Antenna basics from-r&s

Antenna Basics
White Paper
This white paper describes the basic functionality of antennas. Starting with Hertz's Antenna model
followed by a short introduction to the fundamentals of wave propagation, the important general
characteristics of an antenna and its associated parameters are explained.
A more detailed explanation of the functionality of some selected antenna types concludes this white
paper.
MaikReckeweg
11.2014-8GEP_WP01
WhitePaper

Table of Contents
8GEP_WP01 Rohde & Schwarz Antenna Basics 2
Table of Contents
1 Introduction......................................................................................... 3
2 Fundamentals of Wave Propagation................................................. 5
2.1 Maxwell's Equations....................................................................................................5
2.2 Wavelength...................................................................................................................6
2.3 Far Field Conditions ....................................................................................................7
2.4 Free Space Conditions................................................................................................7
2.5 Polarization...................................................................................................................8
3 General Antenna Characteristics ...................................................... 9
3.1 Radiation Density.........................................................................................................9
3.2 Radiation Pattern .......................................................................................................10
3.3 Directivity....................................................................................................................13
3.4 Gain .............................................................................................................................13
3.5 Practical Gain.............................................................................................................14
3.6 Effective Area.............................................................................................................14
3.7 Input Impedance ........................................................................................................14
3.8 Nominal Impedance...................................................................................................15
3.9 Impedance Matching and VSWR..............................................................................15
3.10 Antenna Factor...........................................................................................................18
3.11 Bandwidth of an Antenna .........................................................................................19
4 Basic Characteristics of Selected Antennas .................................. 20
4.1 Half-wave Dipole ........................................................................................................20
4.2 Monopole Antenna.....................................................................................................22
4.3 Directional Antennas.................................................................................................24
4.4 Log-Periodic Dipole Antenna ...................................................................................25
4.5 Active Antennas.........................................................................................................28
5 Appendix ........................................................................................... 31
5.1 References..................................................................................................................31

Introduction
1 Introduction
Antennas act as converters between conducted waves and electromagnetic waves
propagating freely in space (see Figure 1). Their name is borrowed from zoology, in
which the Latin word antennae is used to describe the long, thin feelers possessed by
many insects.
Figure 1: Basic antenna functionality
The oldest existing antennas, such as those used by Heinrich Hertz in 1888 during his
first experiments to prove the existence of electromagnetic waves, were in theory and
in practice not so very different from an RF generator.
Figure 2: Heinrich Hertz's antenna model
An antenna can be derived from a parallel circuit which consists of an inductor and a
capacitor. If the plates of the capacitor are bent open, and the inductor is reduced to
the inductance of the wire itself, one ends up with a dipole antenna as shown at the
very right position of Figure 2.
In fact, resonant circuits are still frequently used even today as a means of explaining
the individual properties of antennas. It was not until around 1900 or even later, when
transmitting and receiving stations were being built, that a clear distinction was made
and antennas were classified as separate components of radio systems.
Antenna
Magnetic field strength
Electric field strength
Receiver or
Transmitter
Radiated wave
propagated in space
Conductive wave

Introduction
In Figure 3 it can be seen that the antenna is an important element in any radio system
because it acts like a link of a chain. So the overall performance is significantly
influenced by the performance of transmit and receive antennas.
Figure 3: Block diagram of a radio link
At first glance, modern antennas may still look very similar to the ancient model.
However they are nowadays optimized at great expense for their intended application.
Communications antenna technology primarily strives to transform one wave type into
another with as little loss as possible.
This requirement is less important in the case of test antennas, which are intended to
provide a precise measurement of the field strength at the installation site to a
connected test receiver; instead, their physical properties need to be known with high
accuracy.
The explanation of the physical parameters by which the behavior of each antenna can
be both described and evaluated is probably of wider general use; however the
following chapters can describe only a few of the many forms of antenna that are in
use today.
Transmitter
Transmit
Antenna
Propagation
path
Receive
Antenna
Receiver

Fundamentals of Wave Propagation
2 Fundamentals of Wave Propagation
2.1 Maxwell's Equations
The equations postulated by the Scottish physicist James Clerk Maxwell in 1864 in his
article A Dynamic Theory of the Electromagnetic Field are the foundations of classical
electrodynamics, classical optics and electric circuits. This set of partial differential
equations describes how electric and magnetic fields are generated and altered by
each other and by the influence of charges or currents.
𝑟𝑜𝑡 𝐻⃗⃗ = 𝑗 +
𝜕𝐷⃗⃗
𝜕𝑡
(1)
𝑟𝑜𝑡 𝐸⃗ = −
𝜕𝐵⃗
𝜕𝑡
(2)
𝑑𝑖𝑣 𝐵⃗ = 0 (3)
𝑑𝑖𝑣 𝐷⃗⃗ = 𝜌 (4)
where rot (or curl) is a vector operator that describes the rotation of a three-
dimensional vector field,
𝑗 is the current density vector,
𝜕𝐷⃗⃗ 𝜕𝑡⁄ is the time derivative of the electric displacement vector 𝐷⃗⃗ ,
𝜕𝐵⃗ 𝜕𝑡⁄ is the time derivative of the magnetic induction vector 𝐵⃗ ,
𝑑𝑖𝑣 𝐷⃗⃗ is the so called source density and 𝜌 is the charge density.
Equation (1) is Ampere's law. It basically states that any change of the electric field
over time causes a magnetic field. Equation (2) is Faraday's law of induction, which
describes that any change of the magnetic field over time causes an electric field. The
other two equations relate to Gauss's law. (3) states that any magnetic field is solenoid
and (4) defines that the displacement current through a surface is equal to the
encapsulated charge.
From Maxwell's equations and the so called material equations
𝐷⃗⃗ = 𝜀 ∙ 𝐸⃗ 𝑗 = 𝜎 ∙ 𝐸⃗ 𝑎𝑛𝑑 𝐵⃗ = 𝜇 ∙ 𝐻⃗⃗
it is possible to derive a second order differential equation known as the telegraph
equation:
𝑟𝑜𝑡 𝑟𝑜𝑡 𝐹 + 𝜎𝜇
𝜕𝐹
𝜕𝑡
+ 𝜇𝜀
𝜕2
𝐹
𝜕𝑡2
= 0
where 𝜀 is the permittivity of a dielectric medium,
𝜎 is the electrical conductivity of a material,
𝜇 is the permeability of a material and

𝐹 is a placeholder which stands for either 𝐸⃗ or 𝐻⃗⃗ .
If one assumes that the conductivity of the medium in which a wave propagates is very
small (𝜎 → 0) and if one limits all signals to sinusoidal signals with an angular
frequency ω, the so called wave equation can be derived:
𝑟𝑜𝑡 𝑟𝑜𝑡 𝐹 − 𝜔2
𝜇𝜀𝐹 = 0
The simplest solution to this equation is known as a plane wave propagating in loss-
free homogenous space. For this wave, the following condition applies:
ı The vectors of the electric and magnetic field strength are perpendicular to each
other and mutually also to the direction of propagation (see Figure 4).
Consequently the electric and magnetic field strengths are connected to each other via
the so called impedance of free space:
𝐸 = 𝑍0 ∙ 𝐻 𝑤𝑖𝑡ℎ 𝑍0 = 120𝜋 Ω ≈ 377 Ω
E
H
Figure 4: Plane wave description
There are two preconditions for the existence of plane waves:
1. Far field conditions must be reached.
2. Free space conditions are present.
Only if both of them are met, the assumption that the electric field strength drops with
the factor 1/r over the distance r, can be made.
2.2 Wavelength
In linear media, any wave pattern can be described in terms of the independent
propagation of sinusoidal components. The wavelength of a sinusoidal waveform
travelling at constant speed is given by:
𝜆 =
𝑣
𝑓
𝑤𝑖𝑡ℎ 𝑣 = 𝑐0 ≈ 300 000
𝑘𝑚
𝑠
The wavelength is a measure of the distance between repetitions of a shape feature
such as peaks, troughs or zero-crossings.

2.3 Far Field Conditions
The distance from an antenna, where far field conditions are met, depends on the
dimensions of the antenna in respect to the wave length. For smaller antennas (e.g. a
half-wave dipole) the wave fronts radiated from the antenna become almost parallel at
much closer distance compared to electrically large antennas. A good approximation
for small antennas is that far field conditions are reached at:
𝑟 ≈ 2 ∙ 𝜆
For larger antennas (i.e. reflector antennas or array antennas) where the dimensions of
the antenna (L) are significantly larger compared to the wave length (L >> λ), the
following approximation for the far field distance applies:
𝑟 ≈
2𝐿2
𝜆
2.4 Free Space Conditions
Free space conditions require a direct line of sight between the two antennas involved.
Consequently no obstacles must reach into the path between them. Furthermore in
order to avoid the majority of effects caused by superposition of direct and reflected
signals, it is necessary that the first Fresnel ellipsoid (see Figure 5) is completely free
of obstacles:
Figure 5: First Fresnel ellipsoid
The first Fresnel ellipsoid is defined as a rotational ellipsoid with the two antennas at its
focal points. Within this ellipsoid the phase difference between two potential paths is
less than half a wavelength.
The radius (b) at the center of the ellipsoid can be calculated based on the formula:
𝑏 = 17.32√
𝑑
4𝑓
where b is the radius in m,
d is the distance between RX and TX in km,
and f is the frequency in GHz.
b
d

2.5 Polarization
The polarization of an antenna is determined by the direction of the electric field 𝐸⃗ . A
distinction must be made between the following types of polarizations:
ı Linear polarization: The 𝐸⃗ field vector changes in magnitude only.
ı Circular polarization: The magnitude of the 𝐸⃗ field vector is constant, but the
direction changes and rotates around the direction of propagation.
ı Elliptical polarization: The magnitude and the direction of the 𝐸⃗ field vector
changes and its peak position can be described by an elliptical equation.
Figure 6: Linear (vertical) polarization and right-hand circular polarization
Polarization mismatch occurs when the polarization of the receiving antenna is not
equal to the polarization of the incoming wave. Figure 7 gives an overview of the
polarization mismatch and the related loss imposed on the received signal. Note that V
means vertical, H horizontal, LHC left-hand circular and RHC right-hand circular
polarization.
Figure 7: Expected loss due to polarization mismatch
The losses that occur when trying to receive a linearly polarized signal with a circularly
polarized antenna amounts to 3 dB (same vice versa) - this can usually be tolerated.
Most critical is the case where the orthogonal antenna polarization is used, because
the attenuation increases beyond all limits theoretically. In practice, most antennas
have a limited polarization decoupling, so that the loss in reality will never reach
infinity.

General Antenna Characteristics
3 General Antenna Characteristics
As mentioned in the introduction, antennas have the function of converting one type of
wave into another. The direction of energy conversion is of no importance for the
operational principle or for the ease of understanding. The transmitting and the
receiving antenna can therefore be looked at in the same way (reciprocity principle),
and the parameters described in this chapter are equally valid for transmission and
reception. This even applies if the parameters are in some cases measurable only for
transmission or for reception or if their specification appears to be meaningful only for
one of these modes. Active antennas are the only exception: being pure receiving
antennas, they are non-reciprocal. Apart from that, a clear distinction between
transmitting and receiving antennas must be made if, for example, the maximum
transmitter power is to be taken into account. However, this is irrelevant to the
characteristics and the principle of operation.
3.1 Radiation Density
The simplest imaginable antenna is the isotropic radiator, which does not exist in
practice, but makes an excellent theoretical model. An isotropic radiator, which is a
dimensionless point in space, generates waves with spherical wave fronts that are
radiated uniformly in all directions. When the ideally matched transmitter power PS is
applied to it, then at distance r this gives rise to the radiation density:
𝑆 =
𝑃𝑆
4𝜋𝑟2
Figure 8: The isotropic radiator in homogenous space
The radiation density (often also known as the power density) can also be determined
in the far field as the product of electric and magnetic field strength in accordance with
𝑆 = 𝐸 ∙ 𝐻
S
PS
r

3.2 Radiation Pattern
The three-dimensional radiation behavior of antennas is described by their radiation
pattern (normally in the far field). As explained before, only an isotropic radiator would
exhibit the same radiation in every spatial direction, but this radiator cannot be
implemented for any specified polarization and is therefore mainly suitable as a model
and comparison standard. Dipoles and monopoles possess directivity. An electrically
short dipole in free space has a three-dimensional radiation pattern shown in Figure 9
with nulls in the direction of the antenna's axis.
Figure 9: Three-dimensional radiation of a dipole antenna
While the radiation pattern is actually three-dimensional, it is common however to
describe this behavior with two planar patterns, also called the principal plane patterns.
They can be obtained from the spatial radiation characteristics by looking at a cut-
plane - usually through the origin and the maximum of radiation. Spherical coordinates
as shown in Figure 10 are commonly used to describe a location in the three-
dimensional space.
The horizontal pattern (see Figure 11) shows the field strength as a function of the
azimuth angle ϕ with a fixed ϑ (usually ϑ = 90°).
The vertical pattern (see Figure 12) shows the field strength as a function of ϑ for a
fixed ϕ (usually ϕ = +/- 90 ° or 0°/180°)
Figure 10: Explanation of spherical coordinates

Characterizing an antenna's radiation behavior with the two principle plane patterns is
adequate for antennas with a well-behaved pattern - meaning that not much
information is lost when just the two planes are shown.
In literature or datasheets the terms azimuth pattern or elevation pattern are also
frequently found. The term azimuth describes the reference to "the horizon" or "the
horizontal" whereas the term elevation describes the reference to "the vertical". If
these two terms are used to describe antenna radiation patterns, they assume that
during the measurement the antenna is mounted in the orientation in which it will be
normally used.
Another common designation for the two principal plane patterns are E-plane pattern
and H-plane pattern. They depend directly on the orientation of the antenna's
radiators. Consequently they are not depending on the mounting orientation of the
antenna.
Please note:
H-plane must not be mixed up with horizontal plane!
Figure 11: Horizontal pattern of a dipole antenna
Figure 12: Vertical pattern of a dipole antenna

Usually antenna patterns are shown as plots in polar coordinates. This has the
advantage that the radiation into all possible directions can quickly be visualized. In
some occasions (i.e. for highly directive antennas) it can also be beneficial to plot the
radiation pattern in Cartesian coordinates - because this reveals more details of the
main beam and adjacent side lobes (see Figure 13).
Figure 13: Radiation pattern in Cartesian coordinates
From the radiation pattern the following additional parameters can be derived (see
Figure 14)
ı The side lobe suppression (or side lobe level) is a measure of the relation
between the main lobe and the highest side lobe.
ı The half-power beamwidth (HPBW) is the angle between the two points in the
main lobe of an antenna pattern that are down from the maximum by 3 dB. It is
usually defined for both principal plane patterns.
ı The front-to-back ratio specifies the level of radiation from the back of a
directional antenna. It is the ratio of the peak gain in forward direction to the gain
in the reverse (180°) direction. It is usually expressed in dB.
Figure 14: Further parameters in the radiation pattern
Main beam
Side lobe
suppression
Nulls
Side lobes
Back
lobe
side
3dB
HPBW
Main lobe
Null
Side lobes

3.3 Directivity
The directivity factor D is defined as the ratio of the radiation intensity Fmax obtained
in the main direction of radiation to the radiation intensity Fi that would be generated by
a loss-free isotropic radiator with the same radiated power Pt. The radiation intensity
can be replaced by the power density represented by the Poynting vector as shown
below:
𝑆 = 𝐸⃗ × 𝐻⃗⃗
with 𝑆 perpendicular to 𝐸⃗ and 𝑆 and 𝐸⃗ perpendicular to 𝐻⃗⃗ in the far field.
The power density is measured at the same distance r from the antennas. The
following thus applies:
𝐷 =
𝐹𝑚𝑎𝑥
𝐹𝑖
𝑤ℎ𝑒𝑟𝑒 𝐹𝑖 =
𝑃𝑡
4𝜋
3.4 Gain
Corresponding to the directivity factor, the gain G is the ratio of the radiation intensity
Fmax obtained in the main direction of radiation to the radiation intensity Fi0, that would
be generated by a loss-free isotropic radiator with the same input power Pt0.
𝐺 =
𝐹𝑚𝑎𝑥
𝐹𝑖0
𝑤ℎ𝑒𝑟𝑒 𝐹𝑖0 =
𝑃𝑡0
4𝜋
In contrast to the directivity factor, the antenna efficiency η is taken into account in
the above equation since the following applies:
𝐷 = 𝜂 ∙ 𝐺
For an antenna with efficiency η = 100%, this means that gain and directivity are equal.
In practice this is hardly the case, so the gain, which can be easily determined during
measurements, is the parameter which is more frequently used.
Gain and directivity are often expressed in logarithmic form:
𝑔 𝑑𝐵⁄ = 10 log 𝐺 𝑜𝑟 𝑑 𝑑𝐵⁄ = 10 log 𝐷
Contrary to common rules and standards, it is well established practice to indicate the
reference with an additional letter after dB:
ı dBi refers to the isotropic radiator
ı dBd refers to the half-wave dipole
For example the following conversion applies: 0 dBd ≈ 2.15 dBi.

3.5 Practical Gain
While the gain definition assumes ideal matching between the antenna and the
connected cable and receiver or transmitter, in practice this is rarely the case. So what
is measured in a non-ideally matched setup is called the practical gain of an antenna.
The gain can be determined from the practical gain with the following formula:
𝐺 = 𝐺 𝑝𝑟𝑎𝑐𝑡
1
1 − |𝑟|2
where the amount of mismatch is expressed by the magnitude of the reflection
coefficient r (see 3.9)
3.6 Effective Area
The effective area Aw of an antenna is a parameter specially defined for receiving
antennas. It is a measure for the maximum received power Pr that an antenna can pick
up from a plane wave of the power density S:
𝑃𝑟 𝑚𝑎𝑥 = 𝑆 ∙ 𝐴 𝑤
Although the effective area of an antenna can well be conceived as a real area
perpendicular to the direction of propagation of the incident wave, it is not necessarily
identical with the geometrical area Ag of the antenna. The relationship between the
effective and the geometrical areas is described by the aperture efficiency q
𝑞 =
𝐴 𝑤
𝐴 𝑔
The effective area of an antenna can be converted to the gain and vice versa by
means of the formula:
𝐴 𝑊 =
𝜆2
4𝜋
𝐺
3.7 Input Impedance
One of the most significant parameters of an antenna is its input impedance:
𝑍𝑖𝑛 = 𝑅𝑖𝑛 + 𝑗𝑋𝑖𝑛
This is the impedance present at the antenna feed point. Its real part Rin can be split up
into the radiation resistance RR and the loss resistance RL
𝑅𝑖𝑛 = 𝑅 𝑅 + 𝑅 𝐿
It should be noted however that the radiation resistance, being the quotient of the
radiated power and the square of the RMS value of the antenna current, is spatially
dependent. This applies also to the antenna current itself. Consequently, when
specifying the radiation resistance, its location on the antenna needs to be indicated.

Quite commonly the antenna feed point is specified, and equally often the current
maximum. The two points coincide for some, but by no means for all types of antenna.
The imaginary part Xin of the input impedance disappears if the antenna is operated at
resonance. Electrically very short linear antennas have capacitive impedance values
(Xin < 0), whereas electrically too long linear antennas can be recognized by their
inductive imaginary part (Xin > 0).
3.8 Nominal Impedance
The nominal impedance Zn is a mere reference quantity. It is commonly specified as
the characteristic impedance of the antenna cable, to which the antenna impedance
must be matched (as a rule Zn = 50 Ω).
3.9 Impedance Matching and VSWR
If the impedance of an antenna is not equal to the impedance of the cable and/or the
impedance of the transmitter, a certain discontinuity occurs.
The effect of this discontinuity is best described for the transmit case, where a part of
the power is reflected and consequently does not reach the antenna (see Figure 15.)
However the same will happen with the received power from the antenna that does not
fully reach the receiver due to mismatch caused by the same discontinuity.
Figure 15: Forward and reflected power due to mismatch
Discontinuity
Forward Power
Reflected power
Total power

The amount of reflected power can be calculated based on the equivalent circuit
diagram of a transmit antenna (see Figure 16).
Figure 16: Equivalent circuit diagram of a transmit antenna
For optimum performance, the impedance of the transmitter (ZS) must be matched to
the antenna input impedance Zin. According to the maximum power transfer theorem,
maximum power can be transferred only if the impedance of the transmitter is a
complex conjugate of the impedance of the antenna and vice versa. Thus the following
condition for matching applies:
𝑍𝑖𝑛 = 𝑍𝑆
∗
𝑤ℎ𝑒𝑟𝑒 𝑍𝑖𝑛 = 𝑅𝑖𝑛 + 𝑗𝑋𝑖𝑛 𝑎𝑛𝑑 𝑍𝑆 = 𝑅 𝑆 + 𝑗𝑋𝑆
If the condition for matching is not satisfied, then some power may be reflected back
and this leads to the creation of standing waves, which are characterized by a
parameter called Voltage Standing Wave Ratio (VSWR).
The VSWR is defined (as implicated by its name) as the ratio of the maximum and
minimum voltages on a transmission line. However it is also possible to calculate
VSWR from currents or power levels as the following formula shows:
𝑠 =
𝑉𝑚𝑎𝑥
𝑉 𝑚𝑖𝑛
=
𝐼 𝑚𝑎𝑥
𝐼 𝑚𝑖𝑛
=
|𝑉𝑓𝑜𝑟𝑤| + |𝑉𝑟𝑒𝑓𝑙|
|𝑉𝑓𝑜𝑟𝑤| − |𝑉𝑟𝑒𝑓𝑙|
=
√ 𝑃𝑓𝑜𝑟𝑤 + √ 𝑃𝑟𝑒𝑓𝑙
√ 𝑃𝑓𝑜𝑟𝑤 − √ 𝑃𝑟𝑒𝑓𝑙
Another parameter closely related to the VSWR is the reflection coefficient r. It is
defined as the ratio of the amplitude of the reflected wave Vrefl to the amplitude of the
incident wave Vforw :
𝑟 =
𝑉𝑟𝑒𝑓𝑙
𝑉𝑓𝑜𝑟𝑤
It is furthermore related to the VSWR by the following formula:
𝑠 =
1 + |𝑟|
1 − |𝑟|
RS XS
RR
RL
Xin
Zin
ZS

The return loss ar derives from the reflection coefficient as a logarithmic measure:
𝑎 𝑟 = −20 log|𝑟| = −20 log (
𝑉𝑟𝑒𝑓𝑙
𝑉𝑓𝑜𝑟𝑤
) = −10 log (
𝑃𝑟𝑒𝑓𝑙
𝑃𝑓𝑜𝑟𝑤
)
So there are in fact several physical parameters for describing the quality of
impedance matching; these can simply be converted from one to the other as required.
For easy conversion please refer to the table below:
VSWR r ar Reflected
power
1.002 0.001 60 dB
1.01 0.005 46 dB
1.1 0.05 26 dB 0.2 %
1.2 0.1 20 dB 0.8 %
1.5 0.2 14 dB 4 %
2.0 0.33 9.5 dB 11.1 %
3.0 0.5 6 dB 25 %
5.0 0.67 3.5 dB 44.4 %

3.10 Antenna Factor
The antenna factor (often also called transducer factor or conversion factor) is defined
as the ratio of electric field strength and the measured output voltage at its feed point.
𝐾 =
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑓𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑂𝑢𝑡𝑝𝑢𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑡 50 Ω
It is used in receivers in order to display the field strength surrounding the antenna
rather than the voltage level of the signal. Often it is more convenient to use the
antenna factor in logarithmic form:
𝑘 = 20 log 𝐾
Typical antenna factor values are usually specified in the antenna's documentation -
either in a table or graphical format. If an antenna was calibrated the exact antenna
factor values are listed in the antenna calibration document. The unit of the logarithmic
form of the antenna factor is dB/m.
When the antenna factor is known, the field strength E surrounding the antenna can be
easily calculated with the formula:
𝐸
𝑑𝐵µ𝑉/𝑚⁄ =
𝑈 𝑅𝑋
𝑑𝐵µ𝑉⁄ + 𝑘
𝑑𝐵/𝑚⁄
where URX is the receiver voltage level measured at its 50 Ω input.
For the sake of completeness it should be mentioned that to obtain a precise field
strength measurement, the cable loss between the test antenna and the receiver has
to be included:
𝐸
𝑑𝐵µ𝑉/𝑚⁄ =
𝑈 𝑅𝑋
𝑑𝐵µ𝑉⁄ + 𝑘
𝑑𝐵/𝑚⁄ + 𝑐𝑎𝑏𝑙𝑒 𝑙𝑜𝑠𝑠
𝑑𝐵⁄
While for field strength measurements the antenna factor is commonly used as the
characterizing value of the antenna, the predominant terms in general antenna
engineering are gain and directivity factor. Therefore, it often proves useful to know the
relationship:
𝐾 =
9.73
𝜆 ∙ √𝐺
in order to convert between antenna factor and practical gain, which is also given in
logarithmic form as:
𝑘 = −29.8 𝑑𝐵 + 20 log (
𝑓
𝑀𝐻𝑧
) − 𝑔

3.11 Bandwidth of an Antenna
The bandwidth of an antenna is defined as the range of usable frequencies within
which the performance of the antenna with respect to some characteristics conforms to
a specified standard.
The parameter most commonly taken into account here is the impedance match (i.e.
VSWR < 1.5) - but other parameters like gain or side lobe suppression may serve as a
bandwidth criteria here, too.
For broadband antennas, the ratio of the highest and lowest usable frequencies is
determined. A ratio of 2:1 is called an octave - a ratio of 10:1 is a decade.
𝐵𝑊 =
𝑓𝐻
𝑓𝐿
where fH is the highest usable frequency and fL is the lowest usable frequency.
An antenna is said to be broadband when BW is equal or greater than 2.
There exists also a different definition of bandwidth which is valid only for narrowband
antennas:
𝐵𝑊 (𝑖𝑛 %) = (
𝑓𝐻 − 𝑓𝐿
𝑓𝐶
) ∙ 100
where fC is the center frequency.
Values here can range from 0 to 200% - in practice this definition is only used up to
about 100%.

Basic Characteristics of Selected Antennas
4 Basic Characteristics of Selected Antennas
4.1 Half-wave Dipole
Dipole antennas are the most fundamental form of antenna that can be implemented.
The best known example is the tuned (half-wave) dipole.
Figure 17: Half-wave dipole
Its length is somewhat less than half a wavelength and its input impedance at
resonance is between 50 Ω and 70 Ω depending on its length/diameter ratio, so that a
feed cable with a common nominal impedance can easily be connected. The current
distribution on the dipole (shown by the red line in Figure 17) can be assumed to be
sinusoidal in good approximation. Its three-dimensional radiation pattern has already
been shown in 3.2 (see Figure 9). The radiation pattern in the E-plane, which is a
reference plane along which the dipole axis lies, looks like the number 8 (see Figure
12), while the radiation pattern in planes perpendicular to its axis (H-plane) is uniform.
The name "half-wave dipole" indicates that this form of antenna can be constructed
and used for one frequency only. However, experience shows that dipoles can actually
be used for receiving purposes for a wider frequency range. It would be possible to
conclude from this that half-wave dipoles could be used at least as test antennas, even
far from their resonance frequency. When used for broadband purposes, however,
conventional dipoles experience the following significant problems in practice:
ı The antenna input impedance strongly depends on the antenna's length to
wavelength ratio (see Figure 18), so that when operated far from the half-wave
resonance frequency very significant matching problems occur. This is particularly
true for a thin dipole, where the ratio of length (l) to diameter (d) is large. If this
ratio is decreased, the amount of mismatch will be reduced. Some possible
shapes for such thick dipoles are shown in Figure 19.
When matching the impedance of the dipole to the impedance of the feed cable, it
also needs to be taken into account that a balanced antenna is usually connected
to an unbalanced (or coaxial) cable by means of a balun. Balun is a contrived
word composed of "balanced" and "unbalanced". It is a device that helps effecting
the before mentioned transition. Without a balun, skin currents form on the outer
conductor of the coaxial cable which can cause strong electromagnetic
interference or significantly alter the radiation pattern of the antenna.
≈λ/2

Figure 18: Input impedance of a dipole with different l/d ratios
In order to save materials and particularly weight, broadband dipoles are often
designed in the form of a cage. Another commonly used test antenna is the
biconical antenna shown in the very right.
Figure 19: Possible shapes of broadband dipoles
ı Above the full-wave resonance, even the radiation pattern changes as a function
of the antenna length to wavelength ratio to such an extent (see Figure 20) that it
is no longer possible to clearly determine the main direction of radiation or the
gain, for example. This effect of "splitting up the radiation pattern" is caused by the
non-ideal current distribution on the dipole when the length to wavelength ratio
becomes too large. One option to avoid this is to design the antenna rods to
function as telescopic elements, so that the antenna length can be varied to match
the operating frequency. The dipole can then be operated at resonance at every
frequency to which it is set. However this is very often not possible in practice, as
the length must be changed whenever the frequency is changed.
d
l
l/λ
Half-wave resonance
l/d≈1000
d
l
Half-wave resonance
l/λ
l/d≈60

Figure 20: Dipole radiation pattern depending on length/wavelength ratio
Another more practical solution is to alter the current distribution on the antenna
(for instance by reactive elements, resonant circuits or ferrite rings) in such a way
that at higher frequencies only part of the antenna is activated. This keeps the
ratio of wavelength to antenna length almost constant even though the frequency
may vary. Electrically this solution is more or less the same as the telescopic
antenna described before, but with no need for the user to go to any effort or
expense.
4.2 Monopole Antenna
The operating principle of rod antennas (or monopoles) is based on the fact that the
current distribution on an antenna structure that is only a quarter wavelength long is
identical to that on a half-wave dipole (see Figure 17) if the antenna element "missing"
from the dipole is replaced by a highly conducting surface. As a result of this reflection
principle (see Figure 21), vertical quarter-wave antennas on conducting ground have
basically the same radiation pattern as half-wave dipole antennas. There is of course
no radiation into the shadowed half of the space. The input impedance is half that of a
dipole, exhibiting values between approx. 30 Ω and 40 Ω.
Figure 21: From a dipole to a monopole antenna
This is the
wanted
direction of
radiation

The conducting surface on which the monopole is erected plays an important part in
enabling the reflection principle to take effect. Even on reasonably conducting ground
(such as a field of wet grass) and particularly on poorly conducting ground (dry sand) it
is usual and helpful to put out a ground net of wires (commonly also called radials).
Figure 22 shows the influence of ground conductivity on the vertical pattern of a
monopole antenna:
Figure 22: Vertical pattern of a monopole for perfectly conducting ground (A) and poor ground (B)
A special form of a monopole antenna is the so called groundplane antenna (see
Figure 23). It is characterized by several wires or rods (known as radials) which are
arranged in a radial configuration from the feed point under a certain angle. Typically
an angle of approx. 135° to the quarter wave monopole is used in order to increase the
feed point resistance to a value of approx. 50 Ω which can easily be matched to
commonly used coaxial cables.
Figure 23: Groundplane Antenna
Groundplane antennas are used as vertically polarized omnidirectional antennas even
in the VHF/UHF frequency range.
≈135°

4.3 Directional Antennas
It has already been mentioned that ideal omnidirectional antennas cannot be produced
in reality. Nonetheless only antennas that focus their radiated power in a particular
spatial direction can properly be called directional antennas. At an equivalent transmit
power, they significantly improve the signal-to-noise ratio, but must be aligned on the
distant station so that in many cases a rotation facility has to be used. For directional
antennas the parameters gain, directivity and all values associated with the radiation
pattern, like front-to-back ratio, side-lobe suppression or half-power beamwidth as
already discussed in 3.2 give an overview about how much the radiated energy is
focused into a certain direction.
The simplest form of a directional antenna is a setup of two monopole antennas at a
predefined distance, which are fed with different phase (see Figure 24).
Figure 24: Principle of a directional antenna
In the example a distance of a quarter wavelength and a phase difference of 90° have
been chosen, resulting in a cardioid shaped radiation pattern (see Figure 25) when the
far field strengths generated by the two individual antennas are added.
Figure 25: Cardioid shaped radiation pattern
90°

Even though this configuration does not produce strongly focused radiation, it however
exhibits a sharply defined null towards the backside which can effectively be used to
suppress interfering signals.
By superimposing the diagrams obtained by combining two or several radiators
arranged at defined distances and with defined phase shifts, directional patterns can
be generated whose directivity is limited mainly by the available space to setup the
number of required radiators.
Instead of feeding the radiators via cables as shown in Figure 24, the principle of
radiation coupling is mostly applied in practice, with only one radiator being fed from
the cable and the remaining elements activated by this radiator. Yagi-Uda antennas,
which are commonly used for the reception of TV and VHF sound broadcast signals,
have typically between 4 and 30 elements and yield gain values of 10 dB and more.
The possibility of changing the direction of the main beam of a highly directive antenna
by purely electronic means is utilized to an increasing extent also with antenna arrays
for very high frequencies (e.g. for satellite radio services). The antennas used are
referred to as planar antennas and mostly consist of a dipole curtain which, in
contrast to curtain antennas, is installed in front of a conductive plane. This array can
also be implemented by etching the radiators as tracks into a printed circuit board
(microstrip antenna). In this way, even large arrays of antennas can be implemented
for the microwave frequency range with high precision and efficiency.
4.4 Log-Periodic Dipole Antenna
A special type of directional antenna is the log-periodic dipole antenna (LPDA), where
beam shaping is performed by means of several driven elements. The LPDA is made
up of a number of parallel dipoles of increasing lengths and spacing (see Figure 26).
Each dipole is fed out of phase to the element on either side by a common feed line.
The angle α formed by the lines joining the dipole ends and by the longitudinal axis of
the antenna remains constant, as well as the graduation factor 𝜏 which is equal to the
ratio of the lengths of neighboring elements and their spacing:
𝜏 =
𝑙 𝑛+1
𝑙 𝑛
=
𝑑 𝑛+1
𝑑 𝑛
= 𝑐𝑜𝑛𝑠𝑡

Figure 26: Log-periodic dipole antenna
This antenna type is characterized by its active and passive regions. The antenna is
fed starting at the front (i.e. with the shortest dipole). The electromagnetic wave passes
along the feed line and all dipoles that are markedly shorter than half a wavelength will
not contribute to the radiation. The dipoles in the order of half a wavelength are
brought into resonance and form the active region, which radiates the electromagnetic
wave back into the direction of the shorter dipoles. This means that the longer dipoles
located behind this active region are not reached by the electromagnetic wave at all.
The active region usually comprises of 3 to 5 dipoles and its location obviously varies
with frequency. The lengths of the shortest and longest dipoles of an LPDA determine
the maximum and minimum frequencies at which it can be used.
Due to the fact that at a certain frequency only some of the dipoles contribute to the
radiation, the directivity (and therefore also the gain) that can be achieved with LPDAs
is relatively small in relation to the overall size of the antenna. However, the advantage
of the LPDA is its large bandwidth which is - in theory - only limited by physical
constraints.
The radiation pattern, of an LPDA is almost constant over the entire operating
frequency range. In the H-plane it exhibits a half-power beamwidth of approx. 120°,
while the E-plane pattern is typically 60° to 80° wide. The beamwidth in the H-plane
can be reduced to values of approx. 65° by stacking two LPDAs in V-shape. (see
Figure 27)
Active region
Direction of radiation
l1
l2
l3
l4
d1d2d3
α

Figure 27: Example of a V-stacked LPDA
V-stacked LPDA antennas have E- and H-plane patterns with very similar half power
beamwidths (see Figure 28). Additionally they feature approx. 1.5 dB more gain
compared to a normal LPDA.
Figure 28: Radiation pattern of a V-stacked LPDA - E-plane (black), H-plane (blue)

4.5 Active Antennas
Active antennas represent another possible way of implementing compact broadband
antennas. They are based on the idea that drastically shortening the dipole length of
an antenna will result in a corresponding reduction in output levels for both the useful
signal PS and the noise PN. As a consequence, the signal-to-noise ratio (S/N), which is
the sole indicator of reception quality, stays constant within fairly wide limits as can be
seen in Figure 29.
Figure 29: Active antenna basic principle
The S/N will get affected only at a point where the level of the external noise PN falls
below the receiver noise PE which is influenced only by the technical parameters of the
receiver itself.
In chapter 3 (see Figure 18) it was already shown that shortening the radiator is
associated with extreme changes in the impedance. For active rod or dipole antennas
this is compensated by feeding the signal voltage on the terminals of the antenna
directly to a very high-impedance active component (usually a field effect transistor)
which acts as an impedance transformer and also commonly amplifies at the same
time. Active antennas are therefore by definition antennas in which an active element
is attached directly to the electrically short radiators (i.e. of a dipole as shown in Figure
30), and are not to be confused with systems in which the output signal of a passive
antenna is looped through a preamplifier, for example.
Active antennas can obviously be used for reception only.
Figure 30: Active dipole antenna in principle
S / N
P
PS
PN
PE
P
PS
PN
PE
Antenna length
S/N
50 Ω

An advantage of using active antennas is the fact that usually their radiation patterns
are no longer a function of frequency because they utilize elements of electrically short
length. By carefully tuning the active circuitry to the antenna geometry and by using
other measures, it is also possible to ensure that the antenna factor is largely
independent of frequency, so that field strength measurements can be carried out very
easily.
Active antennas are mainly but not exclusively used for lower frequencies (up to about
200 MHz) at which the noise floor in the atmosphere is very high. Due to their extreme
broadband characteristics, active antennas are being increasingly used also in the
higher frequency ranges.
One of their biggest advantages is the reduced size requirement. For example an
active rod antenna that covers HF and also part of the LF frequency range can be built
with a radiator as short as approx. 1m, while a passive antenna for a comparable
frequency range easily measures ten times this value.
When an active antenna is designed, the engineer needs to cope with two slightly
contradictory aims:
ı The active antenna should achieve maximum sensitivity in respect to the expected
external noise. Consequently the designer will select the active devices for
optimum noise figure and noise match.
ı The active antenna should have good protection against interfering strong signals
- no matter if they are generated internally or externally of the active antenna
circuitry. Therefore the designer will select active devices with high intercept point
values (IP2 and IP3).
Unfortunately it is not possible to reach both aims simultaneously and the margin
between them is called the dynamic range. Active antenna will always have a limited
dynamic range, which may render their usage difficult in close vicinity of strong
transmitters or at locations where high field strength values exist due to other reasons.
In summary, active antennas have the following advantages and disadvantages
Advantage Disadvantage
Smaller than comparable passive
antennas
Can't be used for transmitting
Wider bandwidth than comparable
passive antennas
More susceptible to interference if
incorrectly installed
Generally frequency independent
radiation pattern
Have less dynamic range
Can be installed relatively close to
each other
Can't be installed in an interfered
environment
Highly suitable as broadband test
antennas
Must be carefully balanced

Care must be taken, when the gain of an active antenna is specified. There are two
definitions to know in this context:
The electronic gain GT is the ratio of the received power into the nominal resistance
and the maximum received power which can be extracted from the field with an
antenna of equal directional characteristics.
The practical gain Gpract is the ratio of received power into the nominal resistance Pr
and the received power of a loss-free omnidirectional reference antenna (isotropic
radiator) Pri.
𝐺 𝑝𝑟𝑎𝑐𝑡 =
𝑃 𝑟
𝑃 𝑟𝑖
= 𝐷 ∙ 𝐺 𝑇
Consequently, the gain alone does not allow drawing any conclusions about the
radiation pattern of the active antenna or its field strength sensitivity.
The field strength sensitivity values are usually specified in the documentation of the
antenna. In order to have comparable results the bandwidth and the achieved signal-
to-noise ratio (S/N) must always be given in conjunction with the minimum field
strength values that can be detected (see Figure 31).
Figure 31: Field strength sensitivity specification of an active antenna

Appendix
5 Appendix
5.1 References
References and recommended further reading
Author Title Publisher
Balanis Antenna Theory John Wiley & Sons
Beckmann Die Ausbreitung der elektromagnetischen Wellen
(The propagation of Electromagnetic Waves)
Beckmann
Braun Planung und Berechnung von
Kurzwellenverbindungen
(The Planning and Calculation of Shortwave
Links)
Siemens
Chatterjee Antenna Theory and Practice John Wiley & Sons
Collin Antennas and Radiowave Propagation McGraw-Hill
Davies Ionospheric Radio Peregrinus
Dombrowski Antennen
(Antennas)
Porta München
Technik Berlin
Grosskopf Wellenausbreitung (2 volumes)
(Wave Propagation)
Hochschultaschenbücher
Heilmann Antennen (3 volumes)
(Antennas)
Hochschultaschenbücher
Hock/Pauli Antennentechnik
(Antenna Engineering)
Expert
Jasik Antennas McGraw-Hill
Kraus Antennas McGraw-Hill
Lee Mobile Communications Design Fundamentals Howard W. Sams
Lee Mobile Cellular Telecommunication Systems McGraw-Hill
Maslin HF Communications Pitman
Meinke/Gundlach Taschenbuch der Hochfrequenztechnik
(Manual of High Frequency Engineering)
Springer
Reithofer Praxis der Mikrowellenantennen
(Microwave Antenna Practice)
UKW-Berichte
Rohner Antenna Basics Rohde & Schwarz internal
Rothammel Antennenbuch
(The Antenna Book)
Franckh-Kosmos
Spindler Das große Antennenbuch
(The Big Book of Antennas)
Franzis
Stirner Antennen (3 volumes)
(Antennas)
Hüthig
Wiesner Fernschreiben und Datenübertragung auf
Kurzwellen
(Shortwave Telephony and Data Transmission)
Siemens
Zuhrt Elektromagnetische Strahlungsfelder
(Electromagnetic Radiation Fields)
Springer

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