Pattern Synthesis in Time-Modulated Arrays Using Heuristic Approach DOI: http://dx.doi.org/10.5772/intechopen.89479

#### Figure 20.

pattern and difference pattern was found as 6.12 and 4.56°, respectively, which are

Figure 19 shows SBLs of the first 30 sidebands for the synthesized patterns as considered in Example 1 and Example 2. It can be observed that at the higher sidebands also, the SBLs are below SBLmax. Further observation shows that the no radiation is produced at 10th, 20th, and 30th sideband with quantized values of τ<sup>p</sup> as at these harmonics the array factor expression becomes zero for all elements.

Example 3: In this example, it is shown that the same time modulator can also be used to synthesize a flattop pattern. Accordingly, a symmetrical TMLA with element number N = 20 and inter-element spacing d0 = 0.5λ is considered. Here, the objective is to synthesize a flattop pattern in the broadside direction with digitally controlled static excitation amplitudes and phases by using five digital attenuators and phase shifters. A flattop pattern with a beamwidth of 30°, maximum ripple level (Rmax) at the flat region of less than 1 dB, and transition width of 8° is selected as the target pattern. Although such pattern with more stringent design specification is reported in [6], analog attenuators and phase shifters are required. Due to symmetry, the dimension of the parameter vector χ = {Ap, ϕp, τp} becomes 30. During optimization, Ap and ϕp∀p ∈ð Þ 1, : … , N are perturbed within the search range of (0.2–1) and (�180 to +180) with step sizes of 0.5/2<sup>5</sup> and 360/2<sup>5</sup>

tively. The number of quantization states for τ<sup>p</sup> is selected as 20. In Eq. (27), both δ1d and δ2d are selected as �30 dB, while δ3d is set to 1 dB. Setting FN = 150, the ABC parameters are obtained as in [38]. ABC converges after 2000 iterations, while the weighting factors are selected as W1 = 2; W2 = 1; and W3 = 5. The ABC optimized 3D space pattern at fundamental frequency along with the first 30 sidebands is shown in Figure 20. Table 4 contains the corresponding discrete values of Ap, ϕp, andτp. The flattop pattern in Figure 20 is obtained with SLL, SBLmax, and Rmax of �29.31, �29.9, and 1.22 dB, respectively. The absolute value of Rmax is measured in the region of 75 ≤ θ ≤ 105°. Hence, only 0.22 dB higher values of Rmax are obtained by satisfying other design specification of the pattern. Also, it is observed that no such improvement in the pattern is obtained when the continuous value of τ<sup>p</sup> is used to

, respec-

quite comparable to 5.88 and 4.59° as for the patterns in [33].

Sideband levels of the first 30 sidebands for the different patterns in examples 1 and 2.

Figure 19.

Advances in Array Optimization

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ABC optimized space pattern at f0 and the first 30 sidebands. At f0, the flattop pattern is obtained with SLL, SBLmax, and Rmax of 29.31, 29.9, and 1.22 dB, respectively.


#### Table 4.

Optimum discrete values of Ap, ϕp, and τ<sup>p</sup> for the flattop power pattern of Figure 20.

synthesize the pattern. However, with Q = 10, almost the same pattern is obtained with Rmax of 1.80 dB.

In the continuous search space of VAS time-modulation method [2, 3–6], the ontime duration of array elements can be of any value between 0 and Tm. In [2], for each time-modulated elements, the current pulse required with pulse width over the range of (0.1Tm < t on <sup>p</sup> < 0.9Tm) is obtained by using the RF switches with individually controlled switching circuits. Other time-modulation schemes such as BOTS [30] and SOTS [21] need a complex programmable logic device (CPLD) for controlling the "on–off" timing of the connected switches. The continuous values of on-time of elements can be controlled by using CPLD accurately [41, 42], but to synthesize a new antenna pattern, by realizing a new set of on-time sequence, the CPLD must be reprogrammed by completely erasing the previous set of on-time values. In contrast, the proposed VAS-QOT needs a simple circuitry as shown in Figure 13, where the new set of on-time sequences according to the need can be obtained simply by altering the appropriate binary input sequence to the selected inputs of the multiplexers. Thus, by fabricating the QTM in integrated circuit (IC) or by using some discrete components on a printed circuit board (PCB), TMAA switching can be done easily.
