EE 4990/6990 Antennas Fall 2002 Page Lecture Material from Balanis Problems 1 Ch. 1, Introduction, antenna types 2 Radiation, Ch. 2, Antenna patterns 2.2 3 Average power, radiation intensity 2.4, 2.7 4 Directivity, numerical evaluation of directivity 2.4, 2.7 5 Antenna gain 2.11, 2.13, 6 Antenna efficiency and impedance 2.17(a), 2.21 7 Loss resistance, transmission lines 2.27, 2.39 8 Transmit/receive systems, Polarization 2.41, 2.46 9 Equivalent areas, effective aperture 2.29, 2.48 10 Friis transmission equation 2.53, 2.56, 2.58 11 Radar systems, radar cross section 2.62, 2.66 12 Problem Session 13 Quiz #1 [Ch. 1,2] 14 Ch. 3, Radiated fields 15 Use of potential functions 16 Far fields, duality, reciprocity 4.1 85 Ch. 4, Wire antennas, infinitesimal dipole 4.3 18 Infinitesimal dipole 4.5 19 Poynting’s theorem, total power 4.11, 4.15 20 Radiation resistance, Short dipole 4.18(b), 4.21 21 Center-fed dipole 4.31 123 Half-wave dipole 4.25, 4.26 23 Dipole characteristics 4.27, 4.33 24 Image theory, antennas over ground 4.37 25 Monopole 4.41, 4.44 26 Ground Effects on Antennas 27 Quiz #2 [Ch. 3,4] 28 Ch. 5, Small loop antenna 5.4 29 Dual sources 5.17 30 Loop characteristics 5.21 162 Ch. 6, Antenna arrays 6.3 32 Broadside arrays 6.6 33 Endfire arrays 6.16 34 Hansen-Woodyard array, Binomial arrays 6.24, 6.28 35 Dolph-Chebyshev array, 6.41 191 Ch. 9, folded dipole 9.8, 9.10, 9.12 37 Ch. 10, Traveling wave antennas 10.4, 10.6 38 Terminations, vee antenna, 10.28 39 rhombic antenna, Yagi-Uda arrays 10.28 40 Ch. 11, Log-periodic antenna 11.8 41 Problem Session 42 Quiz #3 [Ch. 5,6,9,10,11] 43 Ch. 12, Aperture antennas 44 Ch. 13, Horn antennas 13.7, 13.12 45 Course review Antennas Antenna - a device used to efficiently transmit and/or receive electromagnetic waves. Example Antenna Applications Wireless communications Personal Communications Systems (PCS) Global Positioning Satellite (GPS) Systems Wireless Local Area Networks (WLAN) Direct Broadcast Satellite (DBS) Television Mobile Communications Telephone Microwave/Satellite Links Broadcast Television and Radio, etc. Remote Sensing Radar [active remote sensing - radiate and receive] Military applications (target search and tracking) Weather radar, Air traffic control Automobile speed detection Traffic control (magnetometer) Ground penetrating radar (GPR) Agricultural applications Radiometry [passive remote sensing - receive emissions] Military applications (threat avoidance, signal interception) Antenna Types Wire antennas (monopoles, dipoles, loops, etc.) Aperture antennas (sectoral horn, pyramidal horn, slots, etc.) Reflector antennas (parabolic dish, corner reflector, etc.) Lens antennas Microstrip antennas Antenna arrays Antenna Performance Parameters Radiation pattern - angular plot of the radiation. Omnidirectional pattern - uniform radiation in one plane Directive patterns - narrow beam(s) of high radiation Directivity - ratio of antenna power density at a distant point relative to that of an isotropic radiator [isotropic radiator - an antenna that radiates uniformly in all directions (point source radiator)]. Gain - directivity reduced by losses. Polarization - trace of the radiated electric field vector (linear, circular, elliptical). Impedance - antenna input impedance at its terminals. Bandwidth - range of frequencies over which performance is acceptable (resonant antennas, broadband antennas). Beam scanning - movement in the direction of maximum radiation by mechanical or electrical means. Other system design constraints - size, weight, cost, power handling, radar cross section, etc. Fundamentals of Antenna Radiation An antenna may be thought of as a matching network between a wave-guiding device (transmission line, waveguide) and the surrounding medium. Transmitting antenna guided wave input 6 antenna 6 unguided wave output Receiving antenna unguided wave input 6 antenna 6 guided wave output Antenna as the termination of a transmission line The open-circuited transmission line does not radiate effectively because the transmission line currents are equal and opposite (and very close together). The radiated fields of these currents tend to cancel one another. The current on the arms of the dipole antenna are aligned in the same direction so that these radiated fields tend to add together making the dipole and efficient radiator. Antenna as the termination of a waveguide The open-ended waveguide will radiate, but not as effectively as the waveguide terminated by the horn antenna. The wave impedance inside the waveguide does not match that of the surrounding medium creating a mismatch at the open end of the waveguide. Thus, a portion of the outgoing wave is reflected back into the waveguide. The horn antenna acts as a matching network, with a gradual transition in the wave impedance from that of the waveguide to that of the surrounding medium. With a matched termination, the reflected wave is minimized and the radiated field is maximized. Antenna Patterns (Radiation Patterns) Antenna Pattern - a graphical representation of the antenna radiation properties as a function of position (spherical coordinates). Common Types of Antenna Patterns Power Pattern - normalized power vs. spherical coordinate position. Field Pattern - normalized *E* or *H* vs. spherical coordinate position. Antenna Field Types Reactive field - the portion of the antenna field characterized by standing (stationary) waves which represent stored energy. Radiation field - the portion of the antenna field characterized by radiating (propagating) waves which represent transmitted energy. Antenna Field Regions Reactive Near Field Region - the region immediately surrounding the antenna where the reactive field (stored energy - standing waves) is dominant. Near-Field (Fresnel) Region - the region between the reactive near- field and the far-field where the radiation fields are dominant and the field distribution is dependent on the distance from the antenna. 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). Antenna Field Regions Antenna Pattern Definitions Isotropic Pattern - an antenna pattern defined by uniform radiation in all directions, produced by an isotropic radiator (point source, a non-physical antenna which is the only nondirectional antenna). Directional Pattern - a pattern characterized by more efficient radiation in one direction than another (all physically realizable antennas are directional antennas). Omnidirectional Pattern - a pattern which is uniform in a given plane. Principal Plane Patterns - the E-plane and H-plane patterns of a linearly polarized antenna. E-plane - the plane containing the electric field vector and the direction of maximum radiation. H-plane - the plane containing the magnetic field vector and the direction of maximum radiation. Antenna Pattern Parameters Radiation Lobe - a clear peak in the radiation intensity surrounded by regions of weaker radiation intensity. Main Lobe (major lobe, main beam) - radiation lobe in the direction of maximum radiation. Minor Lobe - any radiation lobe other than the main lobe. Side Lobe - a radiation lobe in any direction other than the direction(s) of intended radiation. Back Lobe - the radiation lobe opposite to the main lobe. Half-Power Beamwidth (HPBW) - the angular width of the main beam at the half-power points. First Null Beamwidth (FNBW) - angular width between the first nulls on either side of the main beam. Antenna Pattern Parameters (Normalized Power Pattern) Maxwell’s Equations (Instantaneous and Phasor Forms) Maxwell’s Equations (instantaneous form) % ( ' + Ã- ' % (Ã+Ã'Ã%Ã- - instantaneous vectors [( =( (x,y,z,t), etc.] D t - instantaneous scalar Maxwell’s Equations (phasor form, time-harmonic form) E, H, D, B, J - phasor vectors [E=E(x,y,z), etc.] D - phasor scalar Relation of instantaneous quantities to phasor quantities ... ( (x,y,z,t) = Re{E(x,y,z)ejTt}, etc. Average Power Radiated by an Antenna To determine the average power radiated by an antenna, we start with the instantaneous Poynting vector 6 (vector power density) defined by 6à Ã(ÃðÃ+ÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃ(V/m × A/m = W/m2) Assume the antenna is enclosed by some surface S. = S =s ds 3 The total instantaneous radiated power rad leaving the surface S is found by integrating the instantaneous Poynting vector over the surface. = 3 à ÃçÃ6ÃÃ@ çà (ÃðÃ+à Ã@ rad ds = ( ) ds ds = s ds SS = ds = differential surface s = unit vector normal to ds For time-harmonic fields, the time average instantaneous Poynting vector (time average vector power density) is found by integrating the instantaneous Poynting vector over one period (T) and dividing by the period. 1 à ÃÃçà (ÃðÃ+à Pavg = ( ) dt T T ( = Re{Ee jTt} + = Re{He jTt} The instantaneous magnetic field may be rewritten as + = Re{½ [ He jTt + H*e!jTt ]} which gives an instantaneous Poynting vector of (ÃðÃ+ÃÃà Ãý Re {[E ð H]ej2Tt + [E ð H*]} ~~~~~~~~~~~~~~~ ~~~~~~~ time-harmonic independent of time (integrates to zero over T ) and the time-average vector power density becomes 1 ð * ç Pavg = Re [E H ] dt 2T T * = ½ Re [E ð H ] The total time-average power radiated by the antenna (Prad) is found by integrating the time-average power density over S. à Ãçà @ ç ð * Ã@ Prad Pavg ds = ½ Re [E H ] ds S S Radiation Intensity Radiation Intensity - radiated power per solid angle (radiated power normalized to a unit sphere). à Ãçà @ Prad Pavg ds S In the far field, the radiation electric and magnetic fields vary as 1/r and the direction of the vector power density (Pavg) is radially outward. If we assume that the surface S is a sphere of radius r, then the integral for the total time-average radiated power becomes 2 2 N If we defined Pavg r = U( , ) as the radiation intensity, then where dS = sin2d2dN defines the differential solid angle. The units on the radiation intensity are defined as watts per unit solid angle.