# Design of a Compact Ultra-Wideband Microstrip Bandpass Filter
## 3 Parameter Analysis  
Several key parameters are studied to further analyze the characteristics of this filter. The main parameters for analysis are the bottom width \(W_{2}\) of the U-shaped microstrip lines on the top layer, length \(L_{6}\) of the wider side of the second coupling patch, diameter \(d_{0}\) of the blind holes on the third SIR branch lines, and width \(W_{9}\) of the wider rectangular slots in DGS. In Figure 5, the influence of length \(L_{6}\) of the wider side of the second coupling patch on RL is shown. With the increase of \(L_{6}\), the coupling area between the second coupling patch, the top coupling patch and the third-layer SIR branch lines gradually increases, thus improving reflection characteristics. When \(L_{6}=5.2\) mm, it can be seen that the curve  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(W_{0}\) & \(W_{1}\) & \(W_{2}\) & \(W_{3}\) & \(W_{4}\) & \(W_{5}\) & \(W_{6}\) & \(W_{7}\) & \(W_{8}\) & \(W_{9}\) & \(g_{0}\) \\ \hline
2.5 & 0.5 & 4.8 & 2.4 & 0.8 & 1.1 & 1.2 & 1.6 & 0.8 of reflection coefficient between the two resonance points in the passband is less than \(-20\) dB. It should be noted that the rectangular on the outside of the second coupling patch corresponds to the rectangular slots on the outside etched in the metal ground layer in the vertical position, the position of the resonance points in the passband will also be affected to some extent. \(L_{6}\) = 5.2 mm is finally determined as the optimal value. In Figure 6, the effects of width \(W_{2}\) of U-shaped microstrip line of top coupling patch on the reflection characteristics of the filter passband have been presented. With the increase of \(W_{2}\), the equivalent quarter-wavelength length of U-shaped SIR increases, which leads to the decrease of low-frequency cutoff frequency, and the two SIR branches whose lengths were \(L_{2}\) outside the U-shaped microstrip line will move outward with the increase of \(W_{2}\). It will affect the coupling with the lower layers and the receiving area of the reflected signal energy from the metal ground plane, so the reflection coefficient and the position of resonance frequency point in the passband will also change with the increase of \(W_{2}\). The in-band reflection coefficient achieves the best situation when \(W_{2}\) = 2.4 mm, which is better than 20 dB. Figure 7 shows the influence of diameter \(d_{0}\) of blind holes on high-frequency cutoff frequency and stopband harmonic suppression. Considering limitations of actual processing conditions, the change in \(d_{0}\) should be controlled within an accuracy of 0.1 mm. Generally, the design of blind holes will change coupling strength by adjusting the depth  
Figure 5: Simulation of S parameters when length \(L_{6}\) of the wider side of the second coupling patch is varied from 5 mm to 5.3 mm, with a step of 0.1 mm increment. Figure 6: Simulation of S parameters when width \(W_{2}\) of the U-shaped microstrip lines is varied from 4.4 mm to 5 mm, with a step of 0.2 mm increment. of the blind holes [26], and there are also designs that add vias or blind holes to change the current path, thus changing the resonance frequency [27]. The multilayer design in this paper needs to add RO4450 prepreg, so the change in depth is limited and the diameter of blind holes is changed for further analysis. As for the SIR on the third substrate, it can be regarded as a quarter-wavelength resonator, and the decrease in its length will lead to an increase in the corresponding high-frequency cut-off frequency. While \(d_{0}\) increases, which is equivalent to the decrease of the quarter-wavelength resonators, the corresponding high-frequency cut-off frequency will move to a higher frequency, and characteristics of high-frequency out-of-band harmonic suppression will also change. As \(d_{0}\) increases, the high-frequency cut-off frequency gradually moves to a higher frequency. Finally, \(d_{0}=0.4\) mm is determined as the optimal value under comprehensive consideration.