### antenna array - Dr. Hussein M. Attia

```Lecture 5
Loop Antenna
Antenna Arrays
Dr. Hussein Attia
Zagazig University
Ch. (5, 6) in the textbook of
(Antenna Theory, 3rd Edition) C. A. Balanis
Loop Antennas
Ch. (5) in the textbook of
(Antenna Theory, 3rd Edition) C. A. Balanis
Loop Antenna
Another simple, inexpensive, and very versatile antenna type is the loop antenna.
Loop antennas are formed by a closed loop wire. Most common shapes are circles and
rectangle:
It will be shown that a small loop (circular or square) is equivalent to an
infinitesimal magnetic dipole whose axis is perpendicular to the plane of the loop.
That is, the fields radiated by an electrically small circular or square loop are of
the same mathematical form as those radiated by an infinitesimal magnetic dipole.
Loop antennas
electrically small
(circumference < λ/10)
electrically larger
(circumference ≈ λ)
Loop antennas with electrically small circumferences have small radiation
resistances that are usually smaller than their loss resistances. Thus they are
very poor radiators, and they are seldom employed for transmission in radio
communication.
When they are used in any such application, it is usually in the receiving mode,
such as in portable radios and pagers, where antenna efficiency is not as
important as the signal to noise ratio.
Small Circular Loop (circumference < λ/10)
Assume a loop antenna is positioned symmetrically on the x-y
plane, at z = 0, The wire is assumed to be very thin and the
current spatial distribution is given by Iφ = Io where Io is a
constant.
Where S is the area of the loop (S = πa2 for a circular loop of radius a). Zo = 377 ohm
A comparison of the above equations with those of the infinitesimal magnetic dipole indicates that
they have similar forms. Thus, for analysis purposes, the small electric loop can be replaced by a
small linear magnetic dipole of constant current.
The fields radiated by a magnetic dipole are duals of those of an electric dipole.
(Single turn loop)
Antenna Arrays
Ch. (6) in the textbook of
(Antenna Theory, 3rd Edition) C. A. Balanis
Introduction and general theory
To obtain higher gain/directivity and narrower beams often two or more similar antennas are positioned and fed properly and
used as single antenna system. The resulting system is called an antenna array. Antenna array is a system of N identical
antennas with the same orientation excited by well-defined amplitudes and phases
In fact any type of pattern shape could be realized by appropriate choice of
1) the antenna element type;
2) their position in space; and
3) the element excitation (amplitude and phase).
Furthermore by changing the amplitude and phase of the element excitation, the array radiation pattern can be reshaped in
real time (electronic beamsteering, phased arrays, adaptive arrays, smart antennas, …)
Introduction and general theory
Antenna array systems are being used in almost all types of land based and satellite communication as
well as radar systems. Depending on the geometrical configuration and the arrangement of the elements
most common types of arrays can be classified as linear (1-D arrangement), planar (2-D rectangular or
circular grids), and conformal (conforming to the non-planar surfaces).
The general structure of any array system
consists of two subsystems:
1) antenna elements;
2) feed network.
Feed network generates and controls
excitation amplitudes, Ai , and phases, αi ,
of each antenna element.
The complex excitation coefficient
of the ith element is defined as:
Hint
For an infinitesimal electric dipole of constant current
I0 placed symmetrically about the origin and directed
along the y-axis
The radiated far field at any point in the y-z
plane (φ = 90o) is given by
Derive this
formula yourself!
Two-element Array
Let us assume that the antenna under investigation is an array of two infinitesimal horizontal dipoles positioned
along the z-axis and directed along the y-axis, as shown in Figure (a). The total field radiated by the two elements, is
equal to the sum of the two antennas and in the y-z plane (φ = 90o) it is given by
where β is the difference in phase excitation between the currents in the two elements. The magnitude excitation of
the radiators is identical. ( =  / and  =  −/ )
Assuming far-field observations and referring to Figure on the right,
This is referred to as pattern multiplication for arrays of identical elements, Although it has been illustrated
only for an array of two elements, each of identical magnitude, it is also valid for arrays with any number of
identical elements which do not necessarily have identical magnitudes, phases, and/or spacing between them.
Each array has its own array factor. The array factor, in general, is a function of the number of elements, their
geometrical arrangement, their relative magnitudes, their relative phases, and their spacings.
In order to synthesize the total pattern of an array, the designer is not only required to select the proper
radiating elements but the geometry (positioning) and excitation of the individual elements.
Solve Example 6.1 in page 286
Solve Example 6.2 in page 290
Pattern Multiplication Rule
To better illustrate the pattern multiplication rule, the normalized patterns of the single
element, the array factor, and the total array for each of the three array examples in
Example 6.1 are shown below.
In each figure, the total pattern of the array is obtained by multiplying the pattern of the
single element by that of the array factor.
In each case, the pattern is normalized to its own maximum.
In each case, the formula below is used to plot the total radiation pattern of the array
Etn =
The normalized total
field of the array
Pattern Multiplication Rule
Case (a) of Example 6.1 in page 286
(β = 0o, d = λ/4).
The normalized field is given by
Shown in Figure are ….
Element pattern, array factor pattern, and total field patterns
of a two-element array of infinitesimal horizontal dipoles with
identical phase excitation (β = 0o, d = λ/4).
the total pattern of the array is obtained by
multiplying the pattern of the single element by that
of the array factor.
In each case, the pattern is normalized to its own
maximum.
Since the array factor for this case is nearly isotropic
(within 3 dB), the element pattern and the
total pattern are almost identical in shape◦
Pattern Multiplication Rule
Case (b) of Example 6.1 in page 286
(β = +90o, d = λ/4).
The normalized field is given by
Shown in Figure are ….
Element pattern, array factor pattern, and total field patterns
of a two-element array of infinitesimal horizontal dipoles with
(β = +90o, d = λ/4).
The total pattern of the array is obtained by
multiplying the pattern of the single element by that
of the array factor.
The pattern is normalized to its own maximum.
Because the array factor for this case is of cardioid
form, its corresponding element and total patterns
are considerably different.
In the total pattern, the null at θ = 90o is due to the
element pattern while that toward θ = 0o is due to the
array factor.
Pattern Multiplication Rule
Case (c) of Example 6.1 in page 286
(β = -90o, d = λ/4).
The normalized field is given by
Shown in Figure are
Element pattern, array factor pattern, and total field patterns
of a two-element array of infinitesimal horizontal dipoles with
(β = -90o, d = λ/4).
The total pattern of the array is obtained by
multiplying the pattern of the single element by that
of the array factor.
The pattern is normalized to its own maximum.
Because the array factor for this case is of cardioid
form, its corresponding element and total patterns
are considerably different.
In the total pattern, the null at θ = 90o is due to the
element pattern while that toward θ = 180o is due to
the array factor.
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