# W-Band 4 th Order Waveguide Filter Based on Double Layer SU8 Microfabrication
## 4 Measurement Results and Discussion
### Stress and Deformation Analysis of the Fabricated SU8 Chips during Measurement  
Waveguide transmission lines and many screw holes and alignment pin holes are added to the SU-8 chip, which makes the SU-8 chip discontinuous, resulting in the largest local stress. To ensure that the applied pressure does not exceed the \(-15\)\(\upmu\)m maximum limit of the corresponding deformation amount, it is necessary to analyze the stress and deformation finite element using ANSYS. The most deformed part of the SU-8 chip is mainly concentrated in the filter at the center of the chip. In the actual measurement, the SU-8 chip needs to be measured with the help of two kinds of pressing blocks. Therefore, the stress on the SU-8 chip is mainly concentrated in the z-direction, which has been verified in ANSYS. The physical properties of SU-8 polymer are as follows: Tensile strength of 60 Mpa, Young's Modulus of 2.0 Gpa, Elastic Modulus of 4.6 Gpa, and Poisson's ratio of 0.25. The bottom surface of the lower pressure block of pressure block I is set as a fixed support, and the top screw hole of the upper-pressure block exerts a pressure of 10.55 N/m\({}^{2}\) on the area of the wire of the wire. The deformation of the fabricated filter is 0.11 \(\upmu\)m, as shown in Figure 14a. Under the pressure of 10.55 N/m\({}^{2}\), the deformation of the designed filter under the action of the pressing block II is 0.43 \(\upmu\)m, as shown in Figure 14c. Under the action of pressing block II, the maximum stress that the SU-8 chip can withstand is about 253 N/m\({}^{2}\), so the maximum deformation of the filter is controlled within 15 \(\upmu\)m, as shown in Figure 14d. The same pressure of 253 N/m\({}^{2}\) was applied to the SU-8 chip under the action of pressing block I, and the deformation of the designed filter is 2.6 \(\upmu\)m, as shown in Figure 14b. The above analysis shows that the cavity filter fabricated by the SU-8 process using the pressing blocks-assisted measurement has good mechanical properties for mmW applications. Figure 1d shows the effects of deformation on filter performance under the stress of the above four cases. It illustrates that there is less impact on the overall filter performance in the deformation of 15 \(\upmu\)m.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Design \({}^{\star}\)** & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(r_{4}\) & \(w_{1}\) & \(l_{a}\) & \(l_{b}\) \\ \hline Value & 1233.5 & 1188.9 & 401.4 & 498.2 & 1127.2 & 1631 & 736.2 \\ Measured \({}^{\star}\) & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(r_{4}\) & \(w_{1}\) & \(l_{a}\) & \(l_{b}\) \\ Value & 1206.8 & 1153.8 & 421 & 495.2 & 1106.2 & 1592.5 & 721 \\ \(\Delta l\) & 26.7 & 35.1 & 19.6 & 3 & 21 & 38.5 & 15.2 \\ Steepness & 1.24 & 1.63 & 0.91 & 0.14 & 0.98 & 1.79 & 0.7 \\ \hline \hline \end{tabular} \({}^{\star}\) parameter. \(\Delta l\) = designed dimensions—measured dimensions.  
\end{table}
Table 2: Designed and measured physical dimensions for the SU-8 fabricated filter (unit: \(\upmu\)m).  
Figure 14: Finite element analysis of stress and deformation of the SU-8 chips with applied forces of 0.1 MPa (**a**,**c**) and 0.04 MPa (**b**,**d**) under the action conditions of pressure block 1 (**a**,**b**) and pressure block 2 (**c**,**d**). (**e**) The effects of deformation under the stress of the above four cases.  
Figure 13: Measurement results and simulation results using metal block I. (**a**) Responses over the whole \(W\)-band. (**b**) Expanded view of \(S_{21}\) over the passband.