# A Dual-Band Modified Franklin mm-Wave Antenna for 5G Wireless Applications
## 2 Antenna Design Approach
### Design Steps to Obtain the Proposed Antenna  
In this section, the procedure to obtain the final antenna is described in detail. The proposed Franklin antenna array is designed in four steps. Initially, the first antenna is designed with a full ground plane at the bottom of the substrate and the top portion of the substrate consisting of the patch consisting of a \(3\times 3\) array of a unit cell. This antenna is termed as antenna M. The representation of the antenna structure is shown in Figure 2a,b. This antenna shows a quad band of operation at 24.4, 25.8, 26.6 and 32.7 GHz with very poor impedance matching at the first three bands. So, to improve the impedance matching in the initial antenna M, in the next step, slots are introduced in the ground plane. This antenna is now termed antenna N. The representation of the antenna structure is shown in Figure 3a,b, wherein it can be seen that three cuts are made in the ground plane. Two cuts are of dimensions W\({}_{\text{G}}\times\text{L}_{\text{G}}\), and one cut is of dimensions W\({}_{\text{C}}\times\text{L}_{\text{G}}\). The last column's squares are made with different sizes and are not of the same dimensions as the other squares, in order to make the antenna resonate at a particular frequency. This modification also leads to a triple band of operation at 22.5, 24.9 and 35.3 GHz, with very poor impedance matching at the last two bands. To further improve the performance of the designed antenna N, in the next stage an additional three slots are etched to the ground part. This modified antenna is now termed antenna O. The representation of this antenna structure is shown in Figure 4a,b. The slots are now of a \(2\times 3\) array form. The new row of slots formed consists of two cuts of dimensions W\({}_{\text{G}}\times\text{L}_{\text{C}}\) and one cut of dimensions W\({}_{\text{C}}\times\text{L}_{\text{C}}\). The last cut that lies close to the boundary of the ground is slightly misaligned to the cut made in the previous stage for \begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Parameters** & **(mm)** \\ \hline F\({}_{\text{W}}\) & Folded dipole width & 0.7 \\ S\({}_{\text{W}}\) & Matching stub width & 10.15 \\ S\({}_{\text{L}}\) & Matching stub length & 1.4 \\ f\({}_{\text{L}}\) & Feed length & 3.2 \\ f\({}_{\text{W}}\) & Feed width & 2.4 \\ F\({}_{\text{B}}\) & The gap of the folded dipole & 0.26 \\ L & Length of substrate material & 21.0 \\ W & Width of substrate material & 26.0 \\ W\({}_{\text{G}}\) & Width of first type ground cut & 5.0 \\ W\({}_{\text{C}}\) & Width of second type ground cut & 2.0 \\ L\({}_{\text{G}}\) & Length of first type ground cut & 3.6 \\ L\({}_{\text{C}}\) & Length of second type ground cut & 4.0 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: (**a**). Top view of the antenna (M) showing the patch array structure of the antenna, (**b**) bottom view of the antenna showing the full ground plane. obtaining a proper response. This modification allows the antenna to operate at dual-band, i.e., at 22.6 and 35.05 GHz, with a lower reflection coefficient value at both the bands. To further improve the impedance matching at the dual band, the final modifications are made to the ground part of antenna O by etching one more row of square slots, thereby resulting in 9 cuts in the ground plane. The introduction of these slots further affect the surface current behavior of the antenna, thereby improving the impedance matching of the antenna. This antenna is now termed as P (proposed antenna). The representation of the antenna structure is shown in Figure 5a,b. The cuts that were introduced in the ground plane are in the form of a \(3\times 3\) array structure. The last row of cuts formed consists of two cuts of dimensions \(\mathrm{W_{G}}\times\mathrm{L_{C}}\) and one cut of dimensions \(\mathrm{W_{C}}\times\mathrm{L_{C}}\).