# Metamaterial Integrated Folded Dipole Antenna with Low SAR for 4G, 5G and NB-IoT Applications
## 3 Antenna Design and Result Analysis  
The antenna was designed for wideband operations, to support the wide range of frequencies between 1.8 GHz to 3.8 GHz. The antenna was designed as a patch antenna with a dipole like a patch element on FR4 (lossy) substrate, as shown in Figure 5. The dielectric constant \((\in_{r})\) of the substrate was chosen to be 4.3 with a loss tangent and thickness of 0.02 and 1.574 mm, respectively. The initial dimensions were estimated with the use of the dipole antenna theory. The input impedance of the half wave dipole [28] with infinitesimally thin width can be defined in terms of the length of the dipole antenna \((L_{d})\) and phase constant \((\beta)\) as:  
\[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]  
The dipole length expression can be simplified further by considering the input impedance to be 50 \(\Omega\), considering the impedance matching requirement of the antenna with a feeding port. \[L_{d}=0.422\,\,\lambda \tag{2}\]  
The bandwidth for the thin dipole antenna is much narrower in comparison to the thick dipole antenna. The length of the thick cylindrical dipole with radius '\(a\)' can be corrected as:  
\[L_{d}=0.422\,\,\lambda F \tag{3}\]  
Figure 4: Retrieved refractive index for the structure. Figure 5: Illustration of dipole inspired patch antenna. where \(F\) is the correction factor and is given as:  
\[F=\frac{L_{d}/a}{1+L_{d}/a}=\frac{L_{d}}{L_{d}+a} \tag{4}\]  
For an infinitesimally thin dipole antenna r is negligible and \(F\) is unity, but for a thick dipole antenna, \(F\) is smaller than unity. Therefore, the corrected dipole antenna length can be estimated using Equations (3) and (4) as:  
\[L_{d}=0.422\ \lambda-a \tag{5}\]  
To obtain precise results the feed length (\(l_{f}\)) needs to be included as:  
\[L_{d}+l_{f}+a=0.422\lambda \tag{6}\]  
The equivalent radius theory is applied to approximate the equivalent width (\(W_{d}\)) of the rectangular patch. The equivalent radius represents the radius of a circular wire whose capacitance is equal to that of the noncircular geometry, considering the length to be equivalent. The equivalent radius for the rectangular dipole is approximated as:  
\[W_{d}=4a \tag{7}\]  
The wideband antenna designed in this research is not a wire antenna but a patch antenna with a dielectric layer, which needs to be considered for calculating the effective size and can be modified as:  
\[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]0  
\[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]1  
The constant k is estimated as 1.15 according to the procedure outlined in [29]. Thus, it is clear from the mathematical expression that the larger the length, the smaller the resonating frequency, and vice versa. The same behavior was examined in the full wave electromagnetic simulations and is represented in \[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]2 The resonating frequency observed is inversely proportional to the length of the dipole. The size of the initial design is estimated using Equation (9) for the lowest resonating frequency of 1.85 GHz. The length of feed and width of the rectangular dipole was chosen to be 5.7 and 4 mm, respectively, and the scattering plot obtained for this is illustrated in  
\[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]3 Scattering plot for different dipole lengths. \[R_{in}=24.7\,\left(\frac{\beta L_{d}}{2}\right)^{2.5} \tag{1}\]4 Better bandwidth can be achieved by escalating the radius of the dipole, which is equivalent to dipole width escalation. A multiple width dipole antenna is shown in Figure 7, which is capable of achieving the different resonance frequencies in accordance with the length and width combinations of multiple elements. The width and length of the dipole elements are considered as controlling elements to control the overall bandwidth and resonance of the antenna. The wideband achieved can be understood by arranging the desired resonating frequencies in ascending order.