*2.3.3 Eighth-mode SIW (EMSIW) filters*

The QMSIW can be further bisected into two parts along the symmetrical plane with one electric wall and two magnetic walls forming the EMSIW.

The authors of Ref. [17] reported a systematic research campaign on the EMSIW filter. The authors conducted a series of studies on eighth-mode filters. Compared with the traditional SIW cavity, the one-eighth mold cavity has a compact size. This paper first explores the four feeding modes of the eighth mode, then designs a variety of bandpass filters for the eighth mode utilizing electrical coupling and magnetic coupling, and finally designs two bandpass filters. The first filter takes the form of a combination of an eighth mode and a coplanar waveguide. Through the mutual coupling between the TE101 mode of the two EMSIW cavities and the quasi-TEM mode of the folded coplanar waveguide, a band-pass filter with a center frequency of 9.1 GHz is finally designed. The second filter adopts a multi-layer process, and the upper and lower substrates are coupled through two rectangular slots. Compared with filter 1, this filter has more transmission zeros. The proposed EMSIW BPFs have the merits of being compact in size and high selectivity. The geometry of the two filters is shown in **Figures 12** and **13**.

## *2.3.4 High-mode SIW (SMSIW and TMSIW) filters*

A miniaturized bipolar bandpass filter based on a SMSIW was investigated [18]. The geometry of the filter is shown in **Figure 14**. The filter operates in fundamental mode TM01. Under the same resonant frequency, the size of the SMSIW cavity is only 1/16 of that of the traditional SIW cavity. To suppress the higher-order mode TM02, a rectangular slot is etched in the ground plane below the transmission line. The overall size of the filter is compact and has good out-of-band performance.

**Figure 12.** *Geometry of the triple-order EMSIW BPF with CPW [17].*

**Figure 13.** *Geometry of the triple-order EMSIW BPF with QMSIW cavity [17].*

A TMSIW bandpass filter is presented in Ref. [19]. The geometry of the filter is shown in **Figure 15**. By adjusting the position of the feed and the coupling distance, the frequency position of the passband can be selectively achieved. The TM0n0 mode has a good unloaded quality factor in addition to providing different frequency options. In addition, the perturbation of the arc slot can effectively tune the coupling and achieve high selectivity.
