# An RF-MEMS-Based Digitally Tunable SIW Filter in X-Band for Communication Satellite Applications
## 2 Tunable Resonator Topology  
The design procedure of a resonant SIW cavity is similar to that of a conventional rectangular waveguide cavity. Energy is coupled to the cavity by input/output rises and tapered microstrip lines. The cavity is realized on a 635 um thick alumina substrate (\(\varepsilon\)r = 9.9, \(\mathrm{tg}\delta=3\times 10^{-4}\)). In order to achieve tunability, a metallic inductive post is introduced into the cavity and isolated from the top metallic face by a gap. For consistency, we use the term \"tuning post\" to define the metallic inductive post used as the tuning element. Depending on the position and the state of the tuning post, whether connected or not to the top metallic face of the cavity, the cavity resonance undergoes a frequency shift. Placing the tuning post in the center of the cavity, where the electric field is at its maximum, produces a large frequency shift. As the tuning post is placed further away from the center, the frequency shift decreases, and reaches a minimum close to the edges of the cavity [6]. As a first approach and in order to investigate SIW cavity behavior, the switching described here was executed using four wire bondings. The four wire bondings shown in Figure 1 were manually disconnected one at a time and the electrical response was measured. For consistency, the wire bondings are labeled according to their direction (Figures 1 and 2)--N, W, S and E being North, West, South and East, respectively. Hence, we obtained five different results beginning from the state NWSE, where all wire bondings are connected, and finishing at the state U (standing for unconnected), where no wire bonding remains. Figure 2 illustrates the measurement results. Assuming the state NWSE as the nominal starting state, the cavity resonated at a frequency of 11.68 GHz with all four wire bondings connected. Table 1 summarizes measurements of the frequency shift on the transmission coefficient peak as a function of the disconnected wire bondings. The frequency shift between the two extreme states (NWSE and U) was approximately 817 MHz (\(\mathrm{Xpost}=1.9\) mm). To explain this effect, the extent to which the EM field was perturbed must be considered. When the tuning post was connected with four wire bondings, a surface current was induced on the tuning post, causing a large perturbation inside the cavity. Consequently, each time a wire bonding was disconnected (transitioning from states NWSE to NE to SE to S to U), the induced surface current decreased, causing a smaller perturbation than the previous state until no current was induced on the tuning post, i.e., state (U). Figure 3 shows a simulation of induced currents on a tuning post inside a cavity, as a function of the number of connected wire bondings. The induced current on the tuning post increased as the number of connected wire bondings increased. Another cavity prototype was also realized, with a tuning post at the center of the cavity (Xpost = 0 mm). The same strategy and measurements were applied as previously described, following the procedure of disconnecting wire bondings one at a time. The results, summarized in Table 1, show that the frequency shift with the tuning post at the center was higher than when that at the edge (2910 MHz for Xpost = 0 mm). In both cases, the maximum \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Xpost (mm)** & **States** & **U–S** & **S–SE** & **SE–NSE** & **NSE–NWSE** \\ \hline
1.9 & Freq. Shift (MHz) & 508 & 225 & 67 & 17 \\
0 & Freq. Shift (MHz) & 1670 & 640 & 390 & 210 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Frequency shift as a function of switched states. Figure 2: Measurement results for different connection states: (NWSE) four, (NSE) three, (SE) two, (S) one and (U) no wire bondings. frequency shift was obtained between configurations U and S, whereas the lowest one was between states NWSE and NSE (see Table 1).