**2.2 Array factor**

Microstrip antennas arranged in Array are not only useful for widening bandwidth but also have an impact on the radiation pattern produced. The radiation pattern in the Antenna is generally written with the equation:

*R* ð Þ *θ*, ∅ with i element in the position of *ri* ¼ *xi*, *yi* , *Zi* � �

The relationship with the wave emitted from the antenna array (Y) with the multiplier of complex numbers (wi) in the function (θ, ∅), is obtained:

$$Y = \mathcal{R}\left(\theta, \mathcal{Q}\right) w\_1 e^{-j\ k r\_1} + \mathcal{R}\left(\theta, \mathcal{Q}\right) w\_2 e^{-j\ k r\_2} + \dots \\
\mathcal{R}(\theta, \mathcal{Q}) w\_N e^{-j\ k \cdot r\_N}$$

With k is the wave vector in the incoming wave. Next can be written:

$$Y = R\left(\theta, \mathcal{Q}\right) \sum\_{i=1}^{N} w\_i e^{-j\left(k.r\_i\right)}$$

$$Y = \left(\theta, \mathcal{Q}\right)AF$$

$$\vdots \\ AF = \sum\_{i=1}^{N} w\_i e^{-j\left(k.r\_i\right)}$$

AF = Array Factor (as an Antenna position function) [11].

## **2.3 Antenna design and optimization**

In principle, the microstrip antenna has a characteristic narrow bandwidth. It has several advantages, including a thin, small, light in weight, and can be applied to the Microwave Integrated Circuit (MICs). The bandwidth can be widened using the array technique or by a panel system [11–16]. The panel systems (engineering array) involve strengthening (gain) of an antenna. In contrast, the rationing array technique is commonly used microstrip line. Graphically, microstrip antenna design is shown in **Figure 1**.
