3.1.1 Geometry antenna and design

The designed geometry antenna is shown in Figure 9; the antenna is composed of four different lengths with U-shaped stubs. The lengths and spacing of the elements of LPDA increase logarithmically from one end to the other. The design of the LPDA is used where a wide range of frequencies is needed while still having moderate gain and directionality. The simulator HFSS is used to validate and optimize by simulating the designed antenna. The designed antenna is built on a commercial FR4 substrate with dielectric constant ε<sup>r</sup> = 4.6, and loss tangent tan δ = 0.02. The antenna is fed by a 50 Ω transmission line, which can be easily integrated with other microwave circuits printed on the same substrate. For designing procedure,

Figure 9. Layout of the proposed log periodic dipole antenna (semi-LPDA) [39].

the number of trial steps is needed, the scale-factor τ, spacing factor δ, and the number of the dipole elements N should be determined. Second, the length of the longest arm, which responses to the lowest resonance frequency f1, should be computed by following Eqs. (1)–(6) [39].

$$\frac{W\_{i-1}}{W\_i} = \varepsilon \tag{1}$$

$$\delta = \frac{L\_{isep}}{4W\_i} \tag{2}$$

$$W\_1 = \frac{\lambda\_{1,eff}}{4} \tag{3}$$

$$\mathbf{N} = \mathbf{1} - (\ln \mathbf{B}\_{\mathbf{s}} / \ln \tau) \tag{4}$$

$$\mathbf{B\_{a}} = \mathbf{1.1} + \mathbf{30.7} \,\delta\,(\mathbf{1} - \boldsymbol{\tau}) \tag{5}$$

$$\mathbf{B\_s = B\_a B\_o} \tag{6}$$

where λ1eff, Bo, N, and int i are the longest effective operating wavelength, the operating frequency, number of elements, and i is an integer that varies from 2 to 5, respectively. To improve the impedance, matching the balun circuit with suitable dimensions is used as shown in Figure 9. Table 2 introduces the dimensions of the proposed antenna [39].
