# Design and Development of a Wideband Planar Yagi Antenna Using Tightly Coupled Directive Element
## 5 Antenna Fabrication and Measurements
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Frequency** & **Gain** & **HPBW** & **HPBW** & **SLL** & **SLL** \\
**(GHz)** & **(dBi)** & **(E-plane)** & **(H-plane)** & **(E-plane)** & **(H-plane)** \\ \hline
2.9 & 6.5 & 63 & 88 & \(-15\) & \(-13\) \\
3.5 & 8.4 & 53 & 65 & \(-17\) & \(-12\) \\
3.8 & 8.2 & 45 & 53 & \(-14\) & \(-10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the proposed antenna radiation characteristics. Figure 7: Measured and simulated reflection coefficient response of the printed Yagi antenna. Figure 8: Simulated and measured normalized radiation patterns in E-Plane and H-plane of the proposed antenna, (**a**) \(f=3\) GHz, (**b**) \(f=3.5\) GHz and (**c**) \(f=4.0\) GHz. It is important to calculate the antenna's total efficiency as following [39]:  
\[\epsilon_{T}=\epsilon_{R}\times\epsilon_{lm} \tag{2}\]  
where, \(\epsilon_{R}\) and \(\epsilon_{lm}\), correspond to radiation efficiency and mismatch loss, respectively. Congruently, total efficiency is defined as the ratio of the total power radiated by the antenna to the total power input to the antenna [40]  
\[\epsilon_{T}=\ P_{md}/P_{input} \tag{3}\]  
however, the radiation efficiency comprises the conduction and dielectric losses and it can be calculated by the total power radiated by the antenna to the total power accepted by the antenna [40],  
\[\epsilon_{R}=P_{rad}/P_{accept} \tag{4}\]  
Figure 10: Snapshot photograph presenting the electric field distribution (**a**) with via-holes and (**b**) without via-holes. Figure 9: Simulated 3D radiation pattern patterns of the proposed antenna (**a**) \(f=2.75\) GHz and (**b**) \(f=3.5\) GHz. likewise, mismatch loss is [40]  
\[\epsilon_{lm}=1-\left|\Gamma\right|^{2} \tag{5}\]  
where, \(\Gamma\) correspond to voltage reflection coefficient at antenna's input terminal. If there is no mismatch at the input terminal of the antenna the radiation efficiency will correspond to the total efficiency. Antenna's radiation efficiency is very important figure of merit for its characterization. Many measurements methods such as pattern integration, directivity/gain, wheeler cap, sliding wall cavity and Q-factor has been developed to find antenna's radiation efficiency. A comprehensive discussion on different efficiency measurement methods is found in [40]. Among several state of the art techniques, efficiency calculation based on directivity and gain values is found to be simple, accurate and fast [40]. We know antenna's radiation efficiency is related to gain (G) and directivity (D) as following [34]:  
\[\eta=G/D \tag{6}\]  
and for a directional antenna the directivity is closely linked to the horizontal \(\theta_{HP}\) and vertical \(\varphi_{HP}\) beam-widths as following [41]:  
Figure 7:0  
Figure 7:1 Proposed Antenna’s (**a**) Gain vs. frequency (**b**) % efficiency vs. frequency and (**c**) time-domain excitation response received by the x-oriented probe. due to significant advancement in electromagnetic simulations tools, it is easy to determine antenna's directivity using numerical simulations. Therefore, antenna's radiation efficiency is calculated using measured gain and simulated directivity values as following [34]:  
Figure 7:2  
finally, having simulated and measured reflection coefficients values, the simulated and measured total efficiency is calculated by using (8) and (5). The graph presenting simulated and measured total efficiency is shown in Figure 11b. Due to higher dissipation factor of FR4, proposed antenna's efficiency is worse at higher frequencies. The antenna performance for a wide-band signal transmission can be characterized by calculating the following fidelity factor [42]:  
Figure 7:3  
where, \(x_{1}(t)\) and \(x_{2}(t)\) are transmitted and received signals, respectively. The antenna's response for a wideband excitation signal was recorded in the CST simulation program using an \(x\)-oriented Electric Far-field probe, which was placed at 500 cm toward the radiation direction (along \(y\)-axis).