# Switchable Filter with Four Operating Modes Implemented on a 50-Ohm Microstrip Line
## 3 Wideband BPF and Dual-Band BPF
### Wideband BPF  
Type 4 structure has the same structure at the top and bottom, so it is sufficient to consider only the structure in Figure 3a. As illustrated in Figure 3b, the wideband BPF is constructed using two pairs of coupled transmission lines, each with an electrical length of \(\theta\) and characteristic impedances \(Z_{00}\) and \(Z_{0e}\) for the odd and even modes, respectively. Owing to the filter's symmetrical structure, its behavior can be effectively analyzed through  
Figure 2: (**a**) Various filter structures and (**b**) their corresponding simulation results. odd- and even-mode techniques, with the corresponding equivalent circuits depicted in Figure 3c,d. The even-mode input impedance of Figure 3c can be expressed by  
\[Z_{ine}=-\frac{\dot{j}}{2}(Z_{0e}+Z_{0o})\cot\theta \tag{1}\]  
and the input reflection is  
\[\Gamma_{e}=\frac{Z_{ine}-Z_{o}}{Z_{ine}+Z_{o}} \tag{2}\]  
Likewise, the odd-mode input impedance can be obtained  
\[Z_{ino}=j\;\frac{(Z_{0e}-Z_{0o})^{2}-(Z_{0e}+Z_{0o})^{2}\text{cos}\,\theta^{2} }{(Z_{0e}+Z_{0o})\text{sin}\,2\theta} \tag{3}\]  
Similarly, the corresponding input reflection is  
\[\Gamma_{o}=\frac{Z_{ino}-Z_{o}}{Z_{ino}+Z_{o}} \tag{4}\]  
Therefore, transmission and reflection coefficients of the proposed filter can be obtained as  
\[S_{21}=\frac{\Gamma_{e}-\Gamma_{o}}{2} \tag{5}\]  
\[S_{11}=\frac{\Gamma_{e}+\Gamma_{o}}{2} \tag{6}\]  
Figure 4a shows the simulation results of Type 4 (wideband BPF mode) according to the change in stub length, \(s\). The parameters for the simulation are the same as those mentioned above. From the simulation results, it can be confirmed that the stub length, \(s\), affects\(f_{2}\) and the transmission zero (TZ) frequency located on the right side of the passband in the wideband BPF mode. At this time,\(f_{1}\) hardly changed. As the stub length, \(s\), increases, the right skirt characteristic of the filter improves. In Figure 1, the longest \(s\) that can be implemented is 14.9 mm. Considering this fact, the stub length \(s\) is selected as 14.9 mm. Figure 3: Wideband bandpass filter. (**a**) Layout. (**b**) Transmission line model. (**c**) Even-mode equivalent circuit. (**d**) Odd-mode equivalent circuit. Figure 4b shows the electric field distribution at the TZ frequency of 6.57 GHz when \(s\) is 14.9 mm. The electric field is stronger as it approaches red and weaker as it approaches blue. In the simulation, the RF signal is set to the left for input and the right for output. Type 4 is a symmetrical structure based on the left and right, and the left and right sides operate as bandstop resonators of one wavelength each. As a result, the \(S_{21}\) of the filter exhibits good characteristics of about \(-50\) dB. Figure 5 shows the simulation results of the Type 4 structure according to the total filter length \(L\). From the simulation results, it can be seen that \(L\) has a significant effect on the first resonant frequency \(f_{1}\), and \(f_{1}\) decreases as \(L\) increases. Figure 6 presents the simulation results of Type 4 by changing the length of one of the two C-shaped resonators. In Figure 6, we will explain why the proposed structure operates as a wideband filter for Type 4 and a dual-band filter for Type 3. Here, when \(L_{\mathrm{C}}\) is 31.8 mm, it refers to the Type 4 structure. At this time, the 3 dB operating bandwidth is 1.98-5.18 GHz. The simulation results show that \(L_{\mathrm{C}}\) gradually decreases and when it reaches 28 mm, two TZs start to appear in the passband of the wideband BPF. Figure 4: **(a)** Simulation results of Type 4 according to stub length, \(s\). (**b**) E-field distribution at the transmission zero frequency. Red indicates the maximum e-field magnitude, while blue represents the minimum. Figure 5: Simulation results of Type 4 according to length \(L\). As \(L_{C}\) decreases, the frequency of the two TZs increases and becomes more distinct.