**2.4 SIW filters loaded with complementary Split-ring resonators (CSRR)**

As an electromagnetic metamaterial, CSRR is often used in the miniaturization of filters. CSRR is an electrical resonator that can be excited by an axial electric field, which is proposed by Pendry [20]. In Ref. [21], two HMSIW filters loaded with the stepped-impedance CSRRs are presented. The geometries of the two filters are shown

**Figure 14.** *Geometry of the proposed filter [18].*

**Figure 15.** *Geometry of the triple-order EMSIW BPF with QMSIW cavity [19].*

in **Figure 16**. By loading both CSRR and stepped-impedance complementary split-ring resonator (SICSRR) into the two sides of the HMSIW cavity, a dual-band resonator is formed. By adjusting the size of CSRR and SICSRR, the position of the two passbands can be flexibly adjusted. Compared with other dual-band filters, the HMSIW-SICSRR filter size is reduced by 48.5% and 50%, respectively.

Novel bandpass filters are reported by using HMSIW loaded with CSRR and a capacitive metal patch [22]. The geometry of the proposed filter is shown in **Figure 17**. Based on this combined structure, independent double passbands can be generated. In addition, the external quality factor and coupling factor of the two frequency bands can be adjusted independently.
