Lecture notes on Antennas and wave Propagation

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Lecture Notes on Antennas and Wave Propagation (III B.Tech I SEM,JNTUH R13) Prepared By Course Coordinator: Ms. A.Usha Rani, Assistant professor, Mr. V Naresh Kumar Assistant professor ECE department, INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 ELECTRONICS AND COMMUNICATION ENGINEERING UNIT – 1 Antenna Basics: Introduction, basic Antenna parameters, patterns, beam area, radiation intensity, beam efficiency, directivity and gain, antenna apertures, effective height, bandwidth, radiation efficiency, antenna temperature and antenna filed zones. Introduction:- It is a source or radiator of EM waves, or a sensor of EM waves. It is a transition device or transducer between a guided wave and a free space wave or vice versa. It is an electrical conductor or system of conductors that radiates EM energy into or collects EM energy from free space. is an impedance matching device, coupling EM waves between Transmission line and free space or vice versa. Some Antenna Types Wire Antennas- dipoles, loops and Helical Aperture Antennas-Horns and reflectors Array Antennas-Yagi, Log periodic Patch Antennas- Microstrips, PIFAs 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: 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 r . physical temperature of the antenna itself but isrelated to the temperature of distant objects that the antenna is looking at. R may be thought of as virtual resistance that does r not exist physically but is a quantity coupling the antenna to distant regions of space via a virtual transmission .line 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. Patterns The radiation pattern or antenna pattern is the graphical representation of the radiation properties of the antenna as a function of space. That is, the antenna's pattern describes how the antenna radiates energy out into space (or how it receives energy. It is important to state that an antenna can radiate energy in all directions, so the antenna pattern is actually three-dimensional. It is common, however, to describe this 3D pattern with two planar patterns, called the principal plane patterns. These principal plane patterns can be obtained by making two slices through the 3D pattern ,through the maximum value of the pattern . It is these principal plane patterns that are commonly referred to as the antenna patterns Radiation pattern or Antenna pattern is defined as the spatial distribution of a ‗quantity‘ that characterizes the EM field generated by an antenna. The ‗quantity‘ may be Power, Radiation Intensity, Field amplitude, Relative Phase etc. Normalized patterns It is customary to divide the field or power component by it‘s maximum value and plot the normalized function.Normalized quantities are dimensionless and are quantities with maximum value of unity Half power level occurs at those angles (θ,Φ)for which Eθ(θ,Φ)n =0.707 At distance dλ and d size of the antenna, the shape of the field pattern is independent of the distance Pattern in spherical co-ordinate system Beamwidth is associated with the lobes in the antenna pattern. It is defined as the angular separation between two identical points on the opposite sides of the main lobe. The most common type of beamwidth is the half-power (3 dB) beamwidth (HPBW). To find HPBW, in the equation, defining the radiation pattern, we set power equal to 0.5 and solve it for angles. Another frequently used measure of beamwidth is the first-null beamwidth (FNBW), which is the angular separation between the first nulls on either sides of the main lobe. Pattern in Cartesian co-ordinate system Beamwidth defines the resolution capability of the antenna: i.e., the ability of the system to separate two adjacent targets Examples : 2 o o . 1.An antenna has a field pattern given by E(θ)=cos θ for 0 ≤ θ ≤ 90 Find the Half power beamwidth(HPBW) E(θ) at half power=0.707 2 Therefore, cos θ= 0.707 at Halfpower point i.e., θ -1 1/2 o o =cos (0.707) =33 HPBW=2θ=66 Beam area or Beam solid angle A 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 2 Area of the sphere is 4πr . Therefore the total solid angle of the sphere is 4π steradians 2 1stersteadian= (1radian) 2 = (180 / π) = 3282.8 Square degrees The infinitesimal area ds on a surface of a sphere of radius r in spherical coordinates(with θ as vertical angle and Φ as azimuth angle) is 2 ds r sin θdθdφ Beam area is the solid angle A for an antenna, is given by the integral of the normalized power pattern over a sphere(4π steradians) Beam area is the solid angle through which all of the power radiated by the antenna would stream if P(θ,Φ) maintained it‘s maximum value over A and was zero elsewhere. i.e., Power radiated= P(θ,Φ) watts A Beam area is the solid angle is often approximated in terms of the angles A subtended by the Half Power points of the main lobe in the two principal planes(Minor lobes are neglected) Ω ≈θ φ Α Radiation Intensity Definition: The power radiated from an Antenna per unit solid angle is called the Radiation Intensity. U Units: Watts/Steradians Poyting vector or power density is dependant on distance from the antenna while Radiation intensity is independent of the distance Directivity and Gain From the field point of view, the most important quantitative information on the antenna is the directivity, which is a measure of the concentration of radiated power in a particular direction. It is defined as the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. The average radiation intensity is equal to the total radiated power divided by 4π. If the direction is not specified, the direction of maximum radiation is implied. Mathematically, the directivity (dimensionless) can be written as U (θ ,φ ) max D= U (θ ,φ ) average The directivity is a dimensionless quantity. The maximum directivity is always ≥ 1 Directivity is the ratio of total solid angle of the sphere to beam solid angle. For antennas with rotationally symmetric lobes. Directivity of isotropic antenna is equal to unity , for an isotropic antenna Beam area A =4π • Directivity indicates how well an antenna radiates in a particular direction in comparison with an isotropic antenna radiating same amount of power • Smaller the beam area, larger is the directivity Gain:Any physical Antenna has losses associated with it. Depending on structure both ohmic and dielectric losses can be present. Input power Pin is the sum of the Radiated power P and losses P rad loss P P P in = rad + loss The Gain G of an Antenna is an actual or realized quantity which is less than Directivity D due to ohmic losses in the antenna. Mismatch in feeding the antenna also reduces gain The ratio of Gain to Directivity is the Antenna efficiency factor k(dimensionless) 0 ≤ k ≤ 1 In practice, the total input power to an antenna can be obtained easily, but the total radiated power by an antenna is actually hard to get. The gain of an antenna is introduced to solve this problem. This is defined as the ratio of the radiation intensity in a given direction from the antenna to the total input power accepted by the antenna divided by 4π. If the direction is not specified, the direction of maximum radiation is implied. Directivity and Gain: Directivity and Gain of an antenna represent the ability to focus it‘s beam in a particular direction Directivity is a parameter dependant only on the shape of radiation pattern while gain takes ohmic and other losses into account Effective Aperture Aperture Concept: Aperture of an Antenna is the area through which the power is radiated or received. Concept of Apertures is most simply introduced by considering a Receiving Antenna. Let receiving antenna be a rectangular Horn immersed in the field of uniform plane wave as shown Let the poynting vector or power density of the plane wave be S watts/sq –m and let the area or physical aperture be A sq-m.If the Horn extracts all the power from the Wave p over it‘s entire physical Aperture A , Power absorbed is given by p 2 P=SA = (E /Z)A Watts, S is p p poynting vector , Z is intrinsic impedance of medium, E is rms value of electric field But the Field response of Horn is not uniform across A because E at sidewalls must p equal zero. Thus effective Aperture Ae of the Horn is less than Ap A e Aperture efficiency is defined as ε ap= A p The effective antenna aperture is the ratio of the available power at the terminals of the antenna to the power flux density of a plane wave incident upon the antenna, which is matched to the antenna in terms of polarization. If no direction is specified, the direction of maximum radiation is implied. Effective Aperture (Ae) describes the effectiveness of an Antenna in receiving mode, It is the ratio of power delivered to receiver to incident power density It is the area that captures energy from a passing EM wave An Antenna with large aperture (Ae) has more gain than one with smaller aperture(Ae) since it captures more energy from a passing radio wave and can radiate more in that direction while transmitting Effective Aperture and Beam area: Consider an Antenna with an effective Aperture Ae which radiates all of it‘s power in a conical pattern of beam area A, assuming uniform field E over the aperture, power radiated is a E 2 a P= Ae z 0 Other antenna equivalent areas : Scattering area : It is the area, which when multiplied with the incident wave power density, produces the re-radiated (scattered) power Loss area : It is the area, which when multiplied by the incident wave power density, produces the dissipated (as heat) power of the antenna Capture area: It is the area, which when multiplied with the incident wave power density, produces the total power intercepted by the antenna. Effective height The effective height is another parameer related to the apertures. Multiplying the effective height, h (meters), times the magnitudeof the incident electric field E (V/m) e yields the voltage V induced. Thus V=h E or h V/ E (m). Effective height provides e e= an indication as to how much of the antenna is involved in radiating (or receiving. To demonstrate this, consider the current distributions a dipole antenna for two different lengths. If the current distribution of the dipole were uniform, it‘s effective height would be l Here the current distribution is nearly sinusoidal with average value 2/π=0.64(of the maximum) so that it‘s effective height is 0.64l .It is assumed that antenna is oriented for maximum response. If the same dipole is used at longer wavelength so that it is only 0.1λ long, the current tapers almost linearly from the central feed point to zero at the ends in a triangular distribution. The average current is now 0.5 & effective height is 0.5l For an antenna of radiation resistance R matched to it‘d load , power r 2 delivered to load is P=V /(4R ), voltage is given by V=h E. Therefore P=(h r e e 2 E) /(4R ) r In terms of Effective aperture the same power is given by 2 P=SAe= (E /Z )A 0 e Equating the two, Notes: the above calculations assume that the electric field is constant over the antenna Z is the intrinsic impedance of free space = 120π or 377 0 Bandwidth or frequency bandwidth This is the range of frequencies, within which the antenna characteristics (input impedance, pattern) conform to certain specifications . Antenna characteristics, which should conform to certain requirements, might be: input impedance, radiation pattern, beamwidth, polarization, side-lobe level, gain, beam direction and width, radiation efficiency. Separate bandwidths may be introduced: impedance bandwidth, pattern bandwidth, etc. 14 The FBW of broadband antennas is expressed as the ratio of the upper to the lower frequencies, where the antenna performance is acceptable. Based on Bandwidth antennas can be classified as 1. Broad band antennas-BW expressed as ratio of upper to lower frequencies of acceptable operation eg: 10:1 BW means f is 10 times greater than f H L 2. Narrow band antennas-BW is expressed as percentage of frequency difference over centre frequency eg:5% means (f f ) /f is .05. Bandwdth H – L o can be considered to be the range of frequencies on either sides of a centre frequency(usually resonant freq. for a dipole) The FBW of broadband antennas is expressed as the ratio of the upper to the lower frequencies, where the antenna performance is acceptable Broadband antennas with FBW as large as 40:1 have been designed. Such antennas are referred to as frequency independent antennas. For narrowband antennas, the FBW is expressed as a percentage of the frequency difference over the center frequency The characteristics such as Zi, G, Polarization etc of antenna does not necessarily vary in the same manner. Some times they are critically affected by frequency Usually there is a distinction made between pattern and input impedance variations. Accordingly pattern bandwidth or impedance bandwidth are used .pattern bandwidth is associated with characteristics such as Gain, Side lobe level, Polarization, Beam area. (large antennas) Impedance bandwidth is associated with characteristics such as input impedance, radiation efficiency(Short dipole) Intermediate length antennas BW may be limited either by pattern or impedance variations depending on application If BW is Very large (like 40:1 or greater), Antenna can be considered frequency independent. Radiation Efficiency Total antenna resistance is the sum of 5 components Rr+Rg+Ri+Rc+Rw Rr is Radiation resistance Rg is ground resistance Ri is equivalent insulation loss Rc is resistance of tuning inductance Rw is resistance equivalent of conductor loss Radiation efficiency=Rr/( Rr+Rg+Ri+Rc+Rw). It is the ratio of power radiated from the antenna to the total power supplied to the antenna Antenna temperature The antenna noise can be divided into two types according to its physical source: - noise due to the loss resistance of the antenna itself; and - noise, which the antenna picks up from the surrounding environment The noise power per unit bandwidth is proportional to the object‘s temperature and is given by Nyquist‘s relation where T is the physical temperature of the object in K (Kelvin degrees); and k is P -23 Boltzmann’s constant (1.38x10 J/K Antenna Field Zones The space surrounding the antenna is divided into three regions according to the predominant field behaviour. The boundaries between the regions are not distinct and the field behaviour changes gradually as these boundaries are crossed. In this course, we are mostly concerned with the far-field characteristics of the antennas . Fig: Radiation from a dipole 1.Reactive near-field region: This is the region immediately surrounding the antenna, where the reactive field dominates. For most antennas, it is assumed that this region is a sphere with the antenna at its centre 2. Radiating near-field (Fresnel) region :This is an intermediate region between the reactive near-field region and the far-field region, where the radiation field is more significant but the angular field distribution is still dependent on the distance from the antenna. 3. Far-field (Fraunhofer) region :Here r D and r λ The angular field distribution does not depend on the distance from the source any more, i.e., the far-field pattern is already well established The Electric Dipoles and Thin Linear Antennas Short Electric dipole: Any linear antenna may be considered as consisting of a large number of very short conductors connecter in series. A short linear conductor is often called a ‗short dipole‘. A short dipole is always of finite length even though it may be very short. If the dipole is vanishingly short it is an infinite single dipole. Fig 3.1: A short dipole antenna Fig 3.2: Equivalent of short dipole antenna Consider a short dipole as shown in figure 3.1, the length L is very short compared to the wavelength L λ. The current I along the entire length is assumed to be uniform. The diameter d of the dipole is small compare to its length dL. Thus the equivalent of short dipole is as shown in figure (b). It consists of a thin conductor of length L with uniform current I and point charges at the ends. The current and charge are related by -(3.1) The fields of a short dipole: Fig3.3: Relation of dipole to co-ordinates Consider a dipole of length ‗L‘ placed coincident with the z-axis with its center at the origin. The electric and magnetic fields due to the dipoles can be expressed in terms of vector and scalar potentials. The relation of electric field Electric field Er, Eθ and E is as shown in figure3.3. It is assumed that the medium surrounding the dipole is air. Retardation effect: In dealing with antennas, the propagation time is a matter of great important. Thus if a current is flowing in the short dipole. The effect of the current is not felt instantaneously at the point P, but only after an interval equal to the time required for the disturbance to propagate over the distance ‗r‘. This is known as retardation effect. When retardation effect is considered instead of writing current I as which implies instantaneous propagation of the effect of the current, we introduce propagation time as Where I is called retarded current c - Velocity of propagation Fig3.3: Geometry for short dipole For a dipole as shown in the above figure the retarded vector potential of the electric current has only one component namely A and it is given by 3 I is the retarded current given by Z= distance to a point on the conductor I0= peak value in the time of current -7 -1 µ = permeability of free space = 4π x 10 Hm 0 If the distance from the dipole is large compare to its length (rL) and wavelength is large compare to the length (λL), we can put s=r and neglect the phase difference of the field contributions from different parts of the wire. The integrand in (2) can then be regarded as a constant. So that (2) becomes The retarded scaled potential V of a charge distributed is Where ρ is the retarded charge density given by dη= infinitesimal volume element -10 -1 = permittivity of free space = 8.854 x 10 Fm Since the region of charge in the case of the dipole being considered is confined to the points at the ends as in figure 3.2 equation 3.5 reduce to But, Substituting equation (3.7) in (3.6) Referring the figure Fig 3.4: Relation for short dipole when rL When rL, the lines connecting the ends of the dipole and the point ‗p‘ may be consider as parallel so that Sub S and S in the equation 3.8 1 2 2 The term is negligible compare to r assuming rL If the wavelength is much greater than the length of dipole (λL) then, Thus the above expression reduce to Equation 3.4 and 3.9 express the vector and scalar potentials everywhere due to a short dipole. The only restrictions are rL and λL These equations gives the vector and scalar potentials at a point P in terms of the distance ‗r ‗to the point from the center of the dipole, the angle θ , the length of the dipole L the current on the dipole and some constants. Fig 3.5: resolution of Vector potential into A and A components r θ Knowing the vector potential A and the scalar potential V the electric and magnetic field may then be obtained from the relations It will be desirable to obtain E x H components in polar coordinates. The polar coordinate components for the vector potential are Since the vector potential for the dipole has only ‗z‘ components A =0 and Ar and Aθ are given by In polar coordinates the gradient of V is Expressing E in its polar coordinates components is We have, Substituting these values in equation (3.15) Magnetic Field Component: To find magnetic field component we use the relation Since A has only two components ie A and A which are given by z r θ A = A cosθ r z A = -A Sinθ θ z A has no components in A_ direction therefore and substituting z these two values rsinθ A_=0 Substituting these two values Here A is independent of θ z Substitute for A value z Substituting equations (3.22) and (3.23) in the equation (3.21) The above two equation represents the total electric and magnetic fields due to short dipoles When r is very large the terms and becomes negligible compare to Er is also negligible As H = H =0 r θ Taking the ratio of E and H as in the above equation Intrinsic impedance of free space pure resistance Relation between E , E and H_ r θ Fig 3.6 (a): Near and far field pattern of E and H_ components for short dipole. (b): Near θ field component, E r From the equation (3.26) and (3.27), it is clear that E and H_ components are in phase in θ the field. The field pattern of both is proportional to sinθ. The pattern is independent of _ so that the space pattern is doughnut shaped. When we consider near field ( and is not neglected) for a small r, the electric field has two components Eθ and Er, which are both in time phase quadrature with the magnetic field. i.e., At intermediate distance Eθ and Er can approach time phase quadrature. So that total electric field vector rotates in a plane parallel to the direction of propagation thus referred as cross field. For E and H_ components the near field patterns are same as the far field pattern θ which is proportional to sinθ The near field pattern of E is proportional to cosθ far field E =0 r r Quasi stationary or dc case: It refers to low frequency of operation The retarded current is given by E and E can be written as equations (3.28) (3.29) and (3.30) θ r And magnetic field At low frequency f 0 or w 0, so that

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