# Metamaterial Based Ku-Band Antenna for Low Earth Orbit Nanosatellite Payload System
## 2 Antenna Design Methodology  
The developed antenna is intended to provide effective uplink and downlink communication between small satellites and the earth. The antenna prototype consists of two layers, shown in Figure 1. One layer is a truncated square patch antenna (Figure 1a), and another layer is an interconnected split rectangular metamaterial array (Figure 1b). Both layers are interconnected with conducting reflectors shown in Figure 1c. The space between the antenna and the metamaterial layer is 1.69 mm. Both layers are connected with a 0.25 mm thick conductive reflector wall, which also provides a strong mechanical strength of the structure. The antenna is fabricated on space-quality substrate material Rogers 5880 with a thickness of 1.575 mm, a dielectric constant of 2.2 and a dielectric loss tangent of 0.0009. The antenna is fed by a 50 \(\Omega\) Sub-Miniature version A (SMA) connector. The optimized structural layout parameters are listed in Table 1. The overall size of the antenna will be 15 mm \(\times\) 15 mm. Figure 1b shows the designed net-like hexagonal split ring base metamaterial structure, which has equal dimensions to the antenna and all other design parameters of the antenna listed in Table 1. The metamaterial structure has been characterized by considering perfect magnetic (PMC) and perfect electric (PEC) boundary conditions along the y and x-axis. The designed metamaterial-based antenna has been presented in Figure 1c. The designed metamaterial structure simulation setup is presented in Figure 1d [24].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value (mm)** & **Parameters** & **Value (mm)** \\ \hline L & 14.22 & L7 & 2.0 \\ L1 & 5.93 & Lf & 0.4 \\ L2 & 5.93 & Wf & 0.2 \\ L3 & 2.36 & g1 & 0.2 \\ L4 & 12 & g2 & 0.2 \\ L5 & 1.85 & h & 1.57 \\ L6 & 2 & g & 4.83 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Layout parameters of the presented antenna.  
Figure 1: (**a**) Layer 1, (**b**) Layer 2, (**c**) perspective view and (**d**) Simulation setup of the metamaterial.  
The metamaterial property like relative permittivity (\(\epsilon_{\mathrm{r}}\)) and permeability (\(\mu_{\mathrm{r}}\)) has been calculated from scattering parameters by using Equations (1) and (2) [25; 26; 27].  
\[\epsilon_{\mathrm{r}}=2/\mathrm{j}_{\mathrm{k}\mathrm{o}\mathrm{d}}\times(1-S_{ \mathrm{i}1}-S_{\mathrm{i}2})/(1+S_{\mathrm{i}1}+S_{\mathrm{i}2}) \tag{1}\]  
\[\mu_{\mathrm{r}}=2/\mathrm{j}_{\mathrm{k}\mathrm{o}\mathrm{d}}\times(1-S_{ \mathrm{i}2}+S_{\mathrm{i}1})/(1+S_{\mathrm{i}2}-S_{\mathrm{i}1}) \tag{2}\]  
Figure 2a,b shows the metamaterial property of the designed metamaterial reflector. The higher negative permeability has been achieved at the operating frequency of the antenna (10.18-13.05 GHz), which is \(\mu_{\mathrm{r}}\geq-600\). On the other hand, higher positive permittivity appeared in the same frequency range. This single negative feature reflected back the incident electromagnetic wave. The phase information of the reflected wave can also be understood from the phase value of the reflection coefficient. Figure 2c shows the phase value of the proposed metamaterial reflection operating frequency relayed in the +90\({}^{\circ}\) to \(-90^{\circ}\) range. This is characterized as an artificial magnetic conductor (AMC) because the operating bandwidth of the AMC is considered from +90\({}^{\circ}\) to \(-90^{\circ}\), and the resonant frequency is considered at 0-degree. The AMC-type metamaterial structure mimics the attributes of the perfect magnetic conductor. The AMC, which has PMC characteristics, can reflect the incident wave with a 0-degree phase, which made a constructive interference with the antenna-radiated wave in the forward direction shown in Figure 2d. Hence, the directivity and gain of the antenna improve significantly, and interference of the signal with the back side element of the antenna has been reduced.