Antennas: from Theory to Practice
5. Popular Antennas
Yi HUANG
Department of Electrical Engineering & Electronics
The University of Liverpool
Liverpool L69 3GJ
Email: Yi.Huang@liv.ac.uk
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Objectives of this Chapter
To examine and analyse some of the most
popular antennas using relevant antenna
theories, to see why they have become
popular, what their major features and
properties (including advantages and
disadvantages) are, and how they should
be designed.
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Classification of Antennas
Wire-Type Antennas
Dipoles
Monopoles
Biconical antennas
Loop antennas
Helical antennas
Linearly polarised antennas
Element antennas
Narrow-band
Transmitting
Aperture-Type Antennas
Horn and open waveguide
Reflector antennas
Slot antennas
Microstrip antennas
Circularly polarised antennas
Antenna array
Broad-band
Receiving
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5.1
Wire Type Antennas
Dipole Antennas
Evolution of a dipole of total length 2l and diameter d
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Current distribution of dipoles
Current distribution along an open transmission line is:
Thus the current distribution on the dipole is
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Radiation pattern of dipoles
In the far field:
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Input impedance of dipoles
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Electrically short dipoles
• When the dipole length is much shorter than a
wavelength (< l/10), it can be called an electrically short
dipole
• The input impedance can be approximated as
• Radiation pattern is
E() = sin
• The directivity is
D = 1.5 (1.76dBi)
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Half-wavelength dipole
• The most popular dipole
Radiation pattern:
E() = cos[(/2)cos ]/sin
Radiation resistance: 73 
Directivity:
1.64 (2.15 dBi)
The input impedance is not sensitive to the radius
and is about 73 Ω which is well matched with a
standard transmission line of characteristic
impedance 75 Ω or 50 Ω (with a VSWR < 2).
– Its size and radiation pattern are suitable for many
applications
–
–
–
–
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Example 5.1
A dipole of the length 2l = 3 cm and diameter d = 2 mm is
made of copper wire (s = 5.7  107 S/m) for mobile
communications. If the operational frequency is 1 GHz,
a). obtain its radiation pattern and directivity;
b). calculate its input impedance, radiation resistance and
radiation efficiency;
c). if this antenna is also used as a field probe at 100 MHz
for EMC applications, find its radiation efficiency again,
and express it in dB.
Solution on pages 135 - 137
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Some popular forms of dipole antennas
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Monopole Antennas

l
• Half of a dipole antenna mounted above
the earth or a ground plane
• Normally one-quarter wavelength long
– almost the same feature as a dipole,
except the 37 radiation resistance, higher gain, a
shorter length, and easier to feed!
• Based on the Image Theory
Ground
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Effects of the ground plane
Its size and material property of can change the radiation
pattern (hence the directivity) and input impedance.
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An example
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Some popular forms of monopole antennas
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Duality Principle
Duality means the state of combing two different things
which are closely linked. In antennas, the duality theory
means that it is possible to write the fields of one
antenna from the field expressions of the other antenna
by interchanging parameters:
System 1
System 2
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Loop Antennas
• For a short dipole
• Thus for a small loop
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• Directivity of a loop
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• Current distribution of a resonant loop
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• Radiation pattern of a one wavelength loop – this is
very different from that of a short loop!
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Radiation patterns of loops with various circumferences
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• Input impedance of loops
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Helical Antennas
It may be viewed as a derivative of the dipole or monopole,
but it can also be considered a derivative of a loop.
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• Normal mode Helix
– It may be treated as the superposition of n elements,
each consisting of a small loop of diameter D and a
short dipole of length s, thus the far fields are
– They are orthogonal and 90 degrees out of phase;
– The combination of them gives a circularly or
elliptically polarised wave.
– The axial ratio:
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– When the circumference is equal to
the axial ratio becomes unity and the radiation is
circularly polarised.
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• Axial Mode Helix
– The axial (end-fire) mode occurs when the
circumference of the helix is comparable with the
wavelength (C = D ≈ l) and the total length is much
greater than the wavelength.
– This has made the helix an extremely popular
circularly-polarised broadband antenna at the VHF
and UHF band frequencies
– The recommended parameters for an optimum
design to achieve circular polarisation are:
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– The normalised radiation pattern:
Half power beamwidth:
1st null beamwidth:
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– The directivity:
– The axial ratio
– Radiation resistance
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Example 5.2
Design a circularly polarised helix antenna of an endfire radiation pattern with a directivity of 13 dBi. Find
out its radiation resistance, HPBW, AR and
radiation pattern.
Solution on pages 150 - 152
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Radiation patterns
Which is better?
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Yagi-Uda Antennas
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• The driven element (feeder) is the very heart of the antenna. It
determines the polarisation and centre frequency. For a
dipole, the recommended length is about 0.47l to ensuring a
good input impedance to a 50 Ω feed line.
• The reflector is longer than the feeder to force the radiated
energy towards the front. The optimum spacing between the
reflector and the feeder is between 0.15 to 0.25 wavelengths.
• The directors are usually 10 to 20% shorter than the feeder
and appear to direct the radiation towards the front. The
director to director spacing is typically 0.25 to 0.35
wavelengths,
• The number of directors determines the maximum achievable
directivity and gain.
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Log-periodic Antennas
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– The antenna is divided into the so called active
region and inactive regions.
– The role of a specific dipole element is linked to the
operating frequency: if its length, L, is around half of
the wavelength, it is an active dipole and within the
active region; Otherwise it is in an inactive region and
acts as a director or reflector as in Yagi-Uda antenna
– The driven element shifts with the frequency – this is
why this antenna can offer a much wider bandwidth
than the Yagi-Uda. A travelling wave can also be
formed in the antenna.
– The highest frequency is basically determined by the
shortest dipole length while the lowest frequency is
determined by the longest dipole length (L1).
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Antenna design
• This seems to have too many variables. In fact, there
are only three independent variables for log-periodic
antenna design.
the scaling factor:
the spacing factor:
the apex angle:
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In practice, the most likely scenario is that the frequency
range is given from fmin to fmax, the following equations
may be employed for design
Another parameter (such as the directivity or the length of
the antenna) is required to produce an optimised design.
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Example 5.3
Design a log-periodic dipole antenna to cover all UHF TV
channels, which is from 470 MHz for channel 14 to 890
MHz for channel 83. Each channel has a bandwidth of 6
MHz. The desired directivity is 8 dBi.
Solution on page 160
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5.2
Aperture-Type Antennas
• They are often
used for higher
frequency
applications
(> 1GHz) than
wire-type
antennas.
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Fourier Transform and Radiated Field
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How to link the aperture E field to the radiated field
Directivity:
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Near field and far field
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Example 5.4
An open waveguide aperture of dimensions a long x and b
along y located in the z = 0 plane. The field in the
aperture is TE10 mode and given by
Find
i). the radiated far field and plot the radiation pattern in both
the E and H planes;
ii). the directivity.
Solution on pages 166 - 168
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Horn Antennas
• Horn antennas are the simplest and one of the most widely
used microwave antennas – the antenna is nicely integrated
with the feed line (waveguide) and the performance can be
easily controlled.
• They are mainly used for standard antenna gain and field
measurements, feed element for reflector antennas, and
microwave communications.
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Pyramidal Horn Design
To make this horn, we must have
i.e.
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The directivity:
We can therefore obtain the design equation
This equation in A can be solved using numerical methods.
For the optimum design, use a first guess approximation
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Example 5.5
Design a standard gain horn with a directivity of 20 dBi
at 10 GHz. WR-90 waveguide will be used to feed the
horn.
Solution on pages 172 - 173
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Reflector Antennas
• Reflector antennas can offer much higher gains than
horn antennas and are easy to design and construct.
• The most widely used antennas for high frequency and
high gain applications in radio astronomy, radar,
microwave and millimetre wave communications, and
satellite tracking and communications.
• The most popular shape is the paraboloid – because of
its excellent ability to produce a pencil beam (high gain)
with low sidelobes and good cross-polarisation
characteristics
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Paraboloidal and Cassegrain reflector antennas
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Antenna design
• The reflector design problem consists primarily of
matching the feed antenna pattern to the reflector. The
usual goal is to have the feed pattern about 10 dB down
in the direction of the rim, that is the edge taper = (the
field at the edge)/(the field at the centre) ≈10 dB.
• Directivity:
• Half-power beamwidth
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Offset parabolic reflectors
It reduces aperture blockage while maintaining acceptable
structure rigidity
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Radiation patterns in E and H planes
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Slots Antennas
They are very low-profile and can be conformed to basically
any configuration, thus they have found many
applications, for example, on aircraft and missiles.
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Antenna
Equivalent circuit
Slot waveguide antenna array: widely used for radar
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Equivalence Principle: for field analysis
• The radiated field by the slot is the same as the field
radiated by its equivalent surface electric current and
magnetic current which were given by
where E and H are the electric and magnetic fields within the
slot, and n̂ is the unit vector normal to the slot surface S
For a half-wavelength slot, its equivalent electric surface current JS
= ˆn × H = 0, the remaining source at the slot is its equivalent
magnetic current MS = −ˆn × E (it would be 2MS if the conducting
ground plane were removed using the imaging theory).
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Babinet’s Principle
• The field at any point behind a plane having a screen, if
added to the field at the same point when the
complementary screen is substituted, is equal to the
field at the point when no screen is present.
• Apply this to antennas:
Since the impedance for a half-wavelength dipole is about 73
ohms, the corresponding slot has an impedance of
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Self-complementary antennas – frequency independent
This type of antenna has a constant
impedance of
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Microstrip/Patch Antennas
• Ease of construction and integration, relatively low cost,
compact low profile configuration and good flexibility
• Typical applications for 1 - 20 GHz
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Operational principles
• To be a resonant antenna, the length L should be
around half of the wavelength. In this case, the antenna
can be considered as a l/2 transmission line resonant
cavity with two open ends where the fringing fields from
the patch to the ground are exposed to the upper half
space (z > 0) and are responsible for the radiation.
• This radiation mechanism is the same as the slot line,
thus there are two radiating slots on a patch antenna.
• As a resonant cavity, there are many possible modes
(as waveguides), thus a patch antenna is multi-mode
and may have many resonant frequencies.
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Radiation pattern
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Main properties
• Directivity
• Input impedance
• Bandwidth for VSWR < 2
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Antenna design
Optimised width:
Resonant freq.:
Length:
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Example 5.7
RT/Duroid 5880 substrate ( and d = 1.588 mm) is to be
used to make a resonant rectangular patch antenna of
linear polarisation;
a). Design such an antenna to work at 2.45 GHz for
Bluetooth applications;
b). Estimate its directivity;
c). If it is to be connected to a 50 ohms microstrip using the
same PCB board, design the feed to this antenna;
d). Find the fractional bandwidth for VSWR < 2.
Solution on pages 189 - 191
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5.3
Antenna Arrays
• Motivations: to achieve desired high gain or radiation
pattern, and the ability to provide an electrically
scanned beam.
• It consists of more than one antenna element and
these radiating elements are strategically placed in
space to form an array with desired characteristics
which are achieved by varying the feed (amplitude
and phase) and relative position of each radiating
element;
• The main drawbacks are the complexity of the
feeding network required and the bandwidth
limitation (mainly due to the feeding network)
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A typical antenna array of N elements
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Pattern Multiplication Principle
Since the total radiated field for an array is the summation of
the fields from each element
where An is the amplitude, n is the relative phase, Ee is the
radiated field of the antenna element, and AF is called array
factor.
Thus the radiation pattern of an array is the product of the
pattern of individual element antenna with the (isotropic
source) array pattern.
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Example
element
AF
Total
array
element
AF
Total
array
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For a uniform array of a constant d and identical amplitude (say 1)
Thus
The normalised antenna factor of a uniform array:
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AF: N = 20, d = l and 0 = 0
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AF: N = 10, d = l and 0 = 0
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AF: N = 10, d = l/2 and 0 = 0
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AF for N = 10 and d = l/2, and 0 = 450
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Phased Array
The maximum of the radiation occurs at  = 0
That is:
Normally the spacing d is fixed for an array, we can control
the maximum radiation (or scan the beam) by changing the
phase 0 and the wavelength (frequency) – this is the
principle of phase/frequency scanned array
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Broadside and End-fire Arrays
• An array is called a broadside array if the maximum
radiation of the array is directed normal to its axis ( =
00); while it is called an end-fire array if the maximum
radiation is directed along the axis of the array ( = 900).
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The radiation pattern, SLL, HPBW, and gain for four different
source distributions of eight in-phase isotropic sources spaced by
l/2; there are trade-offs!
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Element mutual coupling
• The interaction between elements due to their close
proximity is called the mutual coupling which affects
the current distribution hence the input impedance as
well as the radiation pattern
• The voltage generated at each element can be
expressed as
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Self-impedance:
Mutual impedance:
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5.4
Some Practical Considerations
• The differences between transmitting and receiving
antennas
– From the reciprocity theorem, the field patterns are
the same for transmitting or receiving.
• Antenna feeding and matching
– Balun (a device to connect a balanced antenna to an
unbalanced transmission line) may be required.
• Polarisation
– Polarisation has to be matched from Tx to Rx.
• Radomes, housings and supporting structures.
– Affecting the antenna performance (impedance,
pattern, …)
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