna, which has a non-directional pattern in a given plane, and a directional pattern in any orthogonal plane (e.g. single-wire antenna). Antenna Field Regions  Reactive Near Field Region – is defined as “that portion of the near-field region immediately surrounding the antenna wherein the reactive field predominates.” The outer boundary of this region is commonly taken to exist at a distance: Where λ is the wavelength and D is the largest dimension of the antenna. For a very short dipole, or equivalent radiator, the outer boundary is commonly taken to exist at a distance λ/2π from the antenna surface.  Near-Field (Fresnel) Region – that region of the field of an antenna between the reactive near-field region and the far-field region wherein radiation fields predominate and wherein the angular field distribution is dependent upon the distance from the antenna. If the antenna has a maximum dimension that is not large (very small) compared to the wavelength, this region may not exist.  Far-Field (Fraunhofer) Region - the region farthest away from the antenna where the field distribution is essentially independent of the distance from the antenna (propagating waves).  Fundamental Parameters of Antennas Radiation power density Electromagnetic waves are used to transport information through a wireless medium or a guiding structure, from one point to the other. It is then natural to assume that power and energy are associated with electromagnetic fields. The quantity used to describe the power associated with an electromagnetic wave is the instantaneous Poynting vector defined as 𝒲 = instantaneous Poynting vector (W/m2) 𝜉 = instantaneous electric-field intensity (V/m) ϰ = instantaneous magnetic-field intensity (A/m) Radiation Intensity: Radiation intensity in a given direction is the power radiated from an antenna per unit solid angle, and has unit of watts per square radian (or steradian) (W/sr).  it can be obtained by simply multiplying the radiation density by the square of the distance. In mathematical form it is expressed as 𝑼 = 𝑾𝒓𝒂𝒅 ∗ 𝒓𝟐 Where U is the radiation intensity (W/unit solid angle) r is the radial distance Wrad is the radiation density (W/m2)  The measure of a plane angle is a radian. One radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure. A graphical illustration is shown in Figure (a).  The measure of a solid angle is a steradian. One steradian is defined as the solid angle with its vertex at the center of a sphere of radius r that is subtended by a spherical surface area equal to that of a square with each side of length r. A graphical illustration is shown in Figure (b). The infinitesimal area dA on the surface of a sphere of radius r, is given by 𝑑𝐴 = 𝑟 2 sin 𝜃 𝑑𝜃 𝑑𝜑 (m2) Therefore, the element of solid angle dΩ of a sphere can be written as 𝑑𝐴 𝑑Ω = = sin 𝜃 𝑑𝜃 𝑑𝜑 (sr) 𝑟2  the radiation intensity of an isotropic source is: U0 = Prad /4π BeamWidth The beamwidth of a pattern is defined as the angular separation between two identical points on opposite side of the pattern maximum. In an antenna pattern, there are a number of beamwidths: a) Half-power beamwidth (HPBW): HPBW is the angle between two vectors, passing through these points of the major lobe where the radiation intensity is half its maximum. b) First-null beamwidth (FNBW): FNBW is the angle between two vectors, the angular separation between the first nulls of the pattern. Often, it is true that FNBW≈2HPBW. The beamwidth of an antenna is a very important is used as a trade- off between it and the side lobe level Also used to describe the resolution capabilities of the antenna to distinguish between two adjacent radiating sources or radar targets. That is, two sources separated by angular distances equal or greater than FNBW/2 ≈ HPBW of an antenna with a uniform distribution can be resolved. If the separation is smaller, then the antenna will tend to smooth the angular separation distance. The HPBW is the best parameter to describe the antenna resolution properties. In radar technology as well as in radio-astronomy, the antenna resolution capability is of primary importance. For example, in the case of the ideal dipole: Directivity : Directivity of an antenna (in a given direction) is the ratio of the radiation intensity in this direction and the radiation intensity averaged over all directions.  The radiation intensity averaged over all directions is equal to the total power radiated by the antenna (P rad) divided by 4𝜋. If a direction is not specified, then the direction of maximum radiation is implied.  It can be also defined as the ratio of the radiation intensity (U) of the antenna in a given direction and the U o of an isotropic radiator fed by the same amount of power : D = directivity (dimensionless); D0 = maximum directivity (dimensionless) U = radiation intensity (W/unit solid angle) U max = maximum radiation intensity (W/unit solid angle) Uo = radiation intensity of isotropic source (W/unit solid angle) P rad = total radiated power (W)  The directivity is a dimensionless quantity. The maximum directivity is always ≥1 Antenna efficiency The total efficiency of the antenna (et ) is used to estimate the total loss of energy at the input terminals of the antenna and within the antenna structure. It includes all mismatch losses and the dielectric/conduction losses:  Reflections because of the mismatch between the transmission line and the antenna  I 2R losses (conduction and dielectric)  Usually 𝒆𝒄 and 𝒆𝒅 are very difficult to compute, but they can be determined experimentally Here: 𝐞𝐫 is the reflection efficiency (impedance mismatch), 𝜞 = voltage reflection coefficient at the input terminals of the antenna 𝐞𝐩 is the polarization mismatch efficiency, 𝐞𝐜 is the conduction efficiency, 𝐞𝐝 is the dielectric efficiency. The gain G Gain of an antenna “is the ratio of the radiation intensity U in a given direction and the radiation intensity that would be obtained, if the power fed to the antenna were radiated isotropically, the isotropically radiated power is equal to the power accepted by the antenna divided by 4𝜋".  The gain of the antenna is closely related to the directivity, it is a measure that takes into account the efficiency of the antenna as well as its directional capabilities.  The amount of power given as input to the antenna is not fully radiated 𝑃𝑟 = ŋ 𝑃𝑖𝑛 where ŋ is the radiation efficiency of the antenna so the gain : G (𝜃,)= ŋ D (𝜃,𝜑).  Radiated power by the antenna is always less than the power fed to the antenna system, Prad ≤ Pin, unless the antenna has integrated active devices. That is why usually G ≤ D.  When the antenna has no losses, i.e. when Pin= Prad , then G(𝜃,𝜑)=D(𝜃,𝜑) (isotropic). Thus, the gain of the antenna takes into account the losses in the antenna system.  Gain is calculated via the input power Pin, unlike the directivity which is calculated via the radiated power P rad.  Usually the gain is given in terms of decibels instead of the dimensionless quantity ,the value of G is expressed logarithmically in units of decibels (dB): G (dB) = 10 * log10 (G) Examples Polarization Polarization of an electromagnetic wave refers to the orientation of the electric field component of the wave (its vectors at a given point) and how it varies with time.  In practice, polarization of the radiated energy varies with the direction from the center of the antenna, so that different parts of the pattern may have different polarizations.  Polarization = Shape of curve traced by tip of E vector (representing the instantaneous electric field) in xy plane  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  The antenna is usually polarized. The electric and magnetic fields lie perpendicular to each other and to the direction of propagation. As the wave progresses in its travel through space, the electric field (and the magnetic field) may (i) continue to lie in the same plane, or (ii) change its orientation within each wavelength traveled. The wave could be circularly or elliptically polarized depending on the whether the amplitude of the electric field remain fixed or change with angle respectively. Rotation of a plane electromagnetic wave and its polarization ellipse at z = 0 as a function of time. Type of Polarization 1. Linear Polarization A time-harmonic wave is linearly polarized at a given point in space if the electric-field (or magnetic-field) vector at that point is always oriented along the same straight line at every instant of time. For the wave to have linear polarization, the time-phase difference between the two components must be ∆φ = φy − φx = nπ n = 0, 1, 2, 3... 2. Circular Polarization A time-harmonic wave is circularly polarized at a given point in space if the electric (or magnetic) field vector at that point traces a circle as a function of time. Circular polarization can be achieved only when the magnitudes of the two components are the same and the time-phase difference between them is odd multiples of π/2. 3. Elliptical Polarization A time-harmonic wave is elliptically polarized if the tip of the field vector (electric or magnetic) traces an elliptical locus in space. At various instants of time the field vector changes continuously with time at such a manner as to describe an elliptical locus.  Elliptical polarization can be attained only when the time-phase difference between the two components is odd multiples of π/2 and their magnitudes are not the same or when the time-phase difference between the two components is not equal to multiples of π/2 (irrespective of their magnitudes). Aperture Efficiency of an Antenna  With each antenna, we can associate a number of equivalent areas. These are used to describe the power capturing characteristics of the antenna when a wave impinges on it. One of these equivalent areas is the effective area (aperture),  The effective aperture area is specific for different type of antennas. For example, the effective aperture area of a dish antenna could be equal to the physical cross sectional area of the dish if the antenna is lossless, whereas for a dipole antenna, this area is generally more than its physical area. The effective usage of the physical aperture depends on the aperture efficiency of the antenna which is the ratio of effective aperture area Ae to the physical aperture area Ap of the antenna and is expressed below: Wavelength, Directivity and Aperture The effective aperture area Ae is related to the wavelength λ and the solid angle ΩM subtended by the main beam as shown below: The directivity D may be obtained from the effective aperture area Ae using the relationship shown below: 1.2 Antenna. types Over the years, a very wide variety of antenna designs have evolved and broadly speaking, they can be divided into single radiators and multiple radiators. Some of the most important types are listed in Table 1.1. The monopole and dipole antennas shown in Fig. 1.1 have been used Table 1.1 Single radiators Multiple radiators Monopole Yagi array Dipole Rhombic array Wire Log-periodic array Helix Linear array Spiral Planar array Horn Adaptive array Reflector Monopole Dipole  6 Antennas Helix Spiral Fig. 1.2 Horn Reflector Fig. 1.3 extensively in the past and are still used individually or as components of more complex arrays such as the Yagi array. The long wire antenna has been used in many applications especially for receiving purposes. 'In a transmitting application, it tends to form a more composite structure such as the rhombic antenna. More recently, the helix and spiral antennas shown in Fig. 1.2 have evolved and found a particular use in satellite of their broadband properties. The microwave horn and parabolic reflectorjshown in Fig. 1.3 have been very popular antennas which are used extensively in radar and satellite systems. Microwave horns very often are used as feeds for large parabolic reflectors. The Yagi array shown in Fig. 1.4 is a very popular TV antenna for the VHF and UHF bånds, due to its yonvenient size, useful gain, simplicity and low cost. In the transmitting case, the antenna and more recently, the log-periodic array shown in Fig. 1.4 are generally used in HF communicationé. They are particularly attractive because of their broadband properties. In recent years, there has been a large amount of work on the design Introduction Yagi array Fig. 1.4 and development of several other types of linear arrays, h which are capable of being scanned over a region of space. These arrays are either of the frequency-scanned 'type or of the phase-scanned ±type (phased arrays). The arrays are usually constructed using basic radiators like the dipole or slotted waveguide. One-dimensional structures are called lineaf arraysu For certain applications especially in satellite communications, linear arrays are used as adaptive arrays which have a signal processing capability. 3 For example, by adjusting the amplitude and phase excitation of the array, a null is produced in the direction of an interfering signal to cancel it out. 1.3 Wave propagation A typical antenna used for radiating electromagnetic waves is the vertical dipole shown in Fig. 1.5. The electric and magnetic field lines near the H field Fig. antenna produce the induction field, while farther away, the radiation field travels outwards with the velocity of light. The field pattern consists of electric lines in the vertical plane and magnetic lines in the horizontal plane which are symmetrical about the antenna. When the dipole is energised by a voltage at a frequency greater than about 16 kHz, the charge distribution on the antenna reverses sign more rapidly than the collapsing field lines near it. The collapsing field lines are pushed away by the reversing field and they close up to form loops. The loops expand and travel away from the antenna. The electromagnetic waves propagated from an antenna consist essentially of a ground wave and a sky wave. The ground wave travels along the earth's surface and is used at the lower frequencies for medium distance communication. The sky wave travels upwards and is refracted back to earth by the ionosphere. It is used at the higher frequencies for long distance communication. Further details are given in Chapter 6. 2 Elementary antennas A very elementary yet important theoretical antenna is the point sour.ce radiator or isotrope. It seryes as a basis for comparison of marry types of antennas whose performance is best expressed in terms of such a basic radiatof. 2.1 The isotrope An isotrope or point source radiator radiates energy equally in all directions. Hence, its radiation is isotropic and the radiation pattern in any plane is a circle. Consider such an isotrope at point O in Fig. 2.1 fed with power P watts. The power flows outwards from O and at any time t it must flow through the spherical surface S of radius r. Hence, the power flow per unit area or power density Pd at point Q is given by Pd = P/4rr2 watts/m2 By Poynting's theorem4, the power density Pd is related to the E and 10 An ten nas H vectors by the equation Pd —Ex H watts/m2 or = E. E 2 1120T since Hence = p/4Tt 1207 or where E and H are r.m.s. values when P is the average power. The isotrope may be considered as a standard lossless reference antenna with power gain G = I. If any other practical antenna with a power gain G were placed at O, then the power reqelved at Q would be increased G times to G x P watts. Hence, the field strength at Q will be increased to The concept of power density is vividly illustrated by a radar system where it leads to the well-known radar equation. Radar equation Suppose a radar transmitter at T in Fig. 2.2 has an antenna gain GT which is fed by the transmitter with power PT. The power density Pd at an object located at O distant r is The target area of the object at O is defined as o m such that the  Fig. 2.2 Elementary antennas 11 intercepted power which is assumed to be reflected bagk isogrepically is PO. It therefore produces a power density På at the transmitter where = watts/m2 If å receiving antenna at T has a gain CR and effective area A, , then the received power is PR = PåAe or This is the basic radar equation relating transmitted and received powers. If the minimum detectable signal-to-noise ratio at the receiver is SIN, then PR = S and N=JcTB where k is Boltzmann's constant, T is the absolute temperature and B is the bandwidth of the system. The radar range r is then given by (47) kTB(S/N) or prGrGROX2 (4T) kTB(S/N) The range depends on the fourth root of PT and so accounts for the large powers used in radar systems. Example 2.1 Calculate the minimum peak transmitter power needed in a pulsed radar required qodetect a target of 10 m2 echoing-area at a range of 120 km, given the following system parameters operating frequency GHz receiver sensitivity -105 dBm aerial gain 34 dB atmospheric attentuation 0-008 dB/km How would the pulse length and pulse repetition frequency of the radar be determined? (C.E.I.) Solution From the previous analysis we obtained (47) 3r4 PR GTGRUX2 or Pi - (47)3r4pe 12 Antennas Due to atmospheric attentuation over the two-way distance there is a path loss given by Path loss = 2 x 120 x = I 92 dB Hence, the transmitted power PT must be increased by 1 92 dB or 1 556 times. Hence Here r = 120 km = 1 2 x 105 m = GR = 34 db = 2512 o = 10 m2 Also 3 x IO S or = 0 23 m Since the receiver sensitivity IS - 105 dBm, - 105 dBm = - 135 dBW= 10 13 5 Watts  (4T)3 x (l 2 X 105) 4 x 10 Hence or In the last part of the question, the pulse length and pulse repetition frequency determine the minimum range and maximum range of the radar respectively.