## 4 Results and Discussion
### Dimensional Analysis  
Table 1 presents the physical and electrical dimensions of some fabricated structures. We normalize the electrical dimensions according to the free-space wavelength (\(\lambda_{0}\)) at the operating frequency. For the 28 GHz 5G band (24.25-29.5 GHz), we use \(f_{c}\) as 26.875 GHz with a \(\lambda_{0}\) of 11.16 mm. For the 39 GHz band, we use \(f_{c}\) as 38.5 GHz with a \(\lambda_{0}\) of 7.8 mm. For the diplexers and integrated versions, we use the 24.25-40 GHz band with a \(\lambda_{0}\) of 9.34 mm. Table 2 compares filters that use various substrate technologies for mm wave applications, highlighting laminated glass-based filters as compact IPD structures. Table 3 compares diplexers regarding center frequency (\(f_{cL}\) and \(f_{cH}\)), bandwidth, insertion loss and size.  
Figure 14: Comparison of simulated and measured results of diplexers: (**a**) interdigital for bands n258 and n260, and (**b**) edge–coupled for combined bands n257 and n258, and n260.  
Figure 15: Comparison of simulated and measured results: (**a**) three-section coupled–line coupler, and (**b**) integrated passive component block.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Structure** & **Physical Dimensions (mm\({}^{3}\))** & **Electrical Dimensions (\(\lambda_{\Phi}^{3}\))** \\ \hline Filter—Hairpin n257 & 4.64 \(\times\) 2.11 \(\times\) 0.202 & 0.42 \(\times\) 0.19 \(\times\) 0.018 \\ \hline Filter—Interdigital n258 & 2.94 \(\times\) 2.76 \(\times\) 0.202 & 0.26 \(\times\) 0.25 \(\times\) 0.018 \\ \hline Filter—Edge-coupled n260 & 6.09 \(\times\) 0.75 \(\times\) 0.202 & 0.78 \(\times\) 0.10 \(\times\) 0.026 \\ \hline Diplexer—Hairpin n257 and n260 & 5.85 \(\times\) 4.42 \(\times\) 0.202 & 0.63 \(\times\) 0.47 \(\times\) 0.022 \\ \hline Diplexer—Hairpin n258 and n260 & 6.42 \(\times\) 4.67 \(\times\) 0.202 & 0.69 \(\times\) 0.50 \(\times\) 0.022 \\ \hline Diplexer—Interdigital n258 & 4.4 \(\times\) 4.6 \(\times\) 0.202 & 0.47 \(\times\) 0.49 \(\times\) 0.022 \\ \hline Diplexer—Edge-coupled n257, n258 and n260 & 11.2 \(\times\) 8.49 \(\times\) 0.202 & 1.2 \(\times\) 0.91 \(\times\) 0.022 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and electrical dimensions of select fabricated structures.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ref.** & **Substar/Structure** & **Order** & **II. (dB)** & \(f_{e}\) (GHz) & **BW (GHz)** & **Footprint (mm\({}^{3}\))** & **Footprint (\(\lambda_{\Phi}^{2}\))** & **Total Substrate Thickness (mm)** \\ \hline
[35] & LTCC/SIW & 2 & 0.53 & 28.1 & 4.29 & 33.5 & 0.294 & 0.47 \\ \hline
[36] & LTCC/SIW & 4 & 2.66 & 27,45 & 0.98 & 43.5 & 0.364 & 0.47 \\ \hline
[37] & LTCC/SIW Cavity & 4 & 2.95 & 30 & 1.4 & 88 & 0.88 & 0.47 \\ \hline
[38] & LTCC/Stacked SIW & 4 & 2.8 & 27,95 & 1.03 & 19.7 & 0.171 & 0.4 \\ \hline
[39] & Rogers Laminate/SIW & 4 & 1.25 & 35 & 1.3 & 121 & 1.65 & 0.508 \\ \hline
[40] & Rogers Laminate/SIW & 4 & 3.6 & 29.375 & 3.75 & 81 & 0.777 & 0.3 \\ \hline
[41] & Alumina/Microstrip & 3 & 3 & 38.5 & 3 & 7.1 & 0.117 & 0.254 \\ \hline
[42] & Rogers Laminate/Air-filled SIW & 4 & 3.9 & 21 & 0.23 & 746 & 3.66 & 1.524 \\ \hline This Work & Laminated Glass/Microstrip & 5 & 2.6 & 28 & 3 & 9.8 & 0.079 & 0.202 \\ \hline This Work & Laminated Glass/Microstrip & 5 & 2.6 & 25.875 & 3.25 & 8.11 & 0.065 & 0.202 \\ \hline This Work & Laminated Glass/Microstrip & 4 & 2.6 & 38.5 & 3 & 4.6 & 0.078 & 0.202 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of filters using various substrate technologies for mm wave applications.