Download Electromagnetic fields and radiation in Antennas ()

Electromagnetic fields and radiation
in antennas
A project in UniK4700, Radio and Mobility
Author:
Thomas Fagerland Wiig
December 1, 2008
Electromagnetic fields and radiation in antennas
UniK 4700
Contents
1 Introduction
2
2 Electromagnetic fields, waves and radiation
2.1 Electromagnetic wave propagation . . . . . . . . . . . . . . . . .
2.2 Radiation model . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Near- and far-field . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
4
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3 Antenna examples
3.1 Hertzian dipole . . . .
3.2 Half-wavelength dipole
3.3 Patch antennas . . . .
3.4 Parabolic antenna . .
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Electromagnetic fields and radiation in antennas
1
UniK 4700
Introduction
An antenna can easily be described as a reformer of the added effect (current
and voltage) to the radiated power in space. Since an antenna is reciprocal,
the antenna has the same qualities whether it is used as the transmitting or
receiving antenna. Meaning that the opposite process will occur when power
from space induce currents or voltages in the antenna.
A simple transmitting antenna can consist of a straight metal wire, or it
can consist of many more or less complicated structures. Antennas can have
small dimensions, from tens of millimetres up to large satellite dishes on dozens
of metres. The frequency, thus wave length, determines the size. Different
wavelengths give different antenna qualities.
A transmitting antenna consisting of a straight metal wire, which is given
an alternating current (AC), creates both a magnetic and electric field near
the wire. Both of these fields will propagate from the wire together and form
what is called an electromagnetic wave (EM-wave). An often used name for an
electromagnetic wave is radio wave. The EM-wave has the same prevalence rate
as light, which is approximately 300,000 km/s.
If it is placed a metal wire in the EM-field from a transmitting antenna, it
will be induced with current and voltage in the wire. If this wire is connected
to a recipient, it is called a receiver antenna. [And91]
Figure 1: Basic principle of how an antenna work [Ama06]
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Electromagnetic fields and radiation in antennas
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2.1
UniK 4700
Electromagnetic fields, waves and radiation
Electromagnetic wave propagation
Electromagnetic waves consist of an electric field (E-field) and a magnetic field
(H-field). E- and H-field are perpendicular to each other as shown in figure 2
[And91], and propagate at the speed of light (c0 ).
Figure 2: Electromagnetic wave propagation
Electromagnetic waves are created by alternating currents. As described in
the introduction, an ordinary metal wire that is given AC
I = I0 cos(wt)
creates a H-field that orbit the metal wire. At the same time the E-field is
created, as figure 3 [And91] shows, in parallel with the metal thread and perpendicular to the H-field.
Figure 3: Propagation of E- and H-fields
For each period (λ) of the added current, a period of the EM-field is produced. Since the effect must be the product of E- and-H fields, it will look like
an effect rectangle (P = EH) for the recipient. The effect rectangle will induce
a current and voltage in a potential recipient which contains a metal wire. The
mathematical relationship between E- and H-fields is complex and has its origins
in the electromagnetic basic laws called Maxwell’s equations.
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Electromagnetic fields and radiation in antennas
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The EM-wave is also characterized by the following expression
λ=
k · c0
f
Where
λ = wavelength
c0 = speed of light (3 · 108 m/s)
f = frequency
k = constant, depending on the medium the EM-wave propagate in.
In vacuum k = 1. In a metal wire the factor k will be 0.95.
The vector, which is perpendicular to both the E- and H-field, is called the
poyntings vector. Poyntings vector is the product of both the E- and H-vectors
and give the propagation direction, as shown in figure 4 [And91]. This is also
the power density and is defined as P = EH (w/m2 ).
Figure 4: Poyntings vector
2.2
Radiation model
By using a small power element, it is possible to show how you can get electromagnetic field by inducing AC. Figure 5 [And91] shows a simplified picture
of how the radiation mechanism occurs, in a fraction of a second. We assume
that the antenna power has a positive direction right up in the start. To make
it easier, the current I consists of positive and negative charge carriers. The
latter moves in the opposite direction compared to the positive charge. After a
while, the current will create a magnetic field H1 that is perpendicular to the
flow direction. There can’t be any electric field in the beginning because the
two charges reset each other. The added current has a start value of zero (t =
0) [And91].
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Electromagnetic fields and radiation in antennas
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Figure 5: Electromagnetic wave propagation model
At t = 180o the charge carrier is back to start, and one complete EH-field
is created. This is before a new magnetic field (H2 ) occurs, which will be in
opposite phase to the established E1 − and H1 -field.
At t = 360o , the charge carrier and the current I are back to their original
position. One period of the induced current is done, and two EM-fields are
created. The distance between these fields are one wavelength (λ).
AC and AC-voltage is continuously induced to create new fields. At the
same time the AC and AC-voltage are ”pushing” the old fields away from the
antenna, resulting in wave propagation out in space.
The radiated energy to a receiver in space will look like a wavefront of the
electromagnetic effect, shown in figure 6 [And91]. In the far-field, the effect
received is a straight wavefront instead of radiated spherical waves. A small
part of a sphere can be considered as a straight line which makes E-and H-field
lines look like a perpendicular field.
Figure 6: Wave front in the far-field
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Electromagnetic fields and radiation in antennas
2.3
UniK 4700
Near- and far-field
In the near-field the electric field-lines are not at the same level as the current.
The near-field decreases with the square of the distance from the antenna, thus
it is declining very quickly. If one measures the field-strength in the near-field,
one will not get the same results as in the far-field.
In radio transmission, the far-field is of more interest. It starts at a distance
from a simple dipole, where the electric field-lines are at the same level as the
power of the antenna. E- and H-fields are now perpendicular to each other.
The distance to the far-field of large antenna systems is called the Rayleighdistance (R).
2D2
λ
Where D is the diameter of a parabolic antenna, or the length of an antenna
system.
R=
3
3.1
Antenna examples
Hertzian dipole
The hertzian dipole is a theoretical dipole antenna that consists of an infinitesimally small current source acting in free-space. It is defined to have a constant
or rectangular power distribution, shown in figure 7 [And91].
Figure 7: Hertzian dipole
In reality, it is impossible to create a dipole with rectangular power distribution. The power distribution will decrease from the center of the antenna to
zero out in the end, as with an open transmission line.
A hertzian dipole is a linear antenna, along with a small linear dipole,
standing-wave antenna and half-wavelength dipole [Orf02].
Like shown in figure 8 [And91], the radiation diagram is directive in relation
to a isotropic antenna (which beams out all power equally in all directions). A
hertzian dipole will therefore have some gain in relation to a isotropic antenna.
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Electromagnetic fields and radiation in antennas
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Figure 8: Radiation diagram for E- and H-fields for a hertzian dipole
To use a hertzian dipole as a model to explain other antennas is useful, because we can say that all antennas are built up by an infinite number of short
hertzian dipoles, each providing a small radiation contribution to the total field
strength from the actual antenna. Since a hertzian dipole is a very short element (or transmission line) it would, if it was created physically, get a very high
reactive input impedance. It would also be difficult to induce effect without a
big loss.
A hertzian dipole has the following data:
• Field strength diversity E = Ksin(θ)
• Gain = 1.75 dBi
• Effect angle = 90o
2
• Radiation resistance RH = 80π 2 ( L
λ ) ohm
• Antenna surface AH =
3λ2
8π
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Electromagnetic fields and radiation in antennas
3.2
UniK 4700
Half-wavelength dipole
A half-wavelength dipole antenna (figure 9 [And91]) is formed by two quarter
wavelength conductors or elements placed back to back for a total length of λ/2.
Figure 9: Half-wavelength dipole
A standing wave on an element of a length λ/4 yields the greatest voltage
differential, as one end of the element is at a node while the other is at an
antinode of the wave. The larger the differential voltage, the greater the current
flow between the elements.
Figure 10: Voltage and current compared to wavelength (λ) [wik]
Assuming a sinusoidal distribution, the current is then given by [wik]
I = Io eiωt cos(k`)
For the far-field case, the formula [wik] for the electric field of a radiating
electromagnetic wave is
−iIo cos( π2 cosθ) j(wt−kr)
e
2πεo cr
sinθ
In a half-wavelength dipole, voltage and current are in phase, which means
that the maximum radiation is perpendicular to the antenna axis. Half-wavelength
dipoles are two threads or metal sticks, combined with a wire where the two
leaders are attached to their ”dipole stick”.
Eθ =
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Electromagnetic fields and radiation in antennas
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The metal sticks will always represent induction in the same way as a regular
conductor. The capacitance will represent the distance between the dipole. In
the same way as regular LC-circuits, a dipole can be brought to resonance at a
certain frequency. This is determined by the length of the dipole. A dipole is
therefore in principle, a type of a LC-circuit.
The Q-value is defined as an electric charge. With thick dipole sticks, the Qvalue will decrease. It means that a dipole antenna can be used with a slightly
greater frequency range without a ”fall-out” inRthe maximum resonance, as
t
shown in figure 11 [And91]. Electric charge Q = tof I dt.
Figure 11: Dipole thickness and frequency dependence
The half-wave dipoles radiation-chart is created by a small portion of the
antenna, which plan to beam as a hertzian dipole, shown in figure 11 [And91].
Figure 12: Radiation diagram for a half-wavelength dipole
A small power element dy gives a small field-power contribution dE. If we
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Electromagnetic fields and radiation in antennas
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add all these small power contributions over the dipoles total length, we will get
the total power contribution which can be written as
cos( π2 sinθ)
sinθ
All power elements dy doen’t radiate equally because the power distribution
of the dipole is cosine shaped. The elements close to the power center radiate
more than the rays further away from center.
According to an example in [Ama06], the E- and H-field expressions for a
half-wavelength dipole antenna (in the far-field) is obtained like
r
−jβr
Imax
πcosθ
~ = ~iθ µ je
cos
E
ε 2πr sinθ
2
−jβr
Imax
πcosθ
~ = ~iθ je
H
cos
2πr sinθ
2
E=K
3.3
Patch antennas
A microstrip or patch antenna is a low-profile antenna that has a number of
advantages compared to other antennas; it is lightweight, inexpensive, and easy
to integrate with accompanying electronics. While the antenna can be 3D in
structure (for example wrapped around an object), the elements are usually flat;
hence their other name, planar antennas [OM00].
Figure 13 [OM00] shows a patch antenna in its basic form. A flat plate is
placed upon a ground level. The center conductor of a coax serves as the feed
probe to connect electromagnetic energy in and/or out of the patch.
Figure 13: A patch antenna in its basic form
The electric field is zero at the center patch, maximum (positive) at one side,
and minimum (negative) on the opposite side. The minimum and maximum
continuously change side according to the instantaneous phase of the applied
signal.
The resonant length determines the resonant frequency and is about λ/2
for a rectangular patch. The patch is, in fact, electrically a bit larger than its
physical dimensions. This is known as fringing fields and cause the patch to
radiate.
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Electromagnetic fields and radiation in antennas
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Figure 14: Voltage (U), current (I) and impedance (|Z|) for a patch antenna
The radiation of patch at the fringing fields results in a certain far-field
radiation pattern. This radiation pattern shows that the antenna radiates more
power in a certain direction than another, giving the antenna some directivity
[OM00] as shown in figure 15 [OM00].
Figure 15: Typical radiation pattern of a simple square patch
3.4
Parabolic antenna
Parabolic antennas are used for both microwave- and radio-communication. A
microwave example is satellite-communication. A parabolic reflector, also called
reflector antenna, has the ability to transform a spherical wavefront incident to a
parallel outgoing wavefront, as illustrated in figure 16 [And91]. Thus we achieve
plan-waves with a strong effect focus.
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Electromagnetic fields and radiation in antennas
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Figure 16: Parabolic reflector
A parabolic surface is mathematically given as
y 2 = 4f x
where y is the height in relation to a corresponding distance x, and f is the
distance to the focus point F. This is where all the incoming rays meet (receiving
antenna) or the point where you feed the antenna (transmitting antenna).
Figure 17 [And91] shows that all rays which leave the focus point F, are
being reflected from the parabolic surface. After being reflected from the Y Y’ plan all the rays are parallel.
Figure 17: Parabolic antenna
This gives us the following geometry [And91]: FA+AB = FC+CD = constant
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Electromagnetic fields and radiation in antennas
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You can use a regular dipole or a horn antenna as a ”feeding antenna”,
either directly or via a ”sub-reflector”. The ”feeding antenna” is usually placed
in focus, whether the antenna is used as transmitter or receiver.
Figure 18: Parabolic antennas with different type of focus [And91]
References
[Ama06] Amanogawa. Antennas, 2006.
http://www.amanogawa.com/archive/docs/antennas1.pdf.
[And91] Svein O. Andreassen. Radio transmisjon, 1991. ISBN 0-13-042232-0.
[OM00] D. Orban and G.J.K. Moernaut. The basics of patch antennas, 2000.
http://www.rfglobalnet.com/article.mvc/
The-Basics-Of-Patch-Antennas-0002.
[Orf02]
Sophocles J. Orfanidis. Electromagnetic waves and antennas, 2002.
http://www.ece.rutgers.edu/~orfanidi/ewa/.
[wik]
Wikipedia. http://en.wikipedia.org/wiki/Dipole_antenna
Search date: 2008.11.26.
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