Dr. S. X-Pol

What is an antenna?

• An antenna is a passive structure that serves as Introduction to transition between a transmission line and air used to transmit and/or receive electromagnetic waves. Antennas

Source Receiver Dr. Sandra Cruz-Pol Circuit Rx Electrical and Computer Engineering Tx University of Puerto Rico at Mayaguez

Antenna Types of antennas

• Can be divided into two groups

– Wire antennas: • dipoles, loops, Yagi-Uda…

– Aperture antennas: • parabolic, horns, microstrip antennas…

http://www.kyes.com/antenna/antennatypes/antennatypes.html Ulaby, 1999 http://en.wikipedia.org/wiki/Antenna_(electronics)#Overview

Wire antennas Wire antennas

Log periodic Yagi Log periodic

Yagi YagiYagi--UdaUda with reflector

Intro to Antennas 1 Dr. S. X-Pol

Aperture antennas Reflector and Pyramidal horn antennas

Dipole with parabolic and corner reflector

Spherical (main reflector) with Gregorian feed

Outline Spherical coordinates

Antenna parameters θ z (zenith) =0 • Solid angle, ΩΑ and Radiation intensity, U

• Radiation pattern, Pn, sidelobes, HPBW • Far field zone, rff • Directivity, D or Gain, G θ • Antenna radiation impedance, Rrad • Effective Area, A e θ=90 φ=90 All of these parameters are expressed in terms of a transmission antenna, but are identically applicable to a receiving antenna. φ y We’ll also study: φ= azimuth x • Friis Transmission Equation θ=90 • Radar Equation θ= elevation φ=0

Solid Angle Radiation Intensity

• Is the power density per solid angle :

= 2 U r Pr [W/sr] where θ θ s1 = r d s2 = r sin dø θ 2 s = r = arco dA = s 1 s2 P = × ˆ dA = r 2 sin θ dø d θ r ½ Re {E H*} r [W/m ] = r2 dΩ θ = ángulo plano dΩ = elemento de ángulo sólido is the power density also •El arco total en un círculo: • El área total en una esfera: = 2 πr = 4 πr2 known as Poynting vector. •Angulo total: = 2 π [radianes] •Angulo sólido total: =4 π [rad 2] =4 π [sr] 1 steradian (sr) = (1 radian) 2

Intro to Antennas 2 Dr. S. X-Pol

Total radiated power by antenna Radiation Pattern • Radiation pattern is the 3D • Can be calculated as; plot of the gain, but usually Field pattern: E(θ,φ) the 2D horizontal and E (θ,φ) = vertical cross sections of the n E (θ,φ) = ⋅ Ω max Prad ∫U d [W] radiation pattern are considered. or Power pattern: P = P ⋅dS [W] • Refers to the variation of P(θ,φ) U (θ,φ) rad ∫ r the relative amplitude of F (θ,φ) = = n P θ φ θ φ the radiation as a function max ( , ) U max ( , ) of direction .

Where U is the radiation intensity to be defined later.

Total Solid Angle of an antenna Isotropic antenna

• It’s an hypothetic antenna , i.e., it z does not exist in real life, yet it’s Ω = F (θ,φ)dΩ [sr] used as a measuring bar for real A ∫∫ n ΩžA A antenna characteristics. 4π

Ω = )1( dΩ • It’s a point source that occupies a isotropic ∫∫ Is as if you changed the 4π negligible space. Has no directional π 2π radiation pattern ∫ ∫ )1( sin θ dθ dφ = 4π preference. θ =0 φ =0 beam of an antenna Patrón

into a pencil beam |Pn | shape and find out • Its pattern is simply a sphere so it Ω Ω π [ ] what’s the equivalent y has A= isotropic = 4 steradians . solid angle occupied by x this pattern.

Radiation Pattern Pattern – polar plot

|En| Patrón |Pn| • Whenever we _ 1 normalizado - 0 dB 1

speak of radiation -.7 -3dB

patterns, we Lóbulo -.25 -10dB principal normally mean we HPBW ("Mainlobe") | | ø | | .5 are at a distance far HPBW HPBW enough from the Patrón de Campo Patrón de campo o de potencia (Escala lineal) (Escala logarítmica) NNBW antenna known as

the far field . COORDENADAS RECTANGULARES }Lóbulos menores

Note that when plotted in PATRON TIPICO decibels, the power and (Coordenadas polares esféricas, 2 dimensiones) field patterns look exactly the same.

Intro to Antennas 3 Dr. S. X-Pol

Dipole antenna pattern Sidelobes

• Antennas sometimes show side lobes in the radiation pattern.

• Side lobes are peaks in gain other than the main lobe (the "beam").

• Side lobes have bad impact to the antenna quality whenever the system is being used to determine the direction of a signal, for example in RADAR systems.

Note the radiation pattern is donut shaped.

Sidelobes of dipole arrays Antenna Pattern with sidelobes

sidelobe

Many applications require sidelobe levels (SLL) to be below -20dB.

Gain or Directivity Directivity and Gain

• All practical antennas radiate more than the isotropic antenna in some directions and less in others. • Gain is inherently directional; the gain of an antenna is usually measured in the direction which it radiates best .

= θ φ = = D Dmax ( , ) Pmax / Pave U max /U ave An isotropic antenna and a practical antenna fed with the same power. Their patterns If lossless antenna, G=D would compare as in the figure on the right.

Intro to Antennas 4 Dr. S. X-Pol

Gain or Directivity Directivity • For an antenna with a single main lobe pointing in the z- • Gain is measured by comparing an antenna to Ω direction , A can be approximated to the product of the a model antenna, typically the isotropic HPBW antenna which radiates equally in all directions. Ω ≅ β β A xz yz P(θ ,φ) π 2P θ φ then θ φ = = = 4 r ( , ) D( , ) P /PAVE 1 P dA P The Directivity: ∫∫ rad 4 π A D = 4π/Ω ≅ A β β 4πU xz yz = max = π Ω = Ω Ω Do 4 / A isotropic / A Prad

Far field Beamwidth, HPBW • Is the “distance” in radians o degrees between • The distance at which the fields transmitted by an the direction of the radiation pattern where antenna (spherical) can be approximated to plane waves. the radiated power is half of the maximum. θ,φ • It’s defined as • Can be found by solving Fn( )=. 5

2 = λ = rff 2D / 10 log 0.5 - 3 dB D = is the largest physical dimension of the 20 log 0.707 = - 3 dB antenna for "pencil beam" shape; λ = wavelength of operation λ rff = distance from the antenna to the observation o point HPBM ≈ 70 D

Antenna Impedance Antenna efficiency, η

• An antenna is “seen" by the generator as a load with impedance ZA , connected to the line. Z • Efficiency is the ratio of A power put into the antenna = ( + )+ Z A Rrad RL jX A terminals to the power = actually radiated Prad ηPin • The real part is the radiation resistance plus the ohmic resistance . • Radiation in an antenna is – Minimizing impedance differences at each interface will reduce SWR and maximize power transfer through each part of the antenna system. caused by radiation resistance which can only – Complex impedance, ZA , of an antenna is related to the electrical length of the antenna at the wavelength in use. be measured as part of total • The impedance of an antenna can be matched to the feed line and radio by resistance including loss adjusting the impedance of the feed line, using the feed line as an impedance =η transformer . resistance. G D • More commonly, the impedance is adjusted at the load (see below) with an antenna tuner , a balun , a matching transformer, matching networks composed of inductors and capacitors , or matching sections such as the gamma match.

Intro to Antennas 5 Dr. S. X-Pol

Radiation Resistance Radar equation • What is a radar? • The antenna is connected to a T.L., and it “sees” it as an impedance. • Received power by a radar is • The power radiated is = 1 2 2λ2 Prad I o Rrad PG − τ 2 P = t o o σe 2 r ()4π 3 R4 • The loss power is 1 P = I 2R loss 2 o L Where σ is the backscattering coefficient of the target [m 2]

P R η = rad = rad + + Prad Ploss Rrad Rloss

APPLICATIONS Antenna polarization

• Application to several research projects: • The polarization of an antenna is the polarization of the signals it emits. CASA, NASA-FAR, NASA-TCESS – The ionosphere changes the polarization of signals unpredictably, so for signals which will be • Show results from undergrads working in reflected by the ionosphere, polarization is not NASA and NSF projects crucial. – However, for line-of-sight communications, it can • Relation to Grad students make a tremendous difference in signal quality to have the transmitter and receiver using the same polarization. – Polarizations commonly considered are vertical , horizontal , and circular .

Antenna Bandwidth Effective Area

• The bandwidth of an antenna is the range of • How a Rx antenna extracts energy from frequencies over which it is effective, incident wave and delivers it to a load? usually centered around the operating or resonant frequency. P λ 2 D – The bandwidth of an antenna may be increased A = rec = by several techniques, including using thicker e π wires, replacing wires with cages to simulate a Pinc 4 thicker wire, tapering antenna components (like in Above is valid for any antenna under matched- a feed horn ), and combining multiple antennas load conditions into a single assembly and allowing the natural impedance to select the correct antenna.

Intro to Antennas 6 Dr. S. X-Pol

Friis Transmission Eq. Example

• In any communication link, there is a • Radar and Friis transmitting antenna and a receiver with a receiver antenna.

TX P A A P P = t = P = t r t isotr π 2 Prec Ar t 2 2 4 R λ R RX

G P A P 2 P = G P = t t = t t G G P λ tx t isotr 4π R 2 λ2 R 2 P = t r t rec ()4π R 2

Antenna Arrays Example

• Uses many antennas synchronized with each • Determine the direction of maximum other to increase radiation , pattern solid angle, directivity and HPBW in the y-z plane for an antenna with • Pattern multiplication normalized radiation intensity given by

 π cos 2 θ for 0 ≤ θ ≤ and 0 ≤ φ ≤ 2π  2 F(θ,φ) =   0 elsewhere

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