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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) Radiated fields and radiation resistance of a small loop 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. Radiated fields and radiation resistance of a small loop (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.