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Guide To Antennas and Propagation

Antennas and Propagation 5
Antennas and Propagation updated: 09/29/2014 Wireless Communication Systems Our focus Multiplexer Modulator Converter Electromagnetic Energy De De Converter Electromagnetic modulator multiplexer Energy Antenna Characteristics o  Radiation patterns o  Radiated power o  Halfpower beam width of the antenna o  Antenna position, shape, and length o  Antenna gain with respect to an ideal case radiating electromagne tic energy Remember: into space Antenna Properties o  An antenna is an electrical conductor (transducer) or system of conductors n  They carry timevarying currents and, consequently, accelerating electrons n  à A Transmission Antenna radiates electromagnetic energy into space n  à A Reception Antenna collects electromagnetic energy from space collecting electromagnet ic energy from space Remember: Waves and Propagation Demo collecting Anntena electromagnet carry time radiating ic energy from varying electromagne space currents tic energy into space http://phet.colorado.edu/simulations/sims.php sim=RadioWavesandElectromagneticFields Remember: Antenna Properties Reciprocal Devices o  Most antennas are reciprocal devices, n  That is they are exhibiting the same radiation pattern for transmission as for reception o  When operating in the receiving mode, the antenna captures the incident wave n  Only that component of the wave whose electric field matches the antenna polarization state is detected o  In twoway communication, the same antenna can be used for transmission and reception n  Antenna characteristics are the same for transmitting or receiving electromagnetic energy o  The antenna can receive on one frequency and transmit on another Polarization http://www.cabrillo.edu/jmccullough/Applets/optics.html Start With Basics: o  We know: n  Q (static charges) à E field– capacitor example1 n  I (moving charges) à H field– compass example2 n  Thus, in the presence of timevarying current à we will obtain interdependent EM fields o  A timevarying current (I) along a wire generates rings of Electromagnetic field (B) around the wire o  Similarly the current passing through a coil generates Electromagnetic field in the Z axis 1 http://micro.magnet.fsu.edu/electromag/electricity/ 2 http://micro.magnet.fsu.edu/electromag/java/compass/ capacitance.html index.html Simple Experiments An induced magnetic field 1 Galvanometer needle moves Faraday confirmed that a moving magnetic field 2 is necessary in order for electromagnetic Electromagnetic induction to occur 3 field (B) Faraday’s Law: Electromotive force (voltage) induced by timevarying magnetic flux: Maxwell Equations Relationships between o  Gauss’s Law charges, current, o  Faraday’s Law electrostatic, electromagnetic, o  Gauss’s Law for Magnetism electromotive force o  Ampere’s Law Maxwell’s Equations – Free Space Set o  We assume there are no charges in free space and thus, = 0 Timevarying E and H cannot exist independently If dE/dt nonzeroà dD/dt is nonzero àCurl of H is nonzero à D is nonzero (Amp. Law) If H is a function of time à E must exist (Faraday’s Law) Interrelating magnetic and electric fields Our Focus: 2 d =(2l )/λ farfield FarField Approximation 1. In close proximity to a radiating source, the wave is farfield range spherical in shape, but at a far distance, it becomes approximately a plane wave as seen by a receiving antenna. 2. The farfield approximation simplifies the math. 3. The distance beyond which the farfield approximation is Very similar to throwing a valid is called the farfield range stone in water (will be defined later). What is the power radiated A far field approximation o  Assuming the alternating current travels in Z directionà radiated power must be in Z o  Antenna patterns are represented in a spherical coordinate system o  Thus, variables R, θ, φ à n  range, n  zenith angle (elevation), n  azimuth angle http://www.flashandmath.com/mathlets/multicalc/coords/ shilmay23fin.html Hertzian Dipole Antenna o  Using Ampere’s Law o  But how is the current I(r) distributed on the antenna o  One way to approximate this rather difficult problem is to use thinwire dipole antenna approximation n  Dipole because we have two poles (wires) n  aL o  We only consider the case when L is very very short (Hertzian Dipole) n  Infinitesimally short n  Uniform current distribution http://whites.sdsmt.edu/classes/ee382/notes/382Lecture32.pdf Hertzian Dipole (Differential Antenna) Radiation Properties o  Very thin, short (lλ/50) linear conductor o  Observation point is somewhere in the space http://www.amanogawa.com/archive/Antenna1/Antenna12.htm lHertzian Dipole (Differential Antenna) Radiation Properties Note that: ω= 2π f; η = µ /ε =120π; 0 0 0 k=ω /c= 2π f /c= 2π /λ; ε  is the free space permittivity (about 1) K=wave number lλ /50; µ  is magnetic Permeability ' η is the intrinsic impedance in Ohm R≈ R =Γ;Hertzian Dipole (Differential Antenna) Radiation Properties A/m V/m In this case: 1/Rà radiation field components 1/R2àinduction field components 1/R3àelecrostatic field components Farfield à only radiation field à Only Eθ and Hφ will be significant R= Range θ=Zenith (elevation) – side view φ=Azimuth – top view Hertzian Dipole (Differential Antenna) Radiation Properties A/m V/m Radiated Power Flux Density Electric and Magnetic Intensity Fields (E 0) R E(0, Eθ,0) H(0,y, Hφ) P(P ,0,z) R Average Power flux Density Cross product of E and H Normalized Radiation Intensity(F) Normalized Radiation Intensity àHow much radiation in each direction Elevation Pattern (side view) So=Smax= Max. Power Density R= Range θ=Zenith (elevation) – side view φ=Azimuth – top view Azimuth Pattern (top view) Radiation Pattern of Hertzian (short) Dipole z=dipole axis / no radiation Note: F(θ,φ)=1 for isotropic antenna Maximum radiation In the broadside direction (θ=90) Doughnutshaped radiation pattern in θφ space Connecting The Dots: Radiated Power Flux Density Electric and Magnetic Intensity Fields (E 0) R For Isotropic Antenna We Obtain: Average Power flux Density 2 2 E E EIRP S =P = = = W/m2 av den 2 η 120π 4π ⋅d 0 2 2 P ⋅G ⋅G ⋅λ E t t r P =P ⋅A = = ×A W r den er er 2 2 Cross product of E and H (4π) ⋅d 120π Note: Sav is the average power radiated or pwr density radiated by an isotropic antenna EIPR is the total power radiated P is power flux density denExample o  Example A (Hertzian Dipole) o  Example B (Isotropic Antenna) Antenna Directionality o  Set the wavelength to 1 o  Set Current to 1 A o  Plot Power o  Change the length o  Q1: What happens to the directivity when l changes o  Q2: What happens to the power when L changes The magic is all here: http://www.amanogawa.com/archive/DipoleAnt/DipoleAnt2.htm lOther Antenna Properties o  We already looked at the radiation intensity and radiation pattern o  Other properties n  Radiation Pattern Characteristics n  Radiation Resistance Principal planes: 1. Elevation plane (xz and yz planes) sides 2. Azimuth plane (xy plane) top Radiation Pattern – Polar and Rectangular Plots Radiation Pattern Halfpower Beamwidth Dimensions beamwidth Null Bandwidth Halfpower beamwidth Since 0.5 corresponds to ‒3 dB, the half power beamwidth is also called the 3dB beamwidth. Halfpower angles: theta1 and theta2 Antenna Radiation/Reception and Loss Resistances (Zin = R + jX) In this case: R = R + R in rad loss Radiation resistance and loss resistance Voc Zin = Rin + iXin We also have Pt = Prad + Ploss Circuit model for TX Antenna P P r r From the receiver point of view η = = eff receiver P P +P r total loss Pr is power received) P P R r r r ad ad ad η = = = Note that Rrad determines the eff transmitter P P +P R +R impedance matching total rad loss rad loss between the TX antenna and the source OR the RX antenna Note: and the LOAD We want Rloss to be minimized Also, when efficiency is 1 à there is no loss Gain, Directivity, Power Radiated Rrad For any antenna: Directionality Gain 2 4πR S S max max D= = P S rad av G=η .D eff 2 4πR S max P = rad D Assuming there is no ohmic loss (lossless antenna) For the Hertzian dipole: S max Smax is the average power radiated or pwr density radiated by an antenna Power Gain = 1.5 o  Set the current to 1 A Analyze a o  Set length of the dipole to half wave Dipole Antenna o  What is the Rrad o  What is Rin resistance o  What is Directionality o  What is the total radiate power o  Go to “Scan Fields and Power”, n  Set φ equal to 90 n  Determine at which angle of θ we get max power n  Determine at which angle of θ we get half power n  What is the 3dB BW for this dipole o  Answer the above questions but this time set the length to ¼ of the wave length. http://www.amanogawa.com/archive/Antenna1/Antenna12.html Example o  Example C (Measuring the received power) o  Example D (Resistance loss in a short dipole) o  Example E (rewrite the average power density in terms of current, distance between the two antennas, length of the antenna, and frequency of operation for a short dipole (loop) Review: Isotropic Antenna 2 4πd o  Radiated Power Approximation: P =EIPR=P ⋅G= S rad t max D 2 2 o  Power Density (W/m2) is V /m 2 2 S =E /η = =W /m max o Ω o  For isotropic antennas Pt=Prad 30P t E= d o  Note that the free space P t H = impedance is ratio of E and H 68.8d fields P t S =P =E⋅H = max den 2 4πd η=E/HDifferent Antenna Types Yagi Antenna Dipole Antenna Fields in HalfWave Dipole Homework Assignment •  Example F: Find the following: •  Find the expression for average power density •  Power Density (Smax) •  Normalized radiation intensity, F •  Directionality, D (from the table) •  Pradiated •  Rradiated •  Prove that 3dB BW is in fact 78 degrees (you can use substitution to prove •  HINT: Use the applet to check your answers All works must be shown Example: Example G Complete the Table Below Antenna Gt=D Rrad Prad 3dB BW Eff. Area Isotropic Short Dipole ½ Wave ¼ Wave Later Later Later Later Later Why dBi = dBd + 2.15dB Explain References o  Ulaby, Fawwaz Tayssir, Eric Michielssen, and Umberto Ravaioli. Fundamentals of Applied Electromagnetics: XE AU.... Prentice Hall, 2001, Chapter 9 o  Black, Bruce A., et al. Introduction to wireless systems. Prentice Hall PTR, 2008, Chapter 2 o  Rappaport, Theodore S. Wireless communications: principles and practice. Vol. 2. New Jersey: Prentice Hall PTR, 1996, Chapter 3 o  Wheeler, Tom. Electronic communications for technicians. Prentice Hall, 2001. Section 121 122