Antennas & Propagation Unit – I Fundamentals of Radiation Prepared By Dr. K. Umapathy / ECE 1 Syllabus • Definition of antenna parameters – Gain, Directivity, Effective aperture, Radiation Resistance, Bandwidth - • Beam width, Input Impedance - Matching Baluns - Polarization Mismatch, Antenna noise temperature, Radiation from oscillating dipole, Half wave dipole, Folded dipole. 2 Aim & Objectives • To give insight of radiation phenomena. • To give thorough understanding of the radiation characteristics of an antenna. • To give exposure to various fundamental parameters of an antenna. Pre-Test MCQ 1. The phenomenon employed in the waveguide operation is a) Reflection b) Refraction c) Total internal reflection d) Adsorption ANSWER: c 2. The dominant mode in waveguide is the mode which has a) Highest frequency b) Highest wavelength c) Lowest phase constant d) Highest attenuation ANSWER: b 3. The modes are calculated from which parameter? a) Frequency b) Wavelength c) Phase constant d) V number ANSWER: d 4. The circular waveguides use which function in the frequency calculation? a) Laplace function b) Schottky function c) Bessel function d) Transfer function ANSWER: c 5. The scattering parameters are used to indicate the a) Permittivity and permeability b) Electric and magnetic field intensities c) Reflection and transmission coefficients d) Frequency and wavelength ANSWER: c 6. Which of the following two parameter models cannot be used to represent a transmission line? a) H parameter model b) T parameter model c) ABCD parameter model d) S parameter model ANSWER: a 7. For the matched line, the parameters S12 and S21 are a) 1 b) 0 c) -1 d) ∞ ANSWER: b 8. The waveguides are materials with characteristics of a) Low bulk resistivity b) High bulk resistivity c) High conductivity d) Low conductivity ANSWER: a Pre-requisite • Basic Knowledge on Electromagnetic Fields and Waveguides Fig 1.1 Wireless Communication Link 9 Definition for Antenna • An antenna is a transitional structure (metallic device: as a rod or wire) between free-space and a guiding device , for radiating or receiving radio waves as shown in Fig. 1-1. • The guiding device may take the form of a transmission line (coaxial line) or a waveguide (hollow pipe), and it is used to transport electromagnetic energy (from the transmitting source to the antenna, or from the antenna to the receiver). 10 Thevenin Equivalent of Antenna 11 Thevenin equivalent of the antenna system in the transmitting mode shown in Fig. 1-2. The source is represented by an ideal generator (with voltage 푽품 and impedance 풁품, [ 풁품 = 푹품 + 풋 푿품]), the transmission line is represented by a line with characteristic impedance 풁풄 , and the antenna is represented by a load with impedance 풁푨 , [ 풁푨 = ( 푹풍풐풔풔 + 푹풓풂풅) + 풋 푿푨] connected to the transmission line. 12 Topic 1 Radiation Pattern 13 Radiation Pattern An antenna radiation pattern - “a mathematical function or a graphical representation of the radiation properties of the antenna as a function of space coordinates”. • Radiation pattern is very important characteristic of an antenna. Radiation properties include radiation density, radiation intensity, field strength, gain, directivity, effective aperture, polarization, etc., • If the radiation from an antenna is represented in terms of field strength (electric or magnetic), then the radiation pattern is called field pattern. • If the radiation from an antenna is represented in terms of power per unit solid angle, then the radiation pattern is called power pattern. • To completely specify the radiation pattern with respect to field intensity and polarization requires three patterns. 14 • The 휃 component of the electric field as a function of the angles 휃 and 휙 or 퐸휃(휃, 휙). • The 휙 component of the electric field as a function of the angles 휃 and 휙 or 퐸휙(휃, 휙). • The phases of these fields as a function of the angles 휃 and 휙 or 훿휃(휃, 휙) and 훿휑(휃, 휙). • Fig. 1-2. shows three-dimensional field pattern (in spherical coordinates) of a directional antenna with maximum radiation in 푧- direction at 휃 = 0°. 15 Fig 1.2 Three Dimensional Field Pattern 16 Radiation Pattern Lobes • Various parts of a radiation pattern are referred to as lobes, which may be sub-classified into major or main, minor, side and back lobes. • A major lobe is defined as the radiation lobe containing the direction of maximum radiation. A minor lobe is any lobe except a major lobe. A side lobe is a radiation lobe in any direction other than the lobe. A back lobe is a radiation lobe whose axis makes an angle of approximately 180° with respect to the beam of an antenna. 17 Fig 1.3 Radiation Lobes & Beamwidth of Antenna 18 • Fig. 1-3 demonstrates a symmetrical three dimensional power pattern with a number of radiation lobes. Fig. 1-4 illustrates a linear plot of power pattern and its associated lobes and beamwidths. • The half-power beamwidth (HPBW) is defined as the angular measurement between the directions in which the antenna is radiating half of the maximum value. • The First-null beamwidth or beamwidth between first two nulls (FNBW) is defined as the angular measurement between the directions radiating no power. 19 Fig 1.4 Linear Plot of Power Pattern 20 • Often the field and power patterns are normalized with respect to their maximum value, yielding normalized field and power patterns. Fig.1-5 shows the normalized field pattern and normalized power pattern. • Dividing a field component by its maximum value, we obtain a normalized or relative field pattern which is a dimensionless number with maximum value of unity. The half power level occurs at those angles 휃 and 휙 for which 푬휽(휽, 흓)풏 = ퟎ. ퟕퟎퟕ (or) 푬흓(휽, 흓)풏 = ퟎ. ퟕퟎퟕ . 21 Fig 1.5 Normalized Field and Power Patterns 22 • Patterns may also be expressed in terms of the power per unit area. • Normalizing this power with respect to its maximum value yields normalized power pattern as a function of angle which is a dimensionless number with a maximum value of unity. • The half power level occurs at those angles 휃 and 휙 for which 푷풏(휽, 흓)풏 = ퟎ. ퟓ. 23 Principle Patterns • For a linearly polarized antenna, performance is often described in terms of its principal 푬-and 푯-plane patterns. • The 푬-plane is defined as “the plane containing the electric-field vector and the direction of maximum radiation,” and the 푯-plane as “the plane containing the magnetic-field vector and the direction of maximum radiation.” • The 푥-푧 plane (elevation plane; 휙 = 0) is the principal 푬-plane and the 푥-푦 plane (azimuthal plane; = 휋/2) is the principal 푯-plane. 24 Types of Radiator An isotropic radiator is defined as “a hypothetical lossless antenna having equal radiation in all directions.” Although it is ideal and not physically realizable, it is often taken as a reference for expressing the directive properties of actual antennas. • A directional antenna is one having the property of radiating or receiving electromagnetic waves more effectively in some directions than in others. An omnidirectional antenna is defined as one “having an essentially non-directional pattern in a given plane and a directional pattern in any orthogonal plane. An omnidirectional pattern is then a special type of a directional pattern. 25 Topic 2 Beam Area or Beam Solid Angle 26 Fig 1.6 Beam Area or Beam Solid Angle 27 • In polar-two dimensional coordinates an incremental area 푑퐴 on the surface of a sphere is the product of the length 푟푑휃 in the 휃 direction and 푟 sin 휃 푑휙 in the 휙 direction, as shown in Fig. 1-6. • The incremental area of a sphere is given by; • 푑퐴 = ( 푟푑휃 ). (푟 sin 휃 푑휙) = 푟2 sin 휃 푑휃푑휙 -------- (1.1) • where 푑Ω = solid angle subtended by the area 푑퐴, and • 푑Ω = 푑퐴/푟2 sin 휃 푑휃푑휙 • (Generally solid angle is nothing but angle subtended by an elementary area on a sphere.) 28 • The beam solid angle of an antenna is given by the integral of the normalized power pattern over a sphere (4휋). • Ω퐴 = ∬ 푃푛(휃, 휙) 푑Ω • Ω=4휋 ------- (1.2) • where 4휋 = solid angle subtended by a sphere (sr, Sterdian) • 2휋 휋 Ω퐴 = ∫ ∫ 푃푛(휃, 휙) sin 휃 푑휃푑휙 • 휙=0 휃=0 -------- (1.3) 29 • The beam area of an antenna can often be described approximately in terms of the angles subtended by the half-power points of the main lobe in the two principal planes. Thus, • Ω퐴 = 휃퐻푃 휙퐻푃 -------- (1.4) • where 휃퐻푃 and 휙퐻푃 are the half-power beam widths (HPBW) in the two principal planes, minor lobes being neglected. – The (total) beam area consists of the main beam area (Ω푀) plus the minor-lobe area(Ω푚). • Ω퐴 = Ω푀 + Ω푚 -------- (1.5) 30 The ratio of the main beam area to the (total) beam area is called the (main) beam efficiency. • e푀 = Ω푀/Ω퐴 -------- (1.6) • The ratio of the minor-lobe area to the (total) beam area is called the (main) stray factor. • e푚 = Ω푚/Ω퐴 -------- (1.7) • It follows that e푀 + e푚 = 1 31 Topic 3 Radiation Density 32 • Electromagnetic waves are used to transport information through a wireless medium or a guiding structure, from one point to the other. The quantity used to describe the power associated with an electromagnetic wave is the instantaneous Poynting vector defined as; • 푾 = 푬 × 푯 • where ; • 푾 = instantaneous Poynting vector , (푾/풎ퟐ) • 푬 = instantaneous electric-field intensity, (푽/풎) • 푯 = instantaneous magnetic-field intensity , (푨/풎) 33 • The total power crossing a closed surface can be obtained by integrating the normal component of the Poynting vector over the entire surface. • 푷 = ∯ 푾. 풅풔 푆 • For time-varying fields, the time average power density (average Poynting vector); • The average power radiated by an antenna (radiated power) can be written as 34 Topic 4 Radiation Intensity 35 • Radiation intensity in a given direction is defined as ” the power radiated from an antenna per unit solid angle”.