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Home , Electrical length, Main lobe, Radiation pattern

What is an ?

n An antenna is a passive structure that Review of serves as transition between a and air used to Antenna transmit and/or receive electromagnetic waves. theory

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

Antenna Types of antennas

n Can be divided into two groups

• Wire antennas:

n dipoles, loops, Yagi-Uda…

• Aperture antennas:

n parabolic, horns, microstrip antennas…

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

Wire antennas

Log periodic Yagi

Yagi

1 Wire antennas Aperture antennas

Dipole with parabolic and corner reflector Log periodic

Spherical (main reflector) with Gregorian feed

Yagi-Uda with reflector

Reflector and Pyramidal horn Far Field antennas

Far field n The distance at which the fields transmitted by an antenna Related parameters (spherical) can be approximated to plane waves. n It’s defined as n Solid angle, ΩΑ and Radiation intensity, U n , Pn, sidelobes, HPBW n Far field zone, rff r 2D2 / n , D or Gain, G ff = λ n Antenna radiation impedance, Rrad n Effective Area, Ae

All of these parameters are expressed in terms of a transmission antenna, but are identically applicable to a receiving antenna. We’ll also study: D = is the largest physical dimension of the antenna λ = of operation n Friis Transmission Equation rff = distance from the antenna to the observation point n Radar Equation

2 Spherical coordinates

z (zenith) θ=0

θ

θ=90 φ=90 y φ φ= azimuth x θ=90 θ= elevation φ=0

Solid Angle Radiation Intensity

n Is the power density per solid angle:

2 U = r Sr [W/sr] where s = r d s = r sin dø 1 θ 2 θ 1 s = θr = arco dA = s s 2 1 2 Sr = Re{E × H*}rˆ [W/m ] dA = r2 sin θ dø dθ 2 = 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: = 2πr = 4πr2 known as Poynting vector. •Ángulo total: = 2π [radianes] •Ángulo sólido total: =4π [rad2] =4π [sr] 1 steradian (sr) = (1 radian)2

Total radiated power by antenna Radiation Pattern

n Radiation pattern is Field pattern: n Can be calculated as; the 3D plot of the gain, but usually the E(θ,φ) En (θ,φ) = two dimensional Emax (θ,φ) P = U ⋅ dΩ [W] horizontal and rad ∫ vertical cross sections of the or Power pattern: radiation pattern are P = S ⋅ dA [W] considered. S(θ,φ) U(θ,φ) rad ∫ r Fn (θ,φ) = = Smax (θ,φ) Umax (θ,φ)

n Refers to the variation of the relative amplitude of Where U is the radiation the radiation as a intensity to be defined later. function of direction.

3 Total Solid Angle of an antenna

z ΩA = Fn (θ,φ)dΩ [sr] ∫∫ ΩšAA 4π

Is as if you changed the radiation pattern beam of an antenna Patrón into a pencil beam |Pn | shape and find out what’s the equivalent y solid angle occupied by x this pattern.

Isotropic antenna Radiation Pattern

|En| Patrón n It’s an hypothetic antenna, n Whenever we _ 1 normalizado - 0 dB i.e., it does not exist in real life, yet it’s used as a speak of -.7 -3dB measuring bar for real radiation -10dB antenna characteristics. patterns, we -.25 | | ø | | normally mean HPBW HPBW n It’s a point source that Patrón de Campo Patrón de campo o de potencia we are at a (Escala lineal) (Escala logarítmica) occupies a negligible space. Has no directional distance far preference. enough from COORDENADAS RECTANGULARES (1)d Ωisotropic = ∫∫ Ω the antenna 4π Note that when plotted in n Its pattern is simply a sphere π 2π known as the , the power and so it has = = 4 ΩA Ωisotropic π (1)sinθ dθ dφ = 4π far field. field patterns look exactly [steradians]. ∫ ∫ θ =0 φ =0 the same.

Pattern – polar plot Radiation Pattern of |Pn| Short 1

Lóbulo principal HPBW ("Mainlobe") .5

NNBW

}Lóbulos menores

PATRON TIPICO (Coordenadas polares esféricas, 2 dimensiones)

4 Dipole antenna pattern

Note the radiation pattern is donut shaped.

Sidelobes

n Antennas sometimes show side lobes in the radiation pattern.

n Side lobes are peaks in gain other than the (the "beam").

n 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.

Sidelobes of dipole arrays Antenna Pattern with sidelobes

sidelobe

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

5 OTG @ Cornelia Gain or Directivity

An isotropic antenna and a practical antenna fed with the same power. Their patters would compare as in the figure on the right.

Directivity and Gain Gain or Directivity n All practical antennas radiate more than the n Gain is measured by comparing an isotropic antenna in some directions and less in others. antenna to a model antenna, n Gain is inherently directional; the gain of an typically the isotropic antenna which antenna is usually measured in the direction radiates equally in all directions. which it radiates best. 4πr 2 4π D(θ,φ) = = F , d Ω D = Dmax (θ,ϕ) = Smax / Save =Umax / Uave ∫∫ n (θ φ) Ω p 4π

If lossless antenna, G=D Do = Ωisotropic /ΩA

Directivity Beamwidth, HPBW n For an antenna with a single main lobe n Is the “distance” in radians o pointing in the z-direction , ΩA can be approximated to the product of the HPBW degrees between the direction of the radiation pattern where the radiated power is half of the maximum.

Ω A ≅ β xz β yz 10 log 0.5 = -3 dB then 20 log 0.707 = -3 dB The Directivity: for "pencil beam" shape; 4π 4π D = 4π/ΩA ≅ = 2 Ae o λ β xz β yz λ HPBM ≈ 70 D

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

Radiation Resistance Antenna polarization

n The antenna is connected to a T.L., and n The polarization of an antenna is the it “sees” it as an impedance. polarization of the signals it emits. • The ionosphere changes the polarization of n The power radiated is signals unpredictably, so for signals which will 1 2 Prad = IoR rad be reflected by the ionosphere, polarization is 2 not crucial. • However, for line-of-sight communications, it n The loss power is 1 2 can make a tremendous difference in signal P = I R loss 2 o L quality to have the and receiver using the same polarization. • Polarizations commonly considered are P R vertical, horizontal, and circular. η = rad = rad Prad + Ploss R rad + Rloss

Antenna Bandwidth Effective Area

n The bandwidth of an antenna is the range of n How a Rx antenna extracts energy frequencies over which it is effective, usually centered around the operating or resonant from incident wave and delivers it to frequency. a load?

• The bandwidth of an antenna may be increased by 2 several techniques, including using thicker wires, Prec λ D replacing wires with cages to simulate a thicker wire, Ae = = tapering antenna components (like in a ), and combining multiple antennas into a single assembly and Sinc 4π allowing the natural impedance to select the correct antenna. Above is valid for any antenna under matched-load conditions

7 Example n Determine the direction of maximum radiation , pattern solid angle, directivity and HPBW in the y-z plane for an antenna with normalized radiation intensity given by

⎧ 2 π cos θ for 0 ≤ θ ≤ and 0 ≤ φ ≤ 2π ⎪ 2 F(θ,φ) = ⎨ ⎪ ⎩⎪0 elsewhere

2π o Answers :(0, 0), , 6, 90 3

Communication set up Friis Transmission Eq.

n In any communication link, there is a transmitting antenna and a receiver with a receiver antenna.

TX

Pt Sisotr = A A P 4π R2 P = A S = t r t rec r t λ 2 R2 RX GtPt AtPt Pt = GtS isotr = 2 = 2 2 4π R λ R 2 G tG rPt λ Prec = (4π R)2

Circular aperture

8 Radiation Pattern for several aperture distributions

Antenna Arrays Linear Arrays n Uses many antennas synchronized with each other to increase n Pattern multiplication, AF ⎡ Nψ ⎤ ⎡Patrón ⎤⎡Factor ⎤ sin ⎢ 2 ⎥ E(r) = ⎢antena ⎥⎢del ⎥ AF = ⎢ ⎥⎢ ⎥ N ⎢ ψ ⎥ ⎣⎢individual⎦⎥⎣⎢Arreglo⎦⎥ ⎢ N sin ⎥ ⎣⎢ 2 ⎦⎥ Uniform illumination Tschebyscheff Illumination

|T4 (x)|

-R

1

x -1 0 1 x °

Uniform Distribution Binomial Distribution

9 Phase (Electronic) Scanning Horn Antennas

Horn Antennas Horn Antennas E-sectorial, H-sectorial

E-plane Sectorial H-plane Sectorial

Optimum Conical Horn

with hyperbolic lens to transform to uniform phase front

10 Radiation thru slots Patch Antennas

Patch Antennas Patch input Impedance

Patch Conventional & Active Array antennas Bandwidth and Radiation Efficiency

11 Analog & Digital

Available at mrs.eecs.umich.edu Planar Arrays

⎡ ⎛ M ⎞⎤⎡ ⎛ N ⎞⎤ ⎢ sin⎜ ψ x ⎟⎥⎢ sin⎜ ψ y ⎟⎥ 1 ⎝ 2 ⎠ ⎢ 1 ⎝ 2 ⎠⎥ AFn (θ,φ) = ⎢ ⎥ ⎢M ⎛ψ x ⎞ ⎥⎢ N ⎛ψ y ⎞ ⎥ sin⎜ ⎟ sin⎜ ⎟ ⎢ 2 ⎥⎢ ⎜ ⎟ ⎥ ⎣ ⎝ ⎠ ⎦⎣ ⎝ 2 ⎠ ⎦

Assigned Problems ch. 3 Antennas

n 1-4, 7-9, 11-13, 15-22, 28-30, 32-34, 36-42

12