## 3 Integration of the Dual-Mode Converter and the Conical Horn Antenna  
This section presents the integration of the previous mode converters into the Dual-Mode Converter (DMC). Furthermore, the DMC will be also integrated later with a Conical Horn Antenna (CHA), leading to the Dual-Mode Conical Horn Antenna (DM-CHA). Integration of the \(TE_{10}{}^{rec}\)-\(TE_{11}{}^{cir}\) and \(TE_{10}{}^{rec}\)-\(TE_{01}{}^{cir}\) Mode Converters for Obtaining the Dual-Mode Converter (DMC)  
The previous Section 2 has introduced two mode converters operating separately. Now, both converters are combined and connected to each other to form a Dual-Mode  
Figure 5: Schematic view of the mode converter from the \(TE_{10}{}^{rec}\) mode in the rectangular waveguide to the \(TE_{01}{}^{cir}\) mode in the circular waveguide. (**a**) Structure for the mode converter. (**b**) The electric field of the modes related to rectangular waveguide (_port_ 1, \(\Delta\)) and circular waveguide (_port_ 2). Figure 6: Simulated S-parameters of the mode converter in Figure 5, from \(TE_{10}{}^{rec}\) mode in the rectangular to the \(TE_{01}{}^{cir}\) mode in the circular waveguide. (**a**) Return loss at the rectangular waveguide for the \(TE_{10}{}^{rec}\). (**b**) Generation of higher order modes at the circular waveguide when the mode converter is excited by the \(TE_{10}{}^{rec}\) mode at the rectangular waveguide. Converter (DMC) as presented in Figure 7. The DMC is a device with three physical ports: two rectangular input ports working with their corresponding \(TE_{10}{}^{rec}\) mode (nominal WR-28 rectangular waveguides in _port_ 1 to excite the sum \(\Sigma\) pattern, and _port_ 2 for the difference \(\Delta\) pattern), and one circular output port of diameter 10 mm (_port_ 3). This last port has two working modes, the \(TE_{11}{}^{cir}\) and \(TE_{01}{}^{cir}\), with cutoff frequencies of 17.5 GHz and 36.5 GHz, respectively (see Figure 2). Excitations by _port_ 1 and _port_ 2 generate the \(TE_{11}{}^{cir}\) and \(TE_{01}{}^{cir}\) modes, respectively. As mentioned earlier, due to the possible asymmetries in the construction of the DMC, it is crucial that the two mode converter modules are precisely connected in order to prevent additional high-order mode excitation. Thus, the accurate placement of the four rectangular arms that are attached to the output is very important, in order to maximize the isolation between the two mode converters. It should be noted that the \(TM_{11}{}^{cir}\) mode at the circular waveguide has the same cutoff frequency of 36.5 GHz as the \(TE_{01}{}^{cir}\). Careful attention is required for this mode, which is sufficiently attenuated as seen in Figure 4b. At the upper end of the design band, the \(TE_{21}{}^{cir}\) mode starts to propagate at 40 GHz. Thus, the dimensioning and design of the DMC allows its proper operation for the design band (37.5-39 GHz). The results for the DMC are presented later in Section 3.3. Integration of the Dual-Mode Converter (DMC) with the Conical Horn Antenna (CHA) for Obtaining the Dual-Mode Conical Horn Antenna (DM-CHA)  
The Dual-Mode Converter (DMC) allows the generation of the \(TE_{11}{}^{cir}\) and \(TE_{01}{}^{cir}\) modes from independent rectangular ports. In this section, the purpose is to integrate the DMC with a conical horn antenna (CHA), designed with an aperture diameter of \(D_{horn}=38.2\) mm and a flare length of \(L_{horn}=64.4\) mm. It is designed for the desired operating bandwidth, providing the required sum or difference pattern under the adequate excitation, as seen in Figure 8. An important parameter to be considered in the design is the length connecting the circular waveguide at the input of the CHA with the circular waveguide at the output of the DMC. The obtained length of \(L=32\) mm, is important for controlling the mutual coupling between modes, and for the final return losses. This step finishes the design of the Dual-Mode Conical Horn Antenna (DM-CHA).