# An In-Line Coaxial-to-Waveguide Transition for Q-Band Single-Feed-Per-Beam Antenna Systems
## 1 Introduction
The in-line coaxial-to-waveguide transition has been proposed since the 1960s [20] and it has been employed to feed open-waveguide arrays [21]. The L-shaped coaxial configurations [22; 23] are a first common technique to short the launcher, but a folded conductor is a challenging task, especially in mm-wave technology, and it is overcome by patch antenna launchers [24] or by shorting the launcher directly on a tapered ridge or multi-section one quarter wavelength-length transformer ridges, which allow the matching over a wide bandwidth [25; 26]. Despite the aforementioned complexity, the L-shaped solution has been widely used for horn antennas, even leading to patented devices, such as [27]. The bandwidth enlargement has been studied and it has been accomplished with different strategies, as a thicker pin (compared to the inner coaxial conductor) surrounded by a shaped cavity [28], or by widening both the width and the height of the waveguide [29]. Dielectric [30] or metallic [31] shaped fins have been shown to be an alternative to provide the desired matching. In [32], the matching is achieved over a wideband via an intermediate rectangular coaxial structure attached to a single ridge waveguide. These solutions presents relevant drawbacks, in particular the cumbersomeness of the technological strategy to meet the required transmission performances and modal conversion. This paper proposes an in-line coaxial-to-waveguide transition with a compact geometry to obtain a good match over the whole Q-band (33-50 GHz). The aim is to reach the desired matching (typically, at least a return loss (RL) \(>\) 20 dB in radioastronomy) without increasing the transverse occupation and limiting the additional components to the strictly necessary, in order to obtain a satisfactory accuracy in the design despite the small operating wavelengths involved. This is an alternative solution to the previous work which involved a microstrip as end-launcher [33]. The shift between a microstrip and a coaxial end-launcher leads to several improvements. First of all, microstrip impedance and propagation constant are dispersive. To this aim, the design and the analysis are carried out by performing numerical experiments which take into account a number of potentially limiting technological scenarios. This dispersion is due both to a dispersivity of the dielectric constant and to the geometric dispersion of the microstrip [34]. The latter can be well modelled but only for \"free space\" microstrip, not in configurations as in [33]. On the other hand, the coaxial conductors have no geometrical dispersion, and the dielectric material dispersion is typically smaller than the dispersion of a microstrip slab [35]. As a consequence, the required bandwidth (33-50 GHz) can be more easily achieved. Moreover, the unavoidable inaccuracy in the knowledge of the permittivity of a microstrip dieletric slab in the Q band reduces the overall accuracy of the matching and, as a consequence, of the performance [36]. This makes the coaxial cable the preferable choice in the radio astronomical receivers [14]. Finally, the field at the microstrip edges is rather large, and this increases the dielectric losses, which become the main loss source of the complete transition. The waveguide is a WR-22 (a \(\times\) b = 5.69 \(\times\) 2.845 mm), whereas the coaxial cable is filled with Teflon (\(\epsilon_{r}\) = 2.1, \(\tan\delta\) = 0.001, radius r\({}_{\text{d}}\) = 0.3386 mm) and ends in a pin with the same radius of the inner conductor r\({}_{\text{i}}\) = 0.1136 mm. The transition has to accomplish both a mode fitting and an impedance matching between the waveguide and launcher. The in-line configuration keeps the same direction of propagation in both the components, so that the E-fields of the TEM mode in the coaxial cable and of the TE\({}_{\text{10}}\) mode of the waveguide are parallel. In addition, the high wave impedance of the hollow waveguide must be matched to the 50 \(\Omega\) of the end launcher.