# Spiral-Resonator-Based Frequency Reconfigurable Antenna Design for Sub-6 GHz Applications
## 2 Antenna Design  
### Simulated Design  
Due to the high demand for the advanced wireless systems, new antenna designs play a crucial role in operating multiple frequency bands. During the design process, it is important that the innovative antenna structures in compact size have to fit into a single wireless device. Hence, this geometric constraint is considered as a main task in this study. A novel antenna geometry is composed of an inner spiral resonator to be connected to the outer split-ring radiator. The main purpose of using resonators and split-ring radiators is to reduce the overall antenna dimension [43; 44; 45; 46; 47]. Different side views of the novel proposed antenna structure are detailed in Figure 1a-c. The reconfigurability is accomplished by using two different switching components including PIN diodes, and SPDT switches to alter the electrical length and shape of the radiating element. The dimension of the reconfigurable antenna is calculated by using Equations (1) and (2). The substrate material is FR-4 with relative permittivity of 4.3, loss tangent of 0.025 and thickness of 1.6 mm. The overall dimension of the designed antenna is 22 \(\times\) 16 \(\times\) 1.6 mm\({}^{3}\). The physical parameters of proposed antenna are labelled in Figure 1a and detailed in Table 1. Two switches are visualized and labelled as D1 and D2 as shown in Figure 1a. CST Studio Suite, a commercial software package for electromagnetic simulations, is used for the analysis of the proposed antenna performance numerically [48]. PIN diodes are modeled by touchstone files including one-port S parameters information as shown in Figure 1d. The calculation of the width of the feed line (_Wf_) is initially justified using standard transmission line theory, as referenced in [17; 49]. This theory provides a well-established framework for determining the appropriate dimensions of transmission lines, ensuring efficient signal propagation. Additionally, we calculated the effective dielectric constant (\(\epsilon_{eff}\)) based on the ratio of the feed line width (\(w_{f}\)) to the substrate height (\(h\)) as given in Equation (1) [49]. To match the impedance of 50 \(\Omega\), we validated the characteristic impedance (\(Z_{0}\)) of the feed line using Equation (2) [49]. After that, the wavelength (\(\lambda\)) for the lower and upper frequencies was calculated via Equation (3) [17; 28; 48] to determine the effective resonant lengths (Lon-on and Loff-off) for the antenna states. These lengths were determined as a proportional ratio of \(\lambda\) to achieve the desired resonance. It is important to explain how to calculate the electrical length of for different states. By using Equation (3) the electrical lengths are initially determined as \(\lambda_{1}=57\) mm and \(\lambda_{2}=125\) mm for the upper and lower frequencies, respectively. After calculating the wavelength, Lon-on and Loff-off of the proposed antenna for each frequency band (5.2, and 2.4 GHz), parametric analysis is utilized to obtain the optimum values for the other labeled dimensions in Figure 1. Byproviding these explanations and calculations based on transmission line theory, Table 1 offers a comprehensive understanding of the design parameters and the process behind determining them. \[\varepsilon_{eff}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}\Bigg{\{} \bigg{(}1+12\frac{w_{f}}{h}\bigg{)}^{-0.5}\Bigg{\}}\quad\text{ where }\Big{(}\frac{w}{h}>1\Big{)} \tag{1}\]  
\[Z_{0}=\frac{120\pi}{\sqrt{\varepsilon_{eff}[\frac{w_{f}}{h}+1.393+\frac{2}{3} ln(w\frac{w_{f}}{h}+1.44)]}} \tag{2}\]  
\[L_{R}=\frac{c_{0}}{4f_{c}\sqrt{\varepsilon_{eff}}} \tag{3}\] \begin{table}
\begin{tabular}{c c} \hline
**Dimension Label** & **Unit (mm)** \\ \hline Ws & 16 \\ Wi1 & 10 \\ Wi2 & 8 \\ Wo & 14 \\ g & 1 \\ Ls & 22 \\ L1i & 8 \\ Lf & 9 \\ Li2 & 6 \\ \(w_{f}\) & 3 \\ Li3 & 3.5 \\ tm & 1 \\ Lo & 12 \\ Lg & 4 \\ \(h\) & 1.6 \\ \hline \end{tabular}
\end{table} 
Table 1: Antenna design parameters.