**5.3 NWSIW EBG filter**

As last illustration in this chapter, **Figure 13** presents the topology of the so-called EBG filter (for Electromagnetic Band Gap) realized in NWSIW technology. The EBG effect associated to periodic structures was introduced in the '90s [11, 30–32]. The filter is based on the cascade of three NWSIW sections partially filled with Nickel MNW and separated by empty NWSIW sections.

Measurement of transmission in **Figure 14** shows that a gap in the transmission occurs at 20 GHz. It is created by the contrast between the dielectric constant of AAO

#### **Figure 13.**

*Topology of EBG filter in NWSIW technology. Blue NW form vertical walls of NWSIW, while red NW having filling height h = 75% are grown in the NWSIW in order to create the EBG effect. Electroplated copper metal layers (orange) form bottom and top walls of NWSIW.*

#### **Figure 14.**

*Measured transmission in EBG filter in NWSIW technology. Inset: Photograph before electroplating realized at step 5 of Figure 10.*

*Challenges and Perspectives for SIW Hybrid Structures Combining Nanowires and Porous… DOI: http://dx.doi.org/10.5772/intechopen.105148*

**Figure 15.** *Influence of filling height of NW on dielectric constant.*

empty sections and the much higher value of dielectric constant for sections partially filled with Ni NW over a relative filling factor h. The behavior of the dielectric constant versus h is shown in **Figure 15** and was initially introduced in [15]. The generation of the bandgap at a dedicated frequency fo requires that the length of each section, empty and filled, is equal to a quarter wavelength at fo. This condition is expressed by equations (7–8):

$$L\_{\text{empty section}} = \frac{\varepsilon\_o}{4 \int\_{\mathcal{O}\_o} \varepsilon\_r \, \text{empty}} = 2.6 \,\text{mm.}\tag{7}$$

$$L\_{\text{filled section}} = \frac{\mathcal{L}\_o}{4 \int\_{\mathcal{O}} \varepsilon\_r \,\mathrm{g}\_{r\,\mathrm{filled}}} = 5.1 \,\mathrm{mm} \tag{8}$$

The realized filter has a filling factor h = 75% yielding 34 as value for εr filled, while dielectric constant of empty AAO with P = 4% is close to 9.8. The contrast between dielectric constant of filled and empty sections is high and responsible for the bandgap at fo = 20 GHz. The depth of the bandgap is �50 dB, which, compared to the maximal transmission level of - 25 dB, means a stopband rejection effect of 25 dB.
