*2.3.1 Half-mode SIW (HMSIW) filters*

The half-mode substrate-integrated waveguide was proposed by Wei Hong et al. in 2006 [13]. This waveguide structure is obtained by cutting the SIW so that the symmetry plane along the transmission direction is equivalent to the magnetic wall.

As shown in **Figure 7**, the HMSIW is 50% smaller in size while keeping the electric field distribution unchanged. Since the volume of HMSIW is reduced by half and the propagation characteristics remain unchanged, it has attracted the attention of many scholars.

A compact dual-band filter based on HMSIW is shown in **Figure 8** [14]. The dualband filter is designed by the quasi-TEM mode and the TE102 mode of the novel HMSIW resonator. The resonant frequency of TE102 can be adjusted by the slot line, which has little effect on the performance of the quasi-TEM mode. To improve the out-of-band rejection, the source negative coupling structure is applied. The measurement results show that the first and second passbands are mainly concentrated at 2.41 and 3.51 GHz, the relative bandwidths are 10.8% and 6.4%, respectively, and the minimum insertion losses of the two passbands are 1.45 and 1.74 dB, respectively.

**Figure 7.** *Dominant field distribution in HMSIW and SIW [13].*

**Figure 8.** *Configuration of the proposed dual-band filter [14].*
