## 4 Results  
By substituting the proposed filter instead of the large \(\lambda/4\) and \(3\lambda/4\) main transmission line branches, the final RRC is achieved. The layout and frequency response of the proposed RRC is depicted in Figure 12. The obtained size of the proposed RRC is 0.20 \(\lambda\)\(\times\) 0.12 \(\lambda\), or 46.5 mm \(\times\) 27.5 mm. This shows a size reduction greater than 82% size reduction in comparison to the conventional RRC.  
The EM simulations response of the proposed RRC is depicted in Figure 12b. The EM simulation results show that the proposed RRC has desirable performance at an operating frequency of 950 MHz, with 180 MHz bandwidth. The insertion loss at 950 MHz is 0.01 dB and return loss is better than 19 dB. Additionally, the proposed RRC has a good performance at higher frequencies and both S\({}_{21}\) and S\({}_{31}\) curves have low values at harmonic frequencies. The harmonic suppression levels for 2 nd, 3 rd, 4 th and 5 th harmonics are more than 20 dB, 15 dB, 48 dB and 42 dB, respectively, which are the worst reported values for two curves of S\({}_{21}\) and S\({}_{31}\).  
The proposed RRC is fabricated on the Rogers 5880 substrate, which is shown in Figure 13. The measured results of the designed RRC are illustrated in Figure 14. As seen, the designed device works correctly at 950 MHz with 180 MHz bandwidth, which shows FBW of 19%. Additionally, the obtained magnitude of S\({}_{11}\), S\({}_{21}\), S\({}_{31}\), and S\({}_{41}\) at the operating frequency are \(-\)18 dB, \(-\)3.15 dB, \(-\)3.2 dB, and \(-\)19 dB, respectively. Four harmonics are suppressed in the proposed device with the suppression levels of, respectively, 23 dB, 15 dB, 46 dB, 42 dB. It can be concluded from Figure 14 that a wide suppression band is achieved for the proposed coupler. Conversely, the fabricated device correctly works at the  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{10}{c}{**Testing Values**} & & & & & & & & & & & \\ \hline \multicolumn{10}{c}{**Input Parameters**} & & & & & & & & & & & & & & \\ \hline \multicolumn{10}{c}{**Real Output Param.**} & & & & & & & & & & & & & \\ \hline \hline \multirow{2}{*}{\begin{tabular}{c} \(\mathrm{W_{1}}\) \\ (mm) \\ \end{tabular} } & \(\mathrm{W_{2}}\) & \(\mathrm{W_{3}}\) & \(\mathrm{L_{1}}\) & \(\mathrm{L_{2}}\) & \(\mathrm{L_{3}}\) & S\({}_{1}\) & S\({}_{2}\) & \(f_{\mathrm{c}}\) & STBW & IL & \(f_{\mathrm{c}}\) & STBW & IL \\  & (mm) & (mm) & (mm) & (mm) & (mm) & (mm) & (mm) & (GHz) & (MHz) & (dB) & (GHz) & (MHz) & (dB) \\ \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} 1 \\ 2 \\ 3 \\ 4 \\ 3.4 \\ 3.8 \\ 3.8 \\ 3.4 \\ 3.8 \\ 3.4 \\ 3.8 \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} 4 \\ 0.8 \\ 0.  
operating bandwidth with desired performance, while it provides harmonic rejection in higher frequencies with a high attenuation level.  
Figure 12: Proposed Rate Race Coupler: (**a**) layout and (**b**) frequency response.  
Figure 13: Fabricated prototype of the proposed Rate Race Coupler.  
The output phase difference of the proposed RRC device is shown in Figure 15. This phase difference corresponds to the phase difference of the output ports in the designed coupler. As is seen, the experimental values of \(-271.2^{\circ}\) are obtained at the operating frequency, which shows the high phase accuracy of the proposed coupler.  
The performance of the proposed coupler is compared with the other related works in Table 3. As can be seen in the table, the proposed RRC has the best performance, compared with the related works, in the terms of harmonic suppression and s  
Figure 14: Measured results of the proposed RRC.  
Figure 15: The output phase difference of the proposed RRC device.