# Compact Multilayer Yagi-Uda Based Antenna for IoT/5G Sensors
## 2 Materials and Methods
### Multilayer Yagi-Uda Design
However, the directors were designed to guide the waves surrounded in dielectric, and the last director has the same length of all the others and is not surrounded as the others are, which led to implementing a slight different scheme. An alternative design was proposed, as shown in Figure 3b, where on the top of the third director, a few extra layers of dielectric were used. Naturally, this alternative design increases the antenna's height, but as it is presented in Figure 4 (circle marker), it is clearly compensated by an increase of the antenna's gain, about 1.8 dBi, using up to three directors. On the other hand, when using four director elements, it is possible to observe a reduction of the gain when the extra dielectric layers are inserted. Considering the results of Figure 4, and taking into account the obtained antenna's gain and its dimensions, using the two possible approaches of Figure 3, three directors were chosen as the optimal compromise for the multilayer Yagi antenna. Using three directors in the multilayer structure, several simulations were performed mainly to understand the impact of increasing the thickness of the extra substrate layer on the top of the third director. The gain variation due to the number of substrate layers that form the extra dielectric (Figure 3b) is illustrated in Figure 5. The substrate used has a thickness of h = 0.762 mm, and so, the height that tops the last director, as well as the various distances between the other elements, are a multiple of this value. According to Figure 5, it can be realised that there is a limit to the thickness of the last substrate layer above the last director. The value that maximizes the antenna gain corresponds to 3 h, which is equivalent to 2.286 mm. Finally, to understand the variation of the structure's gain (using three directors) with the distance between them, in multiples substrate layers (h), a few more simulations were performed, and the results are shown in Figure 6. In this figure, it is verified that the optimal separation between the several directors corresponds to three layers of substrate (3 h), equivalent to h  
Figure 4: Gain variation with the number of director elements in the Yagi antenna. Considering the analysis presented above, the multilayer structure of a Yagi-Uda antenna was designed, as is shown in Figure 7a. The multilayer antenna features an optimized compromise between gain and functionality with compact dimensions. It consists of a printed dipole together with three director elements, spaced by a dielectric layer with thickness 3 h, and with a reflector element placed at an optimized distance of: h\({}_{\text{ref}}\) = 4 h. The feeding part of antenna has the same basis of the design used for the planar antenna. Figure 7b shows the prototype of the proposed Yagi-Uda antenna and its final dimensions are mentioned. After an iterative simulation process, it was possible to achieve the optimal values for the parameters shown in Figure 7a, which are presented in Table 2. Regarding the dipole's length as a function of \(\lambda_{d}\), the optimal length is equivalent to 0.45 \(\lambda_{d}\). Figure 5: Variation of the gain with the usage of extra layers of substrate topping the last director. Figure 6: Variation of the gain with the number of dielectric layers between directors. Figure 7: Multilayer Yagi-Uda antenna: **(a)** layout and parameters; **(b)** photograph of the prototype.