Basics of radiation and antennas

Basics of radiation and antennas

P. Hazdra, M. Mazanek,…[email protected] of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org

v. 23.2.2015

Literature

• C. A. Balanis, Antenna Theory and Design, Wiley, 2005• W. Stutznam, G. Thiele, Antenna Theory and Design, Wiley, 2013• T. A. Milligan, Modern Antenna Design, Wiley, 2005• J. D. Kraus, Antennas, McGraw‐Hill, 1997• S. J. Orfanidis, EM Waves and antennas, online

http://www.ece.rutgers.edu/~orfanidi/ewa/• M. Mazánek, P. Pechač, J. Vokurka, Antény a šíření

elektromagnetických vln, skripta ČVUT, Praha 2007• IEEE XPLORE http://ieeexplore.ieee.org/ (full text papers of

journals involving antennas)

2

Content• Radiation, what is an antenna?• Antenna as a transformer of guided waves into free‐space waves• Circuit model of antenna• Solution of radiation problems in terms of auxiliary vector

potentials• Elementary electric radiator – infinitesimaly small element of

current (Hertz dipole)• Fields and parameters of elementary dipole• Elementary magnetic radiator – small loop• Radiation zones, directional properties (rad. pattern), polarization• Overview of antenna types and their applications

3

The “antenna family”

4

• Wire antennas• Straight wire (dipole), loop, helix, …

• Aperture antennas• Horns, reflectors, lens

• Planar (“microstrip” antennas)• Metallic patch on a grounded substrate

• “Special” antennas• fractal geometry, on‐chip antennas, mm‐wave antennas, metamaterials,

antennas for medical applications (implantable)…

Antenna is…• Passive filter, both in frequency and spatial domain• Component transforming guided waves to waves in free space (that is actually 3D spherical waveguide)

• Very important component of the wholecommunication channel

• „The best amplifier“

5

guided wave

free‐space wave

Antenna link – the low loss link

6

Waveguides

7

• With TEM wave (operation from DC): coaxial cable, multiconductor line• Parameters not function of frequency! (no dispersion)

E

E

H

H

60ln TEM

Quasi‐TE11f ≅

120cosh

E H

Waveguides - metallic

8

• With TE/TM modes (operation above cut‐off frequency): metallic waveguides• Parameters are function of frequency! (dispersion)

Waveguides - planar

9

• With quasi‐TEM wave (operation from DC possible): microstrip, stripline, …• Parameters are function of frequency! (slight dispersion)

Waveguides – planar - microstrip

10

Waveguides – planar - microstrip

11

Radiation• Radiation is caused by accelerating (deccelerating) charge – time

varying current (usually time‐harmonic), discontinuities

• A stationary charge will not radiate EM waves – zero current no magnetic field, no radiated power

Katedra elektromagnetického pole 12

⋅

12

E field linesElectric field lines:• Start on positive charges and end on negative charges• Start on a positive charge and end at infinity• Start at infinity and end on a negative charge• Form closed loops neither starting or ending on any

chargeMagnetic field lines:• Always form closed loops encircling current because

physically there are no magnetic charges• Mathematically it is often convenient to introduce

equivalent magnetic charges and magnetic currents

radiation – process of transformation of guided wave into free‐space wave

Radiation - E

13

Radiation - H

14

Radiation – power flow (Poynting vector)

15

Antenna as a circuit element


Γ S

XA

Rr

RLoss

XG

RG

Transmitter (generator)

Antenna

EM radiation

Γ Γ 20log Γ

Γ1 Γ1 Γ

Fields (E,H) in the whole space:amplitude, phase, orientation (polarization), spatial distribution

Relative impedance bandwidth

Radiation efficiency

Matching


Γ S

Γ

Γ 20log Γ

1 Γ1 Γ

Radiation - E

18

Advantage of potentials – static fields


14

1′scalar potential

41

′1

Electrostatics

Stationary magnetic fields

vector potential

, ,′ ′, ′, ′Source point

Observation point′

Green’s function (static) Sources potentials fields

Radiation – aux. vector potentials A,F


⋅ /⋅ /

Maxwell equations in symmetric form for harmonicsources (

(electric/magnetic sources) ‐ duality

… magnetic current density /(magnetic sources – not real, only equivalent)

Sources of antenna radiation fields:

… electric current density A/(electric sources – real sources)

⋅

⋅

Charges are related to currents through equation of continuity

sources,

radiation fields,

vector potentials,

direct solution of MXW

The wave equation for E with electric sources

∆1

… caused by electric currents ,… caused by magnetic currents ,

(in fact set of two MXW systems, one for electric and one for magnetic sources)

direct solution for E/H difficult because of RHS

Total field = superposition of both sources

Helmholtz equations for A and F


∆

⋅

∆

⋅

1

1

Electric sources Magnetic sources

4 ′

Solution for inhomogenous Helmholtz equations

4 ′

z

x

y

r R

r’

A(x,y,z)F(x,y,z)

x’,y’,z’

J(x’,y’)M(x’,y’)dV’

, ,′ ′, ′, ′Source point

Observation point

Green’s function

′

„solenoidal field“

„potential field“

Elementary electric dipole


dz piece of electric current is placed at origin in the z‐axis, dipole length ≪ →

4 ′

4 ′/

/4

′ for → 0

Transformation between rectangular and spherical vector components(it is convenient here to describe source points in cartesian and observationpoints in spherical coordinates respectively)

Vector potential has the same orientation as current!

0

sin cos sin sin coscos cos cos sin sin

sin cos 0

Spherical components of vector potentials in spherical coordinates:

, , cos 4 cos

, , sin 4 sin

, , 0

⋅

1



Components of electric and magnetic fields generated by an elementary electric dipole

, 4 sin1 1

0

0

, 2 cos1 1

, 4 sin1 1 1

These expressions are valid everywhere except on the source itself. In most cases we are interested only in the far‐field, i.e. retain only 1/ terms. Generally, the radiated fields are vector functions of spherical coordinates , , .

• E field is always greater than H field (its electric dipole)

• 1 ( /2 ) is an important point (radian distance, radian sphere)

• 120 ≅ 377Ω if 1 (distance)

General distance out of sources

Fields are not function of



Short electric dipole ( /10), magnitude of E‐field intensity, radian‐sphere 1 ( /2 ) shown


25

Oscillating electric dipole consisting of two electric charges in simple harmonic motion, showing propagation of an electric field line and its detachment (radiation) from the dipole

Elementary electric dipole - power



, 4 sin1 1

0

0

, 2 cos1 1

, 4 sin1 1 1


12

∗ 12

∗ 12

∗ ∗

Energy density – Poynting vector /

⋅12

∗ ⋅ 2

Complex power (active, reactive) flowing through closed surface S (sphere), enclosing the antenna

10 11

1012

20 80

Radiation resistance of a short dipole (with constant current)

Note that for → ∞, the sphere is at infinity and the power is purely real

/20 80120 ≅ 2Ω

XA

Rr

RLoss

XG

RG

Transmitter (generator)

Antenna

EM radiation

0

Elementary electric dipole, field zones



, 4 sin1 1

0

0

, 2 cos1 1

, 4 sin1 1 1

Near (reactive) field region ≪ 1 ( ≪ /2 )Fields are similar to those of a static electric dipole and to that of a static current element (quasistationary fields)


12

∗ 0

and and out‐of phase with . There is no time‐average power flow, no radiated power, energy is stored in near‐zone

Intermediate field region 1 ( /2 )Fields are similar to those of a static electric dipole and to that of a static current element (quasistationary fields)

and approach time‐phase formation of time‐average power flow in the outward (radial) direction).

Far field region ≫ 1 ( ≫ /2 )Most important region of an antenna, vanishes and only transversal (to ) field components (here and ) remain

12

∗

Elementary electric dipole – FAR FIELD

28

Far field region ≫ 1 ( ≫ /2 )

, 4 sin

0

, 4 sin120

Field structure of an arbitrary antenna in the far‐field, i.e. fields are observed at sphere of very large radius:

, , ,

Constant involving current etc.

Amplitude and phase representing point source (spherical wave)

fieldintensit ~1

Farfield pattern, function involving angular dependence of the field, sin in our case of infinitely small current element. The dependence comes from transformation of unit vectors between cartesian and spherical coordinates

sin cos sin sin coscos cos cos sin sin

sin cos 0

The E and H field components are perpendicular to each other, transverse to the radial direction of propagation, and the variations are separable from those of and . The shape of the pattern is not a function of , and the fields form a transverse (TEM) wave, and are in phase.

Elementary electric dipole – FAR FIELD

29

, 4 sin ,

Let’s concentrate on the electric field only, because we know that in farfield /

Farfield radiation patternRepresentation of the radiation properties of the antenna as a function of space coordinates

, field pattern

, power pattern ~ , ,12

∗ 12

, 154

sin

⋅ sin d 10 Note that we are able to obtain the radiated power from the far‐field only

sin d Ω sin d normalized field pattern

, ,,

, sin

, ,,

, sin

steradian (space angle)

10 log , 20log ,

normalized power pattern

normalized power pattern in dB

Radiation pattern, directivity

30

Isotropic (point) source, power density .

44 4

Radiation intensity is defined as “the power radiated from an antenna per unit space angle (steradian)” and is

related to the far zone E field of an antenna: , , , .

,, ,

/44 ,

Directivity

Isotropic antenna has input power 1W. Radiation intensity is not function of direction, is constant /

Our source (antenna)

Isotropic source

Directivity = radio of radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions (isotropic source)

4 4∯ ,

Maximum directivity

Elementary electric dipole , sin

∯ , /

10 log 3/2 1.76dBi

Effective isotropic radiated power (EIRP)

dBi … decibels over isotropic radiatior

⋅Antenna with 30 dBi and 1W

⋅ 10 ⋅ 1 1000W(equivalent to isotropic source with

Antenna is the best amplifier!!

Antenna efficiency (gain)

31

Antenna gain , ,

1 Γ

Joule losses in metal Joule losses in dielectrics

Mostly only conductive losses are considered,

Radiation pattern

32

• Important antenna characteristic• Value of field, power (directivity) on

observing sphere at infinity• Involves amplitude, polarization, phase• Generally 3D, but usually main cuts are OK• E/H plane

, sin 1/√2 sin 0.707 90∘

Radiation pattern

33

Radiation pattern

34

0∘, . 90∘, .

Full 3D radiation patternz‐directed dipole only component of directivity

,

E‐plane H‐plane

Radiation pattern

35

Full 3D radiation patternx‐directed dipole has both components , and , .

, , ,

,

, ,

Radiation pattern – directional antenna

36

4 4Ω

4Ω ≅

4 41253

half‐power beamwidthsbeam solid angle

Example 10 ⋅ 10 412.5, 26 dBi

Polarization of the radiated field

37

• property of an electromagnetic wave describing the time‐varying direction and relative magnitude of the E.

Linear polarization ‐ fields• only one component or• two orthogonal linear components in‐phase or out‐of‐phase

Circular polarization (LHC/RHC) ‐ fields• must have two orthogonal linear components, and• the two components must have the same magnitude, and• the two components must have a time‐phase difference of 90∘ (+ odd

multiples)

RHC: Wave travels away from observer, rotation is clockwiseLHC: Wave travels away from observer, rotation is counterclockwise

majoraxisminoraxis

1 ∞0 ∞

Axial ratioGeneral elliptical polarization

circularelliptical

linear


38

#1

#2

Two crossed dipoles – equal amplitudes, 90∘ phase shift

#1 … 90∘

LHC RHC Axial Ratio


39

LHC – CCW rotation

RHC

z


40

z

No ∘phase shift (in‐phase) linear polarization

45∘

Slanted linear polarization


41

Antennas

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• Directive• radiated power is concentrated into narrow space angle• Radiowave P2P links, space communication antennas• ~10 50 dBi• Arecibo radiotelescope 70 dBi (10 million linear gain)

• Sector• radiated power is concentrated into given sector• Base station (access point) antennas, satellite antennas• ~10 20 dBi

• “Omnidirectional”• 360 degrees in horizontal plane, vertical plane could be

narrower• Mobile phone antennas, receiving antennas• ~1,5 6 dBi

Radiation zones

43

FAR FIELD: Angular distribution doesn’t depend on distance from the source (antenna)

Radiation zones

• Rayleigh: spherical wave fronts

• Fresnel: parabolic wave fronts

• Fraunhofer: plane wave fronts, field intensities are decreasing as 1/r (FAR FIELD). It corresponds to /8 phase error

′

Radiation zones

44

Field pattern = function of the radial distance, radial field component may be appreciable.

The angular field distribution is independent of the distance from the

antenna. Field components are transverse

Radiation zones

45

Radiation zones

46

~130λ

Ø 3m

f=1.296 GHz, λ=232 mm

Far field R>78 m (336 λ)

47

The small (elementary) dipole and loop

48

, 4 sin

, 4 sin,

, 4 sin

, 4 sin ,

Elementary dipole Elementary loop

Duality

The loop antenna and the electric dipole are said to be duals, because the magnetic field radiated by the electricdipole has the same form as the electric field radiated by the loop antenna. A small electric loop antenna is alsosometimes called a magnetic dipole.

⋅ ⋅

Summary

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• Sources of radiation• The simplest electric radiator – electric dipole, field structure• The simplest magnetic radiator – magnetic dipole (loop)• Antenna parameters: Input impedance, far‐field pattern (amplitude / phase), directivity, radiation resistance, efficiency, gain, bandwidth

• Radiation zones of antennas, near field, properties of far field E is transverse to H, 120 , no radial field component (TEM wave!), locally plane wave

Impedance parameters radiation (directional) parameters

Supplementary material

• Elementary electric dipole – E field during period• Derivation of potentials

50


51

Short electric dipole ( /10), E‐field intensity at specific parts of the period T

Vector potential A (similarly for F)

52

Magnetic flux is always solenoidal, so ⋅ 0 , therefore it can be represented as the curl of another vector ⋅0

1

jFirst MXW

0

Can be written as the gradient of some scalar function (potential) since ∓ 0

“solenoidal field+potential field”

Applying to both sides of (*) and using identity ⋅ ∆ leads to wave equation for

(*)

∆ ⋅

sign – choosed as in electrostatics

⋅ ⋅RHS still complicated but we now specify divergence of

∆Such potential calibration (Lorentz gauge) leads to inhomogenous Helmholtz differential equation with simple RHS

⋅

Using potential calibration, the radiated electric (and magnetic) field is obtained only from knowledge of !

Documents

Basics of radiation and antennas