*2.3.1 Empirical analysis and design*

**Figure 2** shows the microstrip antenna design dimensions.

The following **Table 1** is a dimension parameter of the antenna design:

Antenna arrangement with a transmission line. In the transmission line length l equivalent circuit is described as follows (**Figure 3**):

The first calculation involves finding the total electricity permittivity (εrtot) using the capacitor equation as follows.

$$\frac{1}{\mathbf{C\_{tot}}} = \frac{1}{\mathbf{C\_1}} + \frac{1}{\mathbf{C\_2}}$$

*Antenna Systems*

$$\frac{1}{\varepsilon\_o \varepsilon\_{\text{rot}} \, A/d \, \text{tot}} = \frac{1}{\varepsilon\_o \varepsilon\_{r\_1} A\_1/d\_1} + \frac{1}{\varepsilon\_o \varepsilon\_{r\_2} A\_2/d\_2} \tag{1}$$

where εr1 is ε<sup>r</sup> for air (εr1 = 1), εr2 is ε<sup>r</sup> for substrate (ε<sup>r</sup> FR4 = 4.3), d1 the thickness of the substrate and d2 distance of substrate to the reflector, with d tot, is d1 + d2 [12].

**Figure 1.** *Microstrip antenna design.*

#### **Figure 2.**

*The bi-ellipse microstrip antenna design dimensions.*


#### **Table 1.** *Dimension parameter of the Bi-ellipse Microstripline Array antenna design.*

*Bi-Ellipse Microstripline Antenna Array Varians DOI: http://dx.doi.org/10.5772/intechopen.98834*

**Figure 3.** *Equivalent circuits in transmission lines [12].*

A capacitor equation is used in this empirical analysis because, in principle, this is a device that stores electrical energy in an electric field. The capacitor made of two parallel conducting plates separated by a dielectric that is a parallel plate capacitor. When a battery is connected across the capacitor, one plate gets attached to the positive end and another to the negative. The potential of the battery is then applied across that capacitor. In this case, plate one is in positive potency with respect to plate two. At steady-state conditions, the current tries to flow from the battery through the capacitor from its positive to the negative plate unsuccessfully. This is because of the two separation of these plates with an insulating material. This is in line with the microstrip work principal in specific dielectric substrates.

To calculate the effective permittivity electricity (*εeff* ), the following equation is used:

$$e\_{\rm eff} = \frac{e\_r + \mathbf{1}}{2} + \frac{e\_r - \mathbf{1}}{2} \left(\mathbf{1} + \mathbf{10}\frac{h}{w}\right)^{-0.555} \tag{2}$$

Where ε<sup>r</sup> is the same with εrtot, h is dtot, and w is the width for patch and strip line side [11, 12].

Permittivity is a material property that affects the Coulomb force between two points charges.

The following equation is used to determine the maximum dimension in the patch side (w1):

$$\mathbf{f} = \frac{2\mathbf{c}}{3\mathbf{w}\sqrt{\varepsilon\_r}}$$

$$w\_1 = \frac{2\mathbf{c}}{3\sqrt{\varepsilon\_r}\,\mathbf{f}}\tag{3}$$

where c is lightspeed in air, ε<sup>r</sup> is electricity permittivity, and f is frequency [12].

To calculate the effective width strip line side (w2,3), the following formula is used.

$$\mathbf{W}\_{2,3} = \frac{1}{2\mathbf{f}\sqrt{\mu\_0 Z\_o}} \sqrt{\frac{2}{\varepsilon\_r + 1}} \tag{4}$$

Where f is frequency, μo is permeability constant, and Zo is characteristic impedance [12].

Permeability is derived from a magnetic field's production by an electric current or charge and all other formulas for the magnetic field produced in a vacuum.

The calculation wavelength of the substrate (*λ*g), uses the following equation:

$$
\lambda \mathbf{g} = \frac{\lambda}{\sqrt{\varepsilon\_{\mathbf{f}\overline{\mathbf{f}}}}} \tag{5}
$$

From the analysis above formula (1)–(5), the parameters for antenna fabrication can be fixed [11–13].
