## 2 Delta-Stub-Based Wilkinson Power Divider (WPD) Design Configuration and Characterization Results
### Single-Element Fractal Antenna Design  
In this section, a single-element Minkowski-Sierpinski fractal antenna design is discussed. In order to realize the single-element fractal antenna, the square-shaped MPA, as shown in Figure 3a, is initially designed by using the transmission-line model [8]. CST Microwave Studio is used to simulate and study the behavior of the antenna. Two different substrates materials are employed for this purpose, i.e., a high-end Rogers TMM4 substrate (\(h\) = 1.524 mm, \(\varepsilon_{r}\) = 4.5, \(tan\)\(\delta\) = 0.002) and low-end FR4 epoxy glass substrate (\(h\) = 1.6 mm, \(\varepsilon_{r}\) = 4.3, \(tan\)\(\delta\) = 0.02). The step-by-step procedure of fractal antenna design is shown in Figure 3a-c, and a detailed explanation is also provided in [22]. In step one of the design, a square MPA of length and width equal to 38.5 mm is realized. In step two of the design, the Minkowski carpet structure is applied to the square MPA as shown in Figure 3b based on the calculations from Equations (1)-(4) by choosing the values of \(a_{1}\) and \(a_{2}\) to be 0.64, and 0.064, respectively. \[N_{n}=8^{n} \tag{1}\]  
\[L_{n}=(\frac{1}{3})^{n} \tag{2}\]  
\[w_{1}\left({}^{n+1}\right)=a_{1}\times L_{n} \tag{3}\]  
\[w_{2}\left({}^{n+1}\right)=a_{2}\times L_{n} \tag{4}\]  
Figure 3: Shows (**a**) basic MPA with length \"\(L\)\" and width \"\(W\)\", (**b**) Minkowski structure introduced in basic MPA, and (**c**) combined Minkowski-Sierpinski carpet antenna design with respective dimensions. In step three, the Sierpinski carpet structure is applied up to the third iteration to the remaining portion of step two, as shown in Figure 3c. where \(L\) represents the length of the resonating patch, \(w_{1}\) and \(w_{2}\) are the dimensions of the rectangular slots removed from the sides of the square patch in the first iteration of this structure, and \(a_{1}\) and \(a_{2}\) refer to the indentation ratios, respectively. Table 1 shows the detailed dimensions of the single-element Minkowski-Sierpinski fractal antenna. The simulated \(S_{II}\) (dB) results of the proposed single-element Minkowski-Sierpinski fractal antenna design using two different substrates are summarized in Figure 4. It can be seen from the \(S_{II}\) (dB) result that the proposed antenna is resonating at dual frequency bands, i.e., around 4.1 and 5.97 GHz, respectively. After the S-parameter characterization of the single-element fractal antenna, the 2D radiation pattern results are also studied for a better understanding of antenna performance. Figure 5a-d shows the simulated E-plane and H-plane 2D radiation patterns of the FR4 and TMM4 substrate single-element fractal antennas. It can be seen from the radiation pattern results that the FR4-based single-element antenna exhibits a higher gain at 5.97 GHz, whereas the antenna designed using the TMM4 substrate only shows improvement at low frequency. It is important to observe from the results that the proposed antenna simulated using the FR4 substrate shows a gain of 0.8/7 dB at 4.17/5.97 GHz, respectively. Similarly, using the TMM4 substrate, the antenna exhibits a gain of 2.2/5.5 dB at 4.17/5.97 GHz, respectively. The proposed antenna's primary application is to work at Wi-Fi6 [5; 6] and sub-6 GHz 5G systems, which means we need enhanced gain at a higher frequency. Due to this reason, the FR4-based single-element Minkowski-Sierpinski fractal antenna design is selected for fabrication and further characterization using a 2 \(\times\) 2 antenna array design. Figure 6a shows the final structure of the single-element Minkowski-Sierpinski fractal antenna designed using the FR4 substrate. Figure 6b shows the single-element antenna measurements setup using a Keysight Technologies FieldFox N9916B vector network analyzer (VNA). It can be seen from Figure 6b that the antenna under test (AUT) was resonating at two different frequencies of 4.17 and 5.97 GHz, respectively.