# A Balanced Symmetrical Branch-Line Microstrip Coupler for 5G Applications
## 4 Conclusions  
In this paper, we designed a symmetrical microstrip coupler using a new structure and good performance for 5G applications. It displays a filtering frequency response with suppressed harmonics, while a large number of the previous works did not cover this issue. The design method is based on analyzing a lowpass resonator to calculate the scattering parameters and find the cut-off frequency. Based on changing the significant lengths and width, the final layout structure is optimized. The simulation results extracted from the optimization method verify the presented mathematical formulas. Using the analyzed resonator, two lowpass filters are designed to be embedded in the final layout of the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Refs** & **f\({}_{0}\) (GHz)** & **FR** & **LSFH (GHz)** & \begin{tabular}{c} **S\({}_{21}\)** \\ **(dB)** \\ \end{tabular} & \begin{tabular}{c} **S\({}_{31}\)** \\ **(dB)** \\ \end{tabular} & \begin{tabular}{c} **PU** \\ **(Degree)** \\ \end{tabular} & \
\begin{tabular}{c} **S\({}_{41}\)** \\ **(dB)** \\ \end{tabular} &
\begin{tabular}{c} **Size** \\ **(mm\({}^{2}\)/\({}_{\text{M}_{\text{g}}}\)\({}^{2}\))** \\ \end{tabular} \\ \hline Our coupler & 5.2 & Yes & 15.5 & \(-3.28\) & \(-3.56\) & 0.1 & 28.2 & 83.2/0.04 \\ \hline
[5] & 2.4 & No & No & \(-3.3\) & \(-3.3\) & 0.09 & 42.9 & 175.1/0.023 \\
[6] & 2 & No & No & \(-3.1\) & \(-3.4\) & 3 & 26 * & 1322/... \\ \hline
[7] & 0.93 & Yes & \(1.3\) * & \(-3.5\) & \(-3.5\) & — & Better than 20 & 673/0.017 \\ \hline
[8] & 2 & Yes & \(4.5\) * & \(-3.11\) & \(-3.39\) & 1 & — & 265.69/... \\
[9] & 2.9–4.1 & No & No & \(-5\) & \(-3\pm 1\) & 10 & 21 * & 1524.24/... \\ \hline
[10] & 3 & No & No & \(-7.38\) & \(-2.25\) & 2.3 & 21.5 & 819/... \\ \hline
[11] & 6.3 & No & No & \(-4.07\) & \(-4.39\) & 2.1 & 30 * & 2218/... \\ \hline
[12] & 1.07 & No & No & \(-3.3\) & \(-3.3\) & 1 & 24.2 & 204.9/... \\ \hline
[13] & 5.7 & No & No & \(-2.3\) & \(-2.6\) & 0.8 & 19.4 & 110/0.042 \\ \hline
[14] & 2.17 * & Yes & No & — & — & 5 & 15 & —/0.448 \\ \hline
[15] & 20–28.7 & No & No & \(-3\pm 1\) & \(-3\pm 0.8\) & 3 & 15 * & 595/0.307 * \\ \hline
[16] & 2.8 & Yes & 7 & \(-3.3\) & \(-2.9\) & 0.97 & 31.3 & 710/0.075 \\ \hline
[17] & 3.5 & No & No & \(-2.97\) & \(-3.65\) & 3.6 & 24.46 & 493/0.049 \\ \hline
[18] & 1.87 & Yes & No & — & — & 3 & Better than 20 & —/0.138 \\ \hline
[19] & 1.8 & No & No & \(-2.9\) & \(-3.2\) & 0.01 & 40 & 192.7/0.011 \\
[20] &... & Yes & No & \(-3.6\pm 0.5\) & \(-3.6\pm 0.5\) & — & Better than 20 & 1157.5/0.2379 * \\ \hline
[21] & 2.4 & No & No & \(-3\) & \(-3.08\) & 0.037 & 30 & 354.75/0.037 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison with the previous works (f\({}_{0}\): operating frequency; FR: filtering response; LSFH: last frequency with suppressed harmonics; PU: phase unbalance; *: approximated value; **: triple-band coupler). proposed coupler. Finally, we compared our coupler with previous works. The comparison results showed that we were able to obtain a high phase balance and good S\({}_{21}\) and S\({}_{31}\) without a significant increase in the coupler size. Conceptualization, L.N., M.A.C. and A.R. ; methodology, L.N., S.I.Y., F.H. and A.R. ; software, L.N. ; validation, S.I.Y., F.Z., F.H., M.A.C., M.A., B.N.L., Z.Y. and A.B; formal analysis, L.N., A.R. and F.Z. ; investigation, L.N. and A.R. ; writing--original draft preparation, L.N., F.Z., S.I.Y. and A.R. ; writing--review and editing, S.I.Y., F.Z., B.N.L., L.N., M.A. and Z.Y. ; supervision, F.Z., Z.Y., F.H., B.N.L. and L.N. ; project administration, F.Z., M.A.C., M.A. and L.N. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data Availability Statement: Data sharing is not applicable. The authors would like to acknowledge the funding support provided by the Higher Institution Centre of Excellence (HICOE), Ministry of Higher Education Malaysia, the through Wireless Communication Centre (WCC), Universiti Teknologi Malaysia (UTM) Vot. No.