## 4 Discussion  
The characteristic of the proposed BPF is to insert the T-shaped BSF into the BPF. Therefore, the designed BPF was able to obtain dual-band characteristics. Traditional BPFs simultaneously used the method of increasing mode, SLR method, and SIR method to increase bandwidth [2; 3; 4; 5; 6; 7]. This method was able to adjust bandwidth and size by simultaneously adjusting the ratio of impedance and stub length. In particular, adjusting the length of the stub was able to create a transmission-zero [16]. Therefore, it was possible to design filters with excellent skirt phenomena. However, it is analyzed that these filters still increase in insertion loss and size [8; 9; 12]. The proposed BPF applied SLR and SIR at the same time. Thus, the filter can directly adjust the ratio of impedance to stub length. As a result, the filter was able to expand its bandwidth. The filter was also reduced in size using a folded structure.  
Another attraction of the filter is the transmission-zero characteristics by adjusting the length (\(l_{d}\)) of open stubs (see M\({}_{\Gamma}\) of Figure 1a) as shown in Figure 3b. This can achieve a sharp cut-off frequency characteristic. The proposed filter is an advantage of a wide bandwidth based on dual-mode. Table 2 lists a comparison of the proposed BPF with some others proposed previously. In this table, the bandwidths, insertion losses, and sizes are compared.  
In the table, [20] is quarter-band BPF. Then, the center frequencies are 1.34 GHz, 2.2 GHz, 3.32 GHz, and 4.4 GHz, and the insertion losses are 1.32 dB, 1.26 dB, 2.23 dB, and 1.99 dB at first to fifth center frequencies. In addition, the return losses are 16.37 dB, 24.63 dB, 17.39 dB, and 22.48 dB at first to fifth center frequencies. The bandwidth is 5.22%, 3.63%, 4.2%, and 9.6% at first to fifth center frequencies, respectively. The proposed BPF is lower insertion losses better than the comparison of BPFs, and the BPF is lower return losses less than others. Additionally, the size of a BPF is smaller more than other BPFs, and the bandwidth of a BPF is wider more than others.  
The proposed filter is used for SLR and SIR together. Therefore, the filter is used to short-stub. The characteristic of Stub-filter is very sensitive to impedance [30]. If the filter had a narrow band, the impedance value would be very low. Therefore, the width of the stub will be very wide, and the size of the filter will be increased. If the filter has broadband, the impedance value will be very high. Thus, the filter will have a very narrow stub area. Therefore, it will be very difficult to produce filters.  
When SLR and SIR are used together, both bandwidth and size can be adjusted by adjusting the ratio of impedance value to stub length [10; 11].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref [\#]**} & \multicolumn{3}{c}{\(f_{0}\) [GHz]} & \multicolumn{3}{c}{\(I_{L}\) [dB]} & \multicolumn{3}{c}{\(R_{L}\) [dB]} & \multicolumn{3}{c}{\(\Delta\) [\%]} & \multicolumn{3}{c}{**Size**} \\ \cline{2-13}  & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) & \(f_{\Delta}\) \\ \hline this work & 2.43 & 7.49 & - & 0.102 & 0.102 & - & 19.13 & 19.96 & - & 120 & 105 & - & 0.0708 \(\times\) 0.0533 \\ [2] & 1.57 & 2.40 & 3.45 & 0.41 & 1.39 & 1.97 & 27.7 & 12.3 & 16.2 & 20.0 & 7.40 & 5.50 & 0.54 \(\times\) 0.44 \\ [4] & 2.4 & 5.80 & - & 1.35 & 1.97 & - & 17.0 & 15.0 & - & 4.63 & 3.60 & - & 0.39 \(\times\) 0.25 \\ [6] & 2.45