# Highly Compact Through-Wire Microstrip to Empty Substrate Integrated Coaxial Line Transition
## 2 Design of the Transition  
This through-wire microstrip-to-ESICL transition is inspired in the classical coaxial-to-waveguide transition [15] and in the equivalent through-wire transition for ESIW [16]. In the classical transition, the coaxial line is used as the feeding line to excite a waveguide; it presents a lot of practical performances [17], however, the coaxial probe is never connected to the walls of the waveguide. On the other hand, in the case of the transition to ESIW, the through-wire connects the feeding microstrip line with the bottom layer of the ESIW,achieving impedance matching with a transformer and a pad-gap structure located in the top layer of the ESIW. This new through-wire approach to ESICL presents a smart solution to directly connect a microstrip feeding line with the inner coaxial conductor of the ESICL; as the microstrip and ESICL are designed to have the same impedance, no intermediate transformer is required, only a pad-gap structure is necessary for the through-wire. Consequently, the design procedure is simpler than the former cases and the number of parameters that control the transition are fewer. The proposed structure for the through-wire microstrip-to-ESICL is that shown in Figure 1. The detailed layout of the top and central layers is depicted in Figure 2.  
Figure 1: Longitudinal section of the through-wire transition (orange color represents non-metallized parts, blue color represents the metallic wire, the walls of the holes in top and middle layers are metallized with electrodeposition). The wire is tin soldered to top and middle layers. Figure 2: Detailed layout of the transition: (**a**) Upper (**right**) and bottom (**left**) views of the top cover; (**b**) upper view of the central layer and detail (orange color represents non-metallized parts). As it can be observed, the feeding microstrip and the inner coaxial lines are totally independent and located in different layers. To transfer power to the ESICL structure, a metallic filament is used to electrically connect the microstrip feeding line with the base of the inner coaxial line. The filament is tin soldered to the top and central layers. To avoid short circuiting the microstrip with its ground by the bottom side of the top cover (which is also the ground of the ESICL), the filament of diameter \(d_{cable}\), uses a pad-gap structure, controlled by the parameters \(pad_{T}\), \(pad_{B}\) and \(gap\) (see Figure 2a). On the other hand, the filament requires a hole of diameter \(d_{hole}\), in the inner coaxial to be inserted. Three important details can be noticed in this transition: the first one is that the inner coaxial is totally isolated from its ground (see details in Figure 2b), for which the non-metallic section controlled by the parameter \(l_{inc}\) is used (\(l_{inc_{2}}\) is just used to ease the manufacturing); via holes are non-necessary in the inner coaxial to ensure the confinement of the electromagnetic field as it happens in previous transitions. The second detail is that no transformation is required in the feeding line, as the initial microstrip directly feeds the through-wire transition, given that the impedance of both the microstrip and inner coaxial line is the same. Finally, the third detail is that, given its circular symmetry, this transition is almost insensitive to the rotation of the microstrip around the filament, as it is proved in [16]. The procedure to design this transition, in the band of interest from 0 to 20 GHz, is as follows. The initial step adjusts the width of the lines, \(w_{ms}\) for microstrip and \(w_{cax}\), \(w_{cax_{int}}\) for ESICL, so that both lines have the same impedance of 50 \(\Omega\) at the central frequency of interest (\(f_{0}\) = 10 GHz). Then, the initial values for the through-wire transition (\(pad_{T}\), \(pad_{B}\), \(gap\), \(d_{cable}\)) are set according to the procedure stated in [16], where \(d_{cable}\) is rounded to the nearest available commercial diameter and \(d_{hole}=d_{cable}+0.1\).