Antennas

Transcription

Antennas

Escuela Politécnica
Universidad de
Extremadura

Contenidos
Tema 1. Fundamentos de radiación electromagnética:

Fundamentos de radiación.

Distribuciones de corriente.

Teorema de Poynting.

Potenciales retardados.

Radiación de una fuente elemental.

Campos radiados por una antena.

Propiedades del campo radiado: campo cercano, intermedio y lejano.
Radiación y ondas guiadas – J. M. Taboada
Universidad de
Extremadura

1
Contenidos
Tema 2. Conceptos básicos de antenas.

Tipos de antenas.

La antena como elemento circuital: parámetros de impedancia.

Coeficiente de reflexión y relación de onda estacionaria.

Diagrama de radiación. Directividad. Ganancia y eficiencia.

Polarización.

Ancho de banda.

La antena en recepción.

Fórmula de Friis: propagación en espacio libre.

Ecuación de alcance radar.

Ruido captado por una antena.
2
Universidad de
Extremadura

Contenidos
Tema 3. Antenas de hilo.

Integral de radiación.

Dipolos eléctricos. Monopolo sobre plano de tierra.

Teoría de imágenes.

Dipolos paralelos a plano conductor.

Otras antenas de hilo.

Acoplamientos mutuos entre antenas.

Antenas Yagi.
3
Universidad de
Extremadura
UNIT 1
Fundamentals of electromagnetic radiation
4
Universidad de
Extremadura
Antennas

An antenna is a usually metallic device for radiating or receiving radio waves.

It is the transitional structure between free-space and the transmission line.

The transmission line is used to transport the electromagnetic energy from the
transmitting or to the receiver device.
Properties of a good antenna:

Radiation efficiency.

Radiation pattern.

Transmission line matching.
Free-space spherical
wavefronts
Waveguide
Incoming plane
wavefronts
Waveguide
Rx
Tx
Transmitter
Antenna
Antenna
Receiver
5
Universidad de
Extremadura
Current distribution on a thin wire antenna.
6
Universidad de
Extremadura
Electromagnetic radiation mechanism
a) During the first quarter of wavelength the electric current
accumulates positive charge in the upper arm and negative in
the lower arm. The circuit is closed throughout the
displacement currents (field lines of force).
b) During the next quarter the current decreases, generating fields
lines on the opposite direction, which pushes forward the
previous lines.
c) After the first half of period the net charge on the dipole is
null, which forces the field lines to unite together to form
closed loops
7
Universidad de
Extremadura
Electromagnetic radiation mechanism
E
e(t )
Re Ee jZt 8
Universidad de
Extremadura
Maxwell’s equations.
Fields:
Faraday law:
E: Electric field intensity (V/m)
Ampere law:
H: Magnetic field intensity (A/m)
Gauss law:
D: Electric flux density (Coulombs/m2)
Magnetic flux contin:
B: Magnetic flux density (Weber/m2)
Sources:
Continuity equation:
J: electric current density
Constitutive relations:
Ji : impressed current
U: electric charge density
Constitutive parameters:
H: electric permittivity
P: magnetic permeability
dielectric permittivity in DC
dielectric loss factor (usually it is function of Z)
9
Universidad de
Extremadura
Maxwell’s equations.
The current J is composed of an impressed (excitation known
current), a conduction current:
and the total current is the latter :
Displacement Conduction
current
current
Conductivity
Impressed
current
Conduction and friction
losses in dielectric
Displacement
reactive current
Displacement
dissipative current
10
Universidad de
Extremadura
Maxwell’s equations

Sometimes it is convenient to introduce a fictitious magnetic current density M.

Magnetic currents are useful as equivalent sources that replace complicated electric fields in
some problems.
11
Universidad de
Extremadura
Boundary conditions
Perfect electric conducting (PEC) object
General case: penetrable object
Normally Js = 0; Us=0
Conductividad finita.
Sin cargas ni corrientes
inducidas en interfaz.
Conductividad finita.
Cargas y/o corrientes
inducidas en interfaz.
Conductividad infinita
(PEC).
nˆ u (E1 E2 ) 0
nˆ u (E1 E2 ) 0
nˆ u E1
0 E1,tan
nˆ u (H1 H 2 ) 0
nˆ u (H1 H 2 )
nˆ D1
U s D1,nor
nˆ (D1 D2 ) 0
nˆ (D1 D2 )
nˆ (B1 B 2 ) 0
nˆ (B1 B 2 ) 0
Js
Us
nˆ u H1
nˆ B1
0
Us
J s H1,tan
0 B1,nor
nˆ u J s
0
12
Universidad de
Extremadura
Poyinting vector. Conservation of power.

The complex Poyinting vector represents the complex power density in W/m2 at a point

Complex power flowing out from a closed surface S surrounding the antenna:
with
because
P’source = Pradiated
+ Pstored magn. + Pstored elect. + Pdissipated
Universidad de
Extremadura

13
Poyinting vector. Conservation of power.
We are particularly interested in the real power (the part of the source power that can be
radiated)
Psource
= Pradiated
+
Pdissipated
14
Universidad de
Extremadura
Current distribution

Obtaining the current distribution on antennas or scatterers (in magnitude and phase) is one
of the most complex problems in electromagnetics

It is given by the boundary conditions and the excitation (incident field or voltage source)
of the problem. Depends on geometry, material, feed point, etc.

Nowadays it is addressed using numerical techniques such as the method of moments
(MoM). Depending on the electric size of the problem it could imply solving matrix
systems with millions or hundreds of millions of unknowns.

We are going to suppose that the induced currents J are known. The goal here is to develop
procedures for finding the radiated fields by an antenna or scatterer based on Maxwell’s
equations
15
Universidad de
Extremadura
Potentials

The radiation problem consists of solving for the fields that are created by a source current
distribution (in the further denoted by J instead of Ji). The source currents may represent
either actual or equivalent currents. How to obtain these currents will be discussed in later
courses (it constitutes a hot research topic in computational electromagnetics). For the
moment, suppose we have the source current distribution J and we wish to determine the
fields E and H.

It is possible to obtain directly from the source currents by integration.

However it is much simpler to do it in two steps:

1. Find the auxiliary functions (vector potentials, or potenciales retardados) by
integration.

Magnetic vector potential A

Scalar potential )
2. Find the radiated fields by differentiation.
16
Universidad de
Extremadura

Potentials
Magnetic vector potential A. From the continuity of the magnetic flux law:
because

Scalar potential ). From the Faraday law:
because

So the fields can be obtained in terms of the potential functions. We now discuss the
solution for the potential functions A and ).
Radiación
ad
y ondas guiadas – J. M. Taboada
Universidad de
Extremadura

17
Potentials
The Ampere law can be written in terms of the potential vectors
because
because

Lorentz condition (fixing the divergence of A):
By the uniqueness theorem, if we reach a solution that
fulfills Maxwell’s equations, this is the real only solution to
the problem.

H and P can be replaced
by the equivalent ones in
the case of lossy
dielectrics
We lead to the magnetic vector potential wave equation (or Helmholtz equation for A)
18
Universidad de
Extremadura

Potentials
The same procedure can be applied to the Gauss law:
because

(Lorentz condition)
This is the wave equation or Helmholtz equation for the scalar potential )
19
Universidad de
Extremadura
Calculation of fields from potentials

Once we have the potentials we can calculate the fields:

The electric field can be also obtained using only the vector potential
because
(Lorentz condition)
This is important because in this way we can only work in terms of electric current J,
without explicitly considering the electric charge U

Relation between fields in absence of fonts. From Ampere law with J=0: Radiación y ondas guiadas – J. M. Taboada
20
Universidad de
Extremadura

Radiation from an elemental source
The simplest radiation element is an infinitesimal lineal current density element Jz with
length dl in an isotropic medium.
z
ds
dv dlds
dl
Jz
x

y
because the source is a point
I J zds
The problem has spherical symmetry, so we shall use the spherical coordinate system.
Bessel spherical differential equation

Solution
Universidad de
Extremadura

21
Radiation from an elemental source
Derivation of constants:
z
C 2 0 because it represents an incoming wave
ds
dl
x

Jz
y
I J zds
From the vector potential we obtain the fields:
Medium intrinsic
impedance
22
Universidad de
Extremadura

Radiation from antennas
A real current distribution is composed of infinite current elements J defined inside of
infinitesimal volumes dV placed at points r’.
r r'
dv '
J(r ')
r
r'

The total potential is given by superposition:
Volume
Surface
Wire antenna
Universidad de
Extremadura

23
Antenna radiated field regions
An inspection of the radiated fields of the
infinitesimal dipole
reveals that the space surrounding the
antenna can be subdivided into three regions:

Near-field region (r < O): predomination
of 1/r3 terms
Intermediate region
Far-field region (r >> O): predomination
of 1/r terms
24
Universidad de
Extremadura
Near-field region (r < O)

The 1/r3 terms predominates the field:

The time-average power density reduces to zero because E and H are in quadrature:

The fields are reactive and quasistatic
25
Universidad de
Extremadura
Intermediate-field (or Fresnel) region (kr > 1)

The terms that were predominant for the near region become smaller

As r increases, E and H approach time-phase, which is an indication
of formation of time-average power flow in the outward (radial)
direction (radiation phenomenon)

The radiation fields predominate over the reactive fields. The angular
field distribution is dependent on the distance from the antenna.

E has some component in the radial direction (it is named a cross
field)
E
26
Universidad de
Extremadura

Far-field region (r >> O)
Far field region, or Fraunhofer region
Outgoing power density:
r
E

Important notes:

Fields E and H in the far field region are orthogonal each other and orthogonal to the
radial propagating direction, thus locally behaving like a plane wave.

The magnitude of the E and H fields are related by the medium intrinsic impedance.

Even for an infinitesimal source we have a directional behavior of
it is impossible to obtain a totally isotropic antenna!
, implying that

Complex power density is real indicating dissipated power and it is travelling away
from the source and decreasing as 1/r2, typical for spherical progressive waves. This
power is named radiated power, and the fields radiated fields.
27
Universidad de
Extremadura
Radiation of power

The energy of an harmonically excited antenna dissipates due to: (i) a finite (Ohmic)
resistance felt by the charge carriers in the metal wire and (ii) loss of energy due to
radiation of e.m. waves.

This so-called radiation loss occurs due to the fact that the oscillation eventually creates
time-dependent electric fields at remote distances, which must then be accompanied by
magnetic fields that vary according to Maxwell’s equations.

At large enough distance these fields transform into plane waves which are free-space
solutions of the wave equation. If the dipole oscillation would be suddenly switched off,
those far-away fields, or simply far fields, would continue to propagate since they carry
energy that is stored in the fields themselves and has been removed from the energy
originally stored in the charge distribution we have been starting out with.

On the contrary, the so-called near-field zone corresponds to the instantaneous electrostatic
fields of the dipole, which do not contribute to radiation but return their energy to the
source after each oscillation cycle or when the source is turned off (reactive power).
28
Universidad de
Extremadura
Antenna radiated field regions: summary
Far field condition for an antenna:
D: maximum antenna dimension
29
Universidad de
Extremadura
Far-field approximation

We are in the far-field region when

Approximations
J(r ')
for the amplitude term
for the phase term
r
r'
30
Universidad de
Extremadura

Approximated vector potential:
r
r'

Magnetic field:
negligible
terms 1/r2
E and H far-field relation:

Electric field:
TEM wave
Universidad de
Extremadura

31
Far-field electric and magnetic radiated fields. Vector expressions:
z

Far-field electric and magnetic radiated fields. Scalar expressions:
rˆ
x
y
32
Universidad de
Extremadura

Antenna far-field radiation properties
The far-field radiated fields of an antenna must fulfill the following aspects:

The dependency of E and H with r is that of the spherical wave

E and H depend on T and I because the spherical wave is non homogeneous

The spherical radiated wave locally behaves like a plane wave

The E and H fields do not have radial components