## 2 The Design of the Proposed Antenna
### Designing the Filter for Higher-Mode Suppression  
This section presents a microstrip LPF design method aimed at overcoming the narrow space of the ground of the antenna. A micro-stripline type filter was selected so that it could be integrated with the ground of the antenna and operated as a filter in a narrow space. Recent studies of the micro-stripline type filter exist in various studies, as shown in [19; 20; 21; 22; 23]. The proposed LPF suppresses the radiation gain of the higher-mode radiation and harmonic resonance arising from the DRA. This study aimed to design a seventh-order Chebyshev LPF with a cut-off frequency of 3.5 GHz and a ripple of 0.1 dB, the equivalent circuits of which are shown in Figure 2a.  
The step-impedance [19; 20] structure is widely used to implement LPFs in microstrips. The transmission-line model of the filter, designed according to the step-impedance structure, is shown in Figure 2b, and its optimized shape for microstrip implementation is presented in Figure 2c. Considering the substrate characteristics and the linewidth, the high-impedance line (inductive) was set to 120 \(\Omega\), while the low impedance line (capacitive) was set to 20 \(\Omega\). However, as shown in Figure 2c, the general step-impedance structure cannot escape the linear form from port 1 to port 2. This is because the low impedance line (capacitor) has a very wide linewidth, and even if the narrow linewidth is bent, interference between the capacitive lines will occur.  
Since a filter was needed that could be integrated into the narrow space of the antenna base; we modified the step-impedance structure via stub equivalence. In the equivalent circuit shown in Figure 2a, the portions corresponding to Z0, L1, C2, C6, L7, and ZL could be converted into stubs using Richards' transformation and [PERSON]'s identities [21]. The step-impedance structure was maintained because the parts corresponding to L3, C4,  
\begin{table}
55 & 55 & 60 & 55 & 55 & 60 & 35 & 60 & 55 & 55 & 60 & 55 & 55 \\
55 & 55 & 60 & 55 & 55 & 60 & 35 & 60 & 55 & 55 & 60 & 55 & 55 \\  & 50 & 35 & 55 & 55 & 30 & 55 & 30 & 55 & 55 & 35 & 50 & \\  & 50 & 55 & 45 & 35 & 60 & 45 & 60 & 35 & 45 & 55 & 50 & \\  & & 50 & 60 & 35 & 25 & 25 & 25 & 35 & 60 & 50 & \\  & & & & 20 & 25 & 55 & 25 & 20 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized height (h1–h137) of the 137 DR bars (unit: millimeters).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(w_{0}\) & 3.5 & \(l_{0}\) & 10.77 & \(l_{41}\) & 6.5 \\ \(w_{1}\) & 0.74 & \(l_{1}\) & 6.52 & \(l_{42}\) & 1.1 \\ \(w_{2}\) & 0.63 & \(l_{21}\) & 4.5 & \(l_{5}\) & 4.6 \\ \(w_{3}\) & 4.99 & \(l_{22}\) & 3.  
and L5 did not interfere with the line deformation. The transmission-line model of the modified step-impedance filter was designed accordingly and is shown in Figure 2d; the optimized shape for the microstrip is presented in Figure 2e.  
Figure 3 presents the results of simulating the step-impedance filter structure in Figure 2c and the proposed filter structure in Figure 2e in CST Studio. The two filters reflect almost the same performance, but in the case of the proposed filter, bending the microstrip line is much easier; consequently, it can be placed within a narrow space. Additionally, the skirt characteristics were good, and the filter was optimized and integrated with the antenna. The shape of the proposed LPF could be optimized within a narrow space by easily bending the line. The final optimized filter presented in this paper is illustrated in Figure 4a, and the simulation results are shown in Figure 4b.  
Figure 2: A seventh-order Chebyshev low-pass filter (LPF). (**a**) An equivalent circuit of the lumped element model, (**b**) a transmission-line model of LPF step-impedance, (**c**) an optimized microstrip line model of LPF step-impedance, (**d**) a transmission-line model of the proposed LPF, and (**e**) an optimized microstrip line model of the proposed LPF.