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Array antennas are generally classified according to the arrangement of the units. The array antennas with the center of each unit arranged along a line are called line arrays and the unit spacing can be equal or unequal. The array antennas with the center of each unit arranged in a plane are called planar arrays, and if all the units of the planar array are arranged according to the matrix grid, they are then called rectangular arrays. And the array antennas with the center of all units arranged on a concentric ring or an elliptical ring are called circular or elliptical arrays.

Figure 2.5 shows the arrangement of the four common array antennas. The independent units that make up the antenna array in a linear array, a planar array, and a tri-dimensional array are called antenna units or array elements. The array elements can be various types of antennas.

Fig. 2.5. Common array antennas.

The analysis and synthesis of discrete array antennas mainly depend on the following four factors: the number of array elements, the position of array elements in space, the current amplitude distribution of array elements, and the current phase distribution of array elements.

Array analysis is based on the above four factors and is used to determine the radiation characteristics of the array, including the pattern, gain, impedance, and so on. And the synthesis problem is to design the optimal array parameters (the above four factors) according to their radiation characteristics. As for the selection of the array element type, it is mainly determined by the working bandwidth, the pattern characteristics, and the polarization characteristics. In phased-array antennas, it is also related to the scan range.

In the general array antenna theory, if the mutual coupling effect between the array elements is a fixed factor with less variation, the field pattern function of the array antenna can be expressed by the product of the array factor and the array element pattern function. Let’s take a simple example to illustrate this problem, as shown in Fig 2.6.

The phase factors are (as shown in Fig. 2.6(a))

or (as shown in Fig. 2.6(b))

Fig. 2.6. Linear array antenna. (a) The origin of the coordinate system is at a unit. (b) The origin of the coordinate system is at the center of two units.

Let a = (a₀, a₁) be the array element coefficient, then the array factors are given as follows:

Only one phase constant difference exists between the above two expressions, which will not affect the pattern. When θ = 90°, namely in the xoy plane, the above array factor can be written as

The power pattern can be expressed as

Figure 2.7 shows the antenna pattern when a = (a₀, a₁) = (1, 1), a = (a₀, a₁) = (1, – 1), a = (a₀, a₁) = (1, –j) with excitation values of d = 0.25λ, d = 0.5λ, and d = λ, respectively.

The main beam-pointing direction of the pattern changes with the relative phases of the excitation values a₀ and a₁. When the main beam points to ϕ = 0° or ϕ = 180°, the antenna array is called an end-fire array.

As shown in Fig. 2.7, the main lobe width gradually increases with the main lobe of the pattern moving from ϕ = 90° to ϕ = 0°.

In addition, when d ≥ λ, there will be multiple main lobes in the pattern, which is called the grating lobe as shown in Fig. 2.8.

Consider a two-dimensional array and three half-wave oscillators placed along the z-axis, among which one is at the origin on the x-axis and the other is on the y-axis with a spacing d = λ/2, as shown in Figs. 2.9 and 2.10.

The array element excitation values are a₀, a₁, and a₂, and the corresponding position vectors are d₁ = d and d₂ = d. And then

The array factor of the antenna array is

Fig. 2.7. Patterns of array antenna (Fig. 2.6).

Therefore, the normalized gain of the array is

where g(θ, ϕ) is the pattern function of the half-wave oscillator.

In the xoy plane (θ = 90°), the gain pattern is given as

Fig. 2.8. Antenna patterns when d ≥ λ.

Fig. 2.9. Two-dimensional array.