# Switchable Filter with Four Operating Modes Implemented on a 50-Ohm Microstrip Line
## 3 Wideband BPF and Dual-Band BPF
### Dual-Band BPF  
If the structure includes two L-shaped resonators and one C-shaped resonator, as in Figure 7a, which is the same as Type 3 in Figure 2a, it operates as a dual-band BPF. The dual-band filter has two TZs, one located between the two passbands (\(f_{1}\) and \(f_{2}\)) and one located in the upper frequency band of the upper passband (\(f_{2}\)). The corresponding frequencies are referred to as \(f_{TZ1}\) and \(f_{TZ2}\), respectively. Figure 7b shows the simulation results of Type 3 as the stub length, \(s\), changes. As \(s\) increases, \(f_{TZ1}\) decreases. At this time, \(f_{TZ2}\), which exists on the right side of \(f_{2}\), shows a tendency to decrease slightly.  
Figure 8a,b show the E-field distribution formed at the transmission zero frequency, respectively. As can be seen from the field distribution, the stubs are operating as \(\lambda/4\) resonators and \(\lambda\) resonators, respectively. The field distributi  
Figure 6: Simulation results of Type 4 according to \(L_{C}\) length. (a) \(S_{11}\); (b) \(S_{21}\).  
Figure 7: (a) Structure of Type 3 in Figure 2a is reused for clarity. (b) Simulation results of Type 3 according to length, \(s\).  
identical to that in Figure 4b. When operating in dual-band filter mode, the second TZ is identical to the right TZ in the wideband filter mode.  
Figure 9 shows the simulated \(S_{21}\) response of the Type 3 structure as the length \(L_{\text{C}}\) changes. According to the simulation results, as the length of \(L_{\text{C}}\) decreases, \(f_{2}\) shifts significantly to higher frequencies, and \(f_{1}\) also increases, but the change is relatively small. This indicates that the change in the length \(L_{\text{C}}\) of the C-shaped resonator is more sensitive to the higher resonant frequency \(f_{2}\).  
Figure 10 shows the electric field distribution at two resonant frequencies \(f_{1}\) and \(f_{2}\) of Type 3 with dual-band BPF characteristics. The parameter settings for the simulation are as follows: \(L\) = 30 mm, \(s\) = 14.9 mm, \(L_{\text{C}}\) = 32.7 mm, \(g\) = 0.1 mm. As shown in the figure, in the case of Type 3, the RF signal is well transmitted along the lower path at both resonant frequencies. On the other hand, a strong electric field is formed between the gaps in the upper path, and the electric field cannot pass from left to right. At \(f_{1}\), one null exists in the center, and at \(f_{2}\), two nulls exist, operating at half-wavelength and one-wavelength, respectively.  
Figure 11 shows the \(S_{21}\) simulation results of the Type 3 structure according to the change in length \(L\). The length, \(L\), is a parameter that affects both the main resonant frequencies \(f_{1}\) and \(f_{2}\). According to the simulation results, as the length of \(L\) increases, the two resonant frequencies \(f_{1}\) and \(f_{2}\) shift to lower frequencies, respectively. This occurs because an increase in length, \(L\), extends the structure's effective electrical length, thereby lowering the resonant frequency.  
Figure 8: E-field distribution at (**a**)\(f_{TZ1}\) and (**b**)\(f_{TZ2}\).  
Figure 9: Simulation results of type 3 according to the length \(L_{\text{C}}\) of the C-shaped resonator.