# Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band
## 4 Simulation Processes  
With the foregoing mathematical analysis, a practical square split ring resonator was designed using CST MWS software. The MWS is based on solving [PERSON]'s equations in differential form in the time domain explicitly [54]. Additionally, it is highly desirable to use time domain simulations methods for high frequency electromagnetic applications, especially when broadband results are desired [55]. In this work, a square SRR resonating at 28 GHz and 40 GHz was constructed on an RT5880 substrate with a height of 0.5 mm, as depicted in Figure 4. The metallic layer used was the lossy annealed copper. The desired dimensions were obtained by using design equations discussed in Section 3 and a summary of a step-by-step design procedure is shown in Table 1.  
Following the use of the design procedure, in order to optimize the calculated parameters of the unit cell of the metasurface, the CST optimizer tool from the software was used. Table 2 depicts the dimensions of the unit cell before and after optimization. In order to perform simulation in CST MWS, the boundary conditions have to be defined. For the software to generate EM waves, the boundary conditions of the \(x_{\text{axis}}\), \(y_{\text{axis}}\) and \(z_{\text{axis}}\) were defined as a perfect electric conductor, perfect magnetic conductor and open respectively. This means that for \(x_{\text{min}}\) and \(x_{\text{max}}\) the magnetic fluxes are set to zero, for \(y_{\text{min}}\) and \(y_{\text{max}}\) electric fluxes are set to zero and with \(z_{\text{min}}\) and \(z_{\text{max}}\) waves can pass with minimal reflections. The proposed structure was excited by defining two wave ports which were normal to the \(x_{\text{axis}}\). The time domain solver which comprises of finite difference time domain (FDTD) was used to calculate transmission of energy between excitation sources and obtain broadband frequency behaviour of the simulated structure. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Step** & **Equation** & **Purpose** \\ \hline
1 & Equation (6) & Calculate the width of a characteristic impedance \(Z_{o}\) \\ \hline
2 & Equations (5) and (14) & Calculate the dielectric constant and use it to find the internal and external average lengths \(L_{T1}\) \& \(L_{T2}\) for each frequency \\ \hline
3 & Equation (9) & Calculate the internal and external side lengths of each outer ring using the calculated average lengths in Step 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of calculation of dimensions of a metasurface unit cell. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Dimensions** & **Before Optimization (mm)** & **After Optimization (mm)** \\ \hline \(h\) & 0.5 & 0.56 \\ \hline \(W\) & 1.54 & 1.54 \\ \hline \(l_{1}\) & 3.51 & 3.47 \\ \hline \(l_{2}\) & 4.68 & 4.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Unit cell dimensions before and after software optimization. To achieve reconfigurability, the designed unit cell was made into a 4 \(\times\) 4 element integrated with diodes, as shown in Figure 5. Similar to authors in [56], each unit cell of the metasurface was connected to a diode. In an array of SRR unit cells, there is an increased magnetic response [57], due to an alternating magnetic field perpendicular to the SRR plane. The SRR behaves as a simple LC resonator, with capacitance resulting from the separation of charges across the split and inductance being the result of currents circulating in the ring, exhibiting a resonant response at a specific frequency [58; 59]. The resonant circular currents give rise to a resonant magnetic dipole moment, which is responsible for the negative permeability part of negative refraction [59]. Furthermore, the electromagnetic response can also be influenced by the mutual coupling between SRR unit cells [60]. Mutual coupling is when antenna elements that are near each other, either transmitting or receiving, will leak some of the energy that is intended for one to the other [51].