# Compact Multilayer Yagi-Uda Based Antenna for IoT/5G Sensors
## 2 Materials and Methods
### Multilayer Yagi-Uda Design  
A multilayer version of the printed Yagi antenna was designed with a view to improve the performance and to compact its structure. According to what has been analysed in the literature [23], a gain saturation occurs for planar antennas, especially planar antenna arrays, and developing antennas in a multi-layered arrangement can overcome this limit, because it uses the vertical dimension [19]. The design was based on converting a set of directors and the reflector, properly spaced around the printed dipole. The radiation will be conducted in the upper vertical plane, instead of the horizontal plane, as in the planar version. This radiation characteristic can reveal being a clear advantage for many of the sensors where the antenna will be placed. This type of structure implies that the elements are surrounded in the dielectric substrate. This is one of the differences regarding the planar structure, where the radiation in the antenna follows two different mediums, air and dielectric substrate. Avoiding some air gaps inside the antenna structure keeps it more robust and stable physically, but also in terms of its properties to the environment variations. Thus, in the design process, it is imperative in this application to consider the wavelength in the specified substrate (\(\lambda_{d}\)). Considering that the construction of multilayer antennas has a relative novelty, a study on the dielectric and structure was carried out, as a way of better understanding the antenna's behaviour and the changes produced by structural modifications. The design of this antenna was based on theoretical dimensions, which were then adjusted through simulation. As in the previous planar form, a dipole was printed on a substrate, and a reflector element using the same line width was placed below at a distance \(\mathrm{h_{ref}}\). This separation was guaranteed by using a number of layers of dielectric substrate between the elements. Several simulations were performed varying the number of directors placed on the structure, with a length of 0.25 \(\lambda_{d}\), and spaced by a distance \(\mathrm{h_{dir}}\). Additionally, the impact of adding a new layer of dielectric material over the last director element was studied. These two versions of structure are shown in Figure 3a,b, respectively. Moreover, Figure 3b highlights the layers identification. Thus, layers \(E_{n}\) constitute the extra dielectric layers (which are to be studied), layers named \(D_{n.m}\), represent the distance between each director and the following element, meaning the parameter \(\mathrm{h_{dir}}\), and lastly, \(R_{n}\) layers are representing the distance between the dipole and the reflector. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \(\mathrm{L_{dip}}\) & \(\mathrm{L_{dir}}\) & \(\mathrm{W_{dip}}\) & \(\mathrm{W_{dir}}\) & \(\mathrm{gap}\) & \(\mathrm{DirSpa}\) & \(\mathrm{L_{cps}}\) & \(\mathrm{W_{cps}}\) & \(\mathrm{W_{msc}}\) & \(\mathrm{L_{41}}\) & \(\mathrm{L_{42}}\) & \(\mathrm{W_{41}}\) & \(\mathrm{W_{42}}\) \\ \hline
5.19 & 2.75 & 0.8 & 0.72 & 0.3 & 3 & 1.63 & 0.25 & 0.8 & 1.64 & 1.91 & 0.65 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the 24 GHz planar Yagi-Uda antenna (UNITS: mm). Figure 3: Vertically stacked Yagi antenna: (**a**) without the extra top layers of dielectric; (**b**) with extra layers of substrate. The analysis was focused mainly on the radiation parameters of the antenna, particularly on its radiation pattern and the obtained gain, because it induces the directivity, which is one of the main parameters that it is required to enhance our application, thus maintaining the compactness of the structure. The results are shown in Figures 4-6. Figure 4 (cross marker) shows the evolution of the antenna's gain as a function of the number of directors added after the dipole. As expected, the gain increases as the number of directors increases. In parallel, the volume of antenna structure also grows substantially.