**2.3 Fractional mode substrate-integrated waveguide filters**

The electric field distributions in the conventional SIW, half-mode SIW (HMSIW), quarter-mode SIW (QMSIW), eighth-mode SIW (EMSIW), sixteenth-mode SIW (SMSIW), and 32-mode SIW (TMSIW) cavities at the dominant (TE101) mode are shown in **Figure 5**. The symmetry planes A-A1, B-B1, C-C1, and D-D1 are considered to be magnetic walls, and the remaining planes are electric walls. The full-mode SIW cavity can be cut into half-modes by cutting along the symmetry line B-B1, as shown in **Figure 5b**. It is obvious that the fundamental mode remains unchanged and the volume is reduced by half. The HMSIW cavity can be cut into quarter modes along the O-A1 line, as shown in **Figure 5c**. Compared with HMSIW, QMSIW achieves a 50% reduction. The QMSIW can be reduced to the EMSIW by cutting the QMSIW cavity along the O-D1 line, as shown in **Figure 5d**. Similarly, the electric field distribution is unchanged. SMSIW and TMSIW can be obtained by cutting the EMSIW cavity along the O-E line and O-F line, respectively, as shown in **Figure 5e** and **f**. The resonant frequency and electric field distribution of all sub-modes remain the same.

It is worth noting that since the topology of the fractional mode technique is inherently open-structured, there will be undesired radiation leakage, which can

*SIW-Based Devices DOI: http://dx.doi.org/10.5772/intechopen.105421*

**Figure 5.**

*Electric field distributions of (a) full-mode SIW, (b) HMSIW, (c) QMSIW, (d) EMSIW, (e) SMSIW, (f) TMSIW [11].*

### **Figure 6.**

*Electric field distribution for the fundamental mode of the SIW resonators. (a) Conventional QMSIW cavity, (b) shielded QMSIW cavity [12].*

sometimes significantly reduce the quality factor. To solve this problem, some methods are applied. Taking quarter mode as an example, the shielded QMSIW is used to design the filter in Ref. [12]. As shown in **Figure 6**, the shielded quarter-mode resonator is made by placing two rows of metal through holes in the opening, which are called shield walls. Adding shielding walls can partially block the propagation of waves along the surface, reducing the efficiency of the radiating side of the structure. Compared with the conventional QMSIW, the shielded QMSIW exhibits better performance.
