## 1 Introduction  
The growing need for small microwave devices with integration capabilities in planar technologies and high performance prompted the creation of the substrate integrated waveguide (SIW) [1]. In the quest for increasing the performance, the empty substrate integrated waveguide (ESIW) was developed [2]. In the ESIW, the dielectric is removed, the walls are metalized, and the electromagnetic wave is confined by a bottom and top metal covers. The removal of the dielectric allows a significant reduction of the losses, with the drawback of increasing the overall size. Consequently, the wave is propagated through the air. To validate this promising technology, some common microwave devices have been designed, manufactured, and measured. Some of these devices are filters [3; 4], antennas [5; 6; 7], 90\({}^{\circ}\) hybrid directional couplers [8], circulators [9], and phase shifters [10]. All of the above devices need a transition to connect ESIW to planar technologies. Multiple transitions from microstrip line (ML) to ESIW have been designed with a different approach in the design, solving the matching problems and being functional despite the manufacturing tolerances [2; 11; 12; 13]. However, these transitions have the disadvantage of being well matched in a limited frequency range (monomode propagation in ESIW), resulting in a fractional bandwidth (FBW) of approximately 42%. This fractional bandwidth may be insufficient for some broadband applications. Recently, a new microstrip line to ESIW transition that can achieve a higher fractional bandwidth (57%) has been proposed [14]. This transition is based on introducing a dielectric material inside the waveguide, which allows for a greater bandwidth, but with the drawback of increasing the losses. In this work, we aim to achieve larger fractional bandwidth than 57% without introducing dielectric and therefore increasing the losses. In the ESIW, the fundamental mode \(TE_{10}\) is propagated in a similar way as in a standard rectangular waveguide. The frequency range in which this is the only mode that is propagating determines the usable bandwidth. With the intention of increasing the monomode bandwidth a ridge waveguide can be used. The ridge waveguide consists of a waveguide with one or more metallic ridges. These ridges produce a reduction in the frequency of the fundamental mode and a small increase in the frequency of the next higher order mode. Thus, a significantly larger monomode bandwidth is achieved. Therefore, a ridge waveguide with the same dimensions of a rectangular waveguide without ridge can work at lower frequencies. Conversely, a ridge waveguide can work at the same frequency as the conventional rectangular waveguide, but being smaller and less bulky. This idea of a Ridge ESIW (RESIW) was first presented by [PERSON] et al. [15], and a transition from microstrip line to a single RESIW (RESIW with only one ridge) that allows the use of most of the usable bandwidth was also proposed by [PERSON] et al. [16]. This transition for a WR62 RESIW presents return losses greater than 20 dB in a fractional bandwidth (FBW) of 82%. In this work, a thorough study of possible geometries of a ridge ESIW manufactured with standard Planar Circuit Board (PCB) machinery is performed with the purpose of assessing the pros and cons of using only one o more ridges, and/or using ridges with different cross sectional shapes, and selecting the best geometry with a compromise between monomode propagation bandwidth and ease of manufacturing. Next, a new wideband transition from microstrip line to single RESIW is proposed. This new transition is based in a wider ESIW section with a superelliptical dielectric taper, and it presents better return losses and a broader fractional bandwidth than the previous microstrip to single RESIW transition [16]. The work is structured as follows. Section 2 presents an exhaustive study of the possible geometries of the RESIW. Section 3 presents the transition and it is design procedure.