## 2 Design and Micro-Nano Fabrication
### Design, Optimization and Analysis
#### 2.1.1 Filter Analysis and Optimization Based on Various Parameters  
To explore the influence of different dimensional parameters on the resonance characteristics of the proposed BPF, we varied the metal line width (15 \(\upmu\)m) and metal line gap (15 \(\upmu\)m) for simulation and analysis, as shown in Figure 2a. Tables 1 and 2 summarize the adjustments to line gap and line width, respectively, and a total of 16 detailed dimension information were utilized for the analysis. The line width of the text layer in the middle is always 4 \(\upmu\)m narrower than that of the bond and leads layers. Figure 1: Pattern design of the proposed BPF: (**a**) stereo view of the BPF on a GaAs substrate and enlarged view of the air-bridges; (**b**) side view and three metal layers (leads, text, and bond). Figure 2: Simulation results on the influence of the two parameters on the S-parameter and center frequency: (**a**) top view of the proposed IPD BPF layout with the markers of metal line width and gap; (**b**) simulation results with different line widths; (**c**) simulation results with different line gaps. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Bond Layer** \\ **(Line Width 15)** \\ \end{tabular} & \
\begin{tabular}{c} **Test Layer** \\ **(Line Width 11)** \\ \end{tabular} &
\begin{tabular}{c} **Leads Layer** \\ **(Line Width 15)** \\ \end{tabular} \\ \hline \multirow{4}{*}{**Line Gap**} & 13 & 17 & 13 \\  & 14 & 18 & 14 \\  & 15 & 19 & 15 \\  & 16 & 20 & 16 \\  & 17 & 21 & 17 \\  & 18 & 22 & 18 \\  & 19 & 23 & 19 \\  & 20 & 24 & 20 \\ \hline \hline \end{tabular} All data in the table are in micrometers.  
\end{table} 
Table 1: Dimensional information of the proposed IPD BPF line gap adjustment. As shown in Figure 2, the changes in physical parameters yielded different results. Figure 2b,c shows the influence of different metal line gaps and metal line widths on the resonant frequency and magnitude, respectively. To further explore the linear changes exhibited by the resonance, we conducted a linear analysis based on the experimental data, as shown in Figure 3.  
Figures 2 and 3 shows that the center frequency and magnitude increase as the gap increases, whereas the center frequency decreases as the width increases while the magnitude is barely moved. Combined with theoretical analysis, it can be seen that this result is reasonable. The center frequency increases with the increase of the line gap, because the coupling effect between the metal lines weakens and the capacitance becomes smaller; the center frequency decreases with the increase of the line width (gap remains unchanged), because the length of the metal line increases increased inductance [28; 29]. We decided to maintain the design of 15 \(\upmu\)m gap and 15 \(\upmu\)m width (center frequency of 1.55 GHz, amplitude of \(-26.43\) dB) after the above simulation and analysis, and the current density and group delay simulation are performed to verify the optimized performance of this design. As shown in Figure 4a, the current density at the frequency of the resonance point, that is, the passband, was significantly higher than that at the stopband. Additionally, the group delay is used to judge the distortion of the signal when it passes through the filtering system, that is, the smaller the group delay, the better the ability of the signal to maintain its shape. In this study, we used ADS to simulate the group delay directly. The group delay of the entire design is always lower than 1.25 ns, the time delay of the signal passing through the amplitude envelope of each sine component of the device under test is \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Band Layer** & **Test Layer** & **Leads Layer** \\  & **(Line Gap 15)** & **(Line Gap 19)** & **(Line Gap 15)** \\ \hline  & 13 & 9 & 13 \\  & 14 & 10 & 14 \\
**Line Width** & 15 & 11 & 15 \\  & 16 & 12 & 16 \\  & 17 & 13 & 17 \\  & 18 & 14 & 18 \\  & 19 & 15 & 19 \\  & 20 & 16 & 20 \\ \hline \hline \end{tabular} All data in the table are in micrometers.  
\end{table}