## 4 Conclusions  
In this study, a microscale QFN-packaged BPF consisting of a centrally embedded capacitor and two intertwined spiral inductors was developed using GaAs-based IPD technology. The equivalent circuit model was established, taking capacitive and inductive parasitic effects into consideration. The three-layer IPD technology fabrication flow using thin-film and photolithography processes was presented in 25 steps. The fabricated BPF highlights a miniaturized overall size of 0.021 \(\lambda_{0}\times 0.021\)\(\lambda_{0}\) (0.8 \(\times\) 0.8 mm\({}^{2}\)). The measured results show a relatively good consistency with theoretical prediction and simulation, with a low insertion loss of 0.38 dB, and an ultrawide 3-dB FBW \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Technology**} & **Fractional Band** & **Passband** & **Insertion** & **Return** & \multirow{2}{*}{**Circuit Area**} \\  & & **Width (\%)** & **(GHz)** & **Loss (dB)** & **Loss (dB)** & & \\ \hline
[31] & Silicon IPD & 107.63 (3 dB) & 6.5 & 1.1 & 15 & 0.219 \(\lambda_{0}\times 0.181\)\(\lambda_{0}\) \\
[32] & Silicon IPD & 33.33 (3 dB) & 2.4 & 2.3 & 10 & 0.024 \(\lambda_{0}\times 0.024\)\(\lambda_{0}\) \\
[33] & Silicon IPD & 16 (10 dB) & 1.7 & 2.56 & 12 & 0.039 \(\lambda_{0}\times 0.037\)\(\lambda_{0}\) \\
[34] & Glass IPD & 49.62 (3 dB) & 2.6 & 0.6 & 30 & 0.018 \(\lambda_{0}\times 0.009\)\(\lambda_{0}\) \\
[35] & Glass IPD & 36.73 (10 dB) & 2.1 & 3.2 & 22 & 0.019 \(\lambda_{0}\times 0.019\)\(\lambda_{0}\) \\ This work & GaAs IPD & 71.94 (3 dB) & 2.21 & 0.38 & 26.45 & 0.021 \(\lambda_{0}\times 0.021\)\(\lambda_{0}\) \\  & & & & & & (0.8 \(\times\) 0.8 mm\({}^{2}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of proposed BPF and published BPFs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Technology**} & **Fractional Band** & **Insertion** & **Return** & **Passband** & \multirow{2}{*}{**Circuit Area**} \\  & & **Width (\%)** & **Loss (dB)** & **Loss (dB)** & **(GHz)** & \\ \hline
[36] & Microstrip & 13.3 & 1.1 & \(>\) 20 & 0.975 & 0.094 \(\lambda_{0}\times 0.08\)\(\lambda_{0}\) \\
[37] & HTS & 2.6/2.4 & 0.18/0.32 & \(>\) 16 & 1.9/2.6 & 0.182 \(\lambda_{0}\times 0.156\)\(\lambda_{0}\) \\
[38] & HTCC & 5.5 & 1.8 & \(>\) 15 & 2.25 & 6.9 \(\times\) 39.9 mm\({}^{2}\) \\
[39] & LTCC & 12.5 & 2.4 & 15 & 2.4 & 0.058 \(\lambda_{0}\times 0.058\)\(\lambda_{0}\) \\ This work & GaAs IPD & 71.94 & 0.38 & 26.45 & 2.21 & 0.021 \(\lambda_{0}\times 0.021\)\(\lambda_{0}\) \\  & & & & & & (0.8 \(\times\) 0.8 mm\({}^{2}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons between this work and other works using various manufacturing technologies. Figure 7: Simulation and measurement results: (**a**) parameters S\({}_{11}\) and S\({}_{21}\); (**b**) group delay. of 71.94%. The proposed BPF can be employed in a modern communication system owing to its high performance and miniaturized size as a result of the GaAs-based IPD fabrication technology. However, the lifecycle and compatibility of the proposed BPF in practical application were not investigated in this study; furthermore, its selectivity is limited by it as a low-order device, and its sensitivity will be verified in our future research to promote the practical application of the IPD technology. Conceptualization, [PERSON] and E.-S.K. as co-first authors; methodology, [PERSON]; software, J.C.; validation, J.C.; formal analysis, J.C.; investigation, J.C.; resources, J.C.; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, Z.-J.W., B.-H.Z., E.-S.K., and N.-Y.K. ; visualization, [PERSON]; supervision, N.-Y.K. ; project administration, E.-S.K. and N.-Y.K. ; funding acquisition, E.-S.K. and N.-Y.K. as co-corresponding authors. All authors have read and agreed to the published version of the manuscript.