## 2 Transition Structure and Design  
### Working Principle and the Design of Transition  
E-plane probes are a class of typical structures for achieving mode conversion from the quasi-TEM mode of the microstrip line and the TE\({}_{10}\) mode of the rectangular waveguide. Figure 1 shows electric field diagrams of modes to clarify the working principle. When the E-plane probe is embedded in the rectangular waveguide, it can be considered as a coaxial line surrounded by the adjacent waveguide walls. The cross-sectional electric field (\(E\)-field) of the probe is shown in Figure 1a. The E-field is generated between the probe and the waveguide wall above the probe. Figure 1b displays the cross-sectional \(E\)-field of rectangular waveguide TE\({}_{10}\) mode. The wave vector (k) is along the z-direction. Therefore, to convert microstrip mode to waveguide mode, the extension direction of the E-plane probe should be parallel to the vector \(E\)-field of TE\({}_{10}\) mode. This relationship can be described as  
\[\overset{\rightarrow}{P}_{e}\parallel\overset{\rightarrow}{E}_{w}\]  
where \(\mathbf{P}_{e}\) and \(\mathbf{E}_{w}\) are the extension direction of the E-plane probe and the vector E-field of TE\({}_{10}\) mode, respectively. Figure 2 presents the E-field distribution of a backshort-circuited waveguide. It can be found that the E-field at the center reaches maximum at a quarter wavelength from the short-circuited surface. Thus, the above transition structure requires a backshort-circuited waveguide with a quarter wavelength for sufficient energy coupling and good impedance matching. Figure 1: The electric field distribution of different structures. (**a**) The probe embedded in waveguide. (**b**) The TE\({}_{10}\) mode of rectangular waveguide. Based on the above operating mechanism, a microstrip-to-waveguide transition is designed in the W-band. Figure 3 shows the configuration of the proposed microstrip-to-waveguide transition. It consists of an input 50 \(\Omega\) microstrip line, an E-plane probe with parasitic patch, a backshort-circuited waveguide, and an output WR 10 waveguide. The probe is connected to the end of the microstrip line and they are printed on a Ro 5880 substrate (permittivity \(\varepsilon_{r}=2.2\), loss tangent \(\delta=0.0009\)) with the thickness of 0.127 mm. To suppress parallel plate modes and prevent the leakage of energy, the waveguide in the substrate metal is surrounded by metal vias. The E-plane probe is embedded along the center of the waveguide broadside to excite the TE\({}_{10}\) fundamental mode. The backshort waveguide at the upper is usually \(\lambda\)g/4 (\(\lambda\)g is the operating wavelength at the center frequency). A groove is cut in the backshort waveguide to avoid contact between the microstrip line and the backshort waveguide. The transition is designed and optimized with the assistance of Ansys HFSS. Figure 4 shows the simulated S-parameters of the proposed transition. It can be seen that the reflection coefficient is less than \(-20\) dB in the entire W-band. The transmission coefficient varies between \(-0.3\) and \(-0.5\) dB from 70 to 112 GHz. The optimized design parameters are given in Table 1.  
Figure 3: The configuration of the proposed transition. (**a**) 3D view. (**b**) Top view. Figure 2: The electric field distribution of short-circuited waveguide. To verify the working principle, when the transition works at center frequency 90 GHz, the vector E-field on the probe and the cross-sectional E-field distribution in the rectangular waveguide are plotted in Figure 5. As shown in Figure 5a, the probe can couple energy to the parasitic patch through the gap. Thus, there is an intense E-field between the parasitic patch and probe. Then, a strong electric field is generated between the parasitic patch and the waveguide wall. The total E-field is along the -y-direction and it is similar to the E-field distribution of TE\({}_{10}\) mode. As a result, it can be seen from Figure 5b that the TE\({}_{10}\) mode is excited.