# Compact Ultra-Wideband Series-Feed Microstrip Antenna Arrays for IoT Communications
## 2 Materials and Methods
### Design of the Antenna Array  
Using the microstrip element before designed, shown in Figure 1, and using the principles stated above about antenna arrays with log-periodic structure, the dimensions for a group of elements were estimated, for a central band of 28 GHz. In this sense, the crucial parameter to find was the scalability factor \(\tau\), to ensure a good relationship among the functionality of the antenna, the bandwidth obtained, and the overall size. In this work,  
Figure 1: Structure layout of an inset-fed microstrip patch antenna with its design parameters. bandwidth and size are of special importance, as already mentioned, because they are crucial aspects in emerging communication systems. The scalability factor obtained after some simulations was \(\tau=1.04\). That said, the various dimensions \(L_{n}\), \(W_{n}\), \(I_{n}\) and \(y_{n}\) were calculated, as well as the respective resonant frequencies. Nine elements were considered (i.e., \(n=1...9\)), of which the first four are resonant below 28 GHz, one exactly at this frequency, while the remaining four operate at above frequencies, in such a way that respect the relationship (2). The list of frequencies using this scalability factor is displayed in the second column of Table 1.  
In the remaining columns of Table 1, the estimates of the various parameters for each element to operate at each referred frequency are presented, always respecting the relation in (1), and starting from the sizes of the element estimated to operate at 28 GHz (\(n=5\)). Additionally, these dimensions were corrected through simulation and are also shown so that the respective element is resonant at that frequency, as well as the obtained \(f_{n}\). Figure 2 shows the simulated S\({}_{11}\) for each of the resonant elements present in Table 1, where it is possible to identify the respective operating frequency for each patch. Considering the various elements identified above, designed according to a log-periodic structure, they were grouped into sets of 5, 7, and 9 elements, centered on (and including) patch 5 (\(f_{c}=28\) GHz), and using them, three series-fed microstrip arrays were created. In Figure 2, it is possible to distinguish different areas shaded with different colors, theoretically limited by the elements that make up each of the three arrays. Hanging on a transmission line with characteristic impedance identical to the respective impedances of each element (\(Z_{0}=90\)\(\Omega\)), the various patches were arranged and intercalated on each side of the line. This characteristic impedance corresponds to  
\begin{table}
\begin{tabular}{c|c c c c|c c c} \hline \(n\) & \(f_{n}\) (GHz) & \(L_{n}=W_{n}\) (mm) & \(y_{n}\) (mm) & \(I_{n}\) (mm) & \(L_{n}=W_{n}\) (mm)  
a compromise between the dimensions of the microstrip line, and the impedances of all patches, in order to ensure the structure is small and efficient, as intended. Regarding the different dimensions of the patches, \(I_{n}\) corresponds to a quarter-wavelength, the spacing of the \(g_{n}\) feeding line does not follow any formula, but requires a minimum aperture that guarantees the proper functioning of the feeding structure. In this sense, it is usually adopted a value half of the feedline width \(w_{line}\). The only non-periodic parameter is the distance between patches, \(D_{n}\), illustrated in Figure 3a, and these separations were obtained through an optimization process so that all input impedances are properly associated along the central microstrip line, to obtain an input impedance equal to \(Z_{0}\). To complete the design of the antenna array, and since the characteristic impedance of the main line is different from the standard 50 \(\Omega\), a quarter wavelength microstrip line was added to transform the 90 \(\Omega\) characteristic impedance to 50 \(\Omega\). Although this matching step is essential, this solution in a wideband array is not ideal because only one frequency is fully adapted, instead of the entire band of frequencies.