# An In-Line Coaxial-to-Waveguide Transition for Q-Band Single-Feed-Per-Beam Antenna Systems
## 2 Design  
The high frequencies involved, up to 50 GHz, which correspond to a guided wavelength of 7.1 mm [37], strongly limit the degrees of freedom in the design. Since the precision required in microwave components is related to the operative wavelength, and usually it is smaller than an order of magnitude respect with the latter, transitions which match the coaxial cable using small metallic parts, such as folded pins [21; 23], fins [30] or metallic bricks suspended with respect to the metallic walls as rectax [26] are rather demanding in realization accuracy when the operating frequency rises. Additionally, modification in the pin radius [28] or in its shape [32] is critical in Q-band due to the reduced physical dimensions. None of the mentioned solutions is proposed in the literature for operating frequencies up to 50 GHz. In the same time, it is important to reduce the number of design parameters, so it has been chosen not to modify the WG transverse section [29] and use a single ridge cascade. The purpose of this work is to obtain a wideband transition without increasing the WG transverse occupation and with an as simple as possible geometry with respect to the solutions proposed in literature: no intermediate steps (except for a multistep impedance transformer) [29] or shaped pins [23; 28] have been introduced in the design, and the waveguide transverse section has been modified only in the backshort, in the section where the launcher is inserted. The geometry of the proposed transition is shown in Figure 1, where the left and the upper walls are removed for the sake of a clearer internal geometry display. The coaxial cable is inserted in the WG backshort of (a \(\times\) b) size, where a circular hole with the same radius of the dielectric coaxial layer is realized, in central position with respect to the WG long side a. The pin is shorted to a ridge, this in turn is connected to a cascade of ridged waveguide steps which implement a Chebyshev stepped impedance transformer, in charge of achieving the impedance matching with the full WG [38]. In order to achieve the modal conversion, only the coaxial inner conductor (pin) enters inside the guide, whereas the WG outer walls act as the coaxial outer conductor, so that the field configuration in this waveguide step is similar to a TEM. As a by product of this choice, no dielectric parts are needed in the mode converter as it would be required by using a microstrip end-launcher, and this significantly increases the achievable accuracy. In addition, such a field must be matched to a full WG. The introduction of a ridge for the pin short eases in the same time the modal conversion. As a matter of fact, by introducing an offset in the pin position along the short side b with respect to the center (Figure 2), and so approaching it to the WG upper wall, a large field is concentrated in the small gap g between the two aforementioned conductors. Such a field configuration is similar to a single-ridged waveguide (R-WG) whose ridge is centered in the long side with an height equal to the offset of the pin [33]. Moreover, the field lines in the pin section gather in the gap between the pin and the upper wall, and they are oriented parallel to the lines in the ridged area. Figure 3 shows the transverse field configuration in correspondence of the pin (a) and of the first ridge (b) in the waveguide: both cases concentrate the energy in the center of the wide side, whereas it is weak in the rest of the transverse section. In addition, the ridge reduces the WG impedance, making it comparable to the coaxial cable one [39]. Figure 1: Geometry of the coaxial-to-waveguide transition: isometric view (the left and the upper walls are not displayed). The coaxial probe (displayed in orange) is inserted at the center of the waveguide (WG) backshort: the coaxial dielectric layer terminates in correspondence of the WG backshort face, whereas the inner conductor is shorted on the ridge. The resulting ridge WG structure is then matched to the hollow waveguide via a ridged steps cascade.