# A Review on SIW and Its Applications to Microwave Components
## 3 SIW Design Basics  
The structure of the substrate-integrated waveguide transmission line is presented in Figure 3. This physical geometry indicates the formation of the SIW by inserting a dielectric substrate in the middle of two opposite metal plates. The side walls of the SIW structure are achieved using two lines of regular metallic vias positioned adjacent to the lengths of the substrate. This is equivalent to the metal sidewalls of the conventional waveguide.  
Figure 1: SIW structure development. (**a**) Air-filled rectangular waveguide. (**b**) Dielectric-filled rectangular waveguide. (**c**) Substrate-integrated waveguide.  
Figure 2: The \(TE_{1,0}\) mode surface current distribution of a conventional rectangular waveguide with metallic holes on the thin side walls.  
Three fundamental design parameters must be considered when designing the substrate-integrated waveguide to function at an assigned frequency. These parameters are shown in Figure 4 and include the substrate-integrated waveguide width, \(w\), the metal via diameter, \(d\), and the space or separation length between adjacent metal vias (that is, the pitch), \(p\). Similar to the width of the conventional rectangular waveguide, the substrate-integrated waveguide width relates to the cut-off frequency of its propagation mode. The \(d\) and the \(p\) parameters define the close relationship between the substrate-integrated waveguide structure and the rectangular waveguide. Reducing the value of \(p\) to to \(d\)/2 essentially reduces the SIW to a regular dielectric-filled waveguide. Increasing the value of \(p\) increases the amount of the SIW deviation from the conventional rectangular waveguide, with more EM energies emitting outward in the middle of the vias. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) show that radiation loss is negligible for an electrically small metallic via; that is, \(d<0.2\lambda\) (\(\lambda\) is the dielectric material wavelength), with a d/p ratio of half.  
The physical size of the substrate-integrated waveguide cavity, at its basic \(TE_{101}\) mode, is calculated based on the matching resonance frequency, \(f_{101}\) as provided in Equation (1) [16]. The design parameter \(w_{\mathit{eff}}\) gives the substrate-integrated waveguide effective width, \(l_{\mathit{eff}}\) gives its effective length, \(\mu_{r}\) is the substrate relative permeability (\(\mu_{r}=1\) if substrate material is non-magnetic), \(\varepsilon_{r}\) is the substrate material dielectric constant, while \(c_{0}\) gives the free space speed-of-light. Experimental formulations for the \(w_{\mathit{eff}}\) and the \(l_{\mathit{eff}}\) are provided in Equation (2) [12], with the simplified versions given in Equation (3) [13; 17]. It is important to note that Equations (2) and (3) are different versions of the same formula  
Figure 4: Substrate-integrated waveguide fundamental design parameters.  
Figure 3: Physical structure of the substrate-integrated waveguide transmission line.  
tion. Hence, both equations will return approximately the same value when applied in a calculation. Equation (3) is just a simplified version of Equation (2).  
\[f_{101}=\frac{c_{0}}{2\pi\sqrt{\mu_{F}\epsilon_{F}}}\Bigg{[}\left(\frac{\pi}{w_{ eff}}\right)^{2}+\left(\frac{\pi}{l_{eff}}\right)^{2}\Bigg{]}^{0.5} \tag{1}\]  
\[\left\{\begin{array}{c}w_{eff}=w-1.08\frac{d^{2}}{P}+0.1\frac{d^{2}}{w}\\ l_{eff}=l-1.08\frac{d^{2}}{P}+0.1\frac{d^{2}}{T}\end{array}\right\} \tag{2}\]  
\[\left\{\begin{array}{c}w_{eff}=w-\frac{d^{2}}{0.95P}\\ l_{eff}=l-\frac{d^{2}}{0.95P}\end{array}\right\} \tag{3}\]