# A Novel Magnetic Coupling for Miniaturized Bandpass Filters in Embedded Coaxial SIW
## 1 Introduction  
Presently, substrate integrated waveguide (SIW) technology is considered to be a fruitful approach for the design and implementation of microwave and mm-wave components, such as cavity filters, antennas, directional couplers, oscillators, or power amplifiers among others [1]. The fusion of planar and non-planar structures enabled by SIW technology presents an optimal compromise in terms of EM performance, cost, size, and manufacturability. Indeed, moderate-to-high quality factor (Q), excellent planar integration, low weight, and low-cost manufacturing processes in printed circuit board (PCB) and LTCC technology are some of the key advantages that can be obtained conveniently in SIW technology. Nevertheless, wireless communication systems are imposing increasingly stringent requirements for the performance of microwave filters to be employed for the next-generation wireless and mobile applications. In this context, compactness represents a crucial feature to be addressed in the future microwave BPFs, and for this reason, considerable effort has been recently deployed to increase the miniaturization of SIW filters whose footprint is considered to be still rather large. As is well known, the combine topology, which can be modeled as a TEM-mode transmission line short-circuited at one end and terminated with a capacitor on the other, has been widely applied in waveguide and planar technologies for the compact implementation of high-order BPFs [2; 3]. Recently, such a scheme has been successfully introduced in SIW technology by using LTCC [4; 5] and PCB [6] manufacturing processes, showing remarkable advantages in terms of size and EM performance with respect to standard SIW implementations. The latter are usually based on TE\({}_{101}\)-mode cavities or on more compact alternatives by bisecting the SIW resonator at quasi-perfect magnetic walls [7; 8]. These are defined as half-mode SIW (HMSIW) and quarter-mode SIW (QMSIW) topologies, and usuallyexperience increased radiation losses. For instance, in [8], an ultra-miniature two-pole filter based on eight-mode SIW resonators loaded with circular-ring miniaturized element (CRME) structures was designed in UHF band showing FBW\(=10\%\) and good spurious-free band. However, the extracted quality factor (\(Q\)) of the filter was just 90, which is comparable to lumped element implementations. On the one hand, in [6; 9], the authors proposed to implement the loading capacitance of the coaxial topology by means of an isolating air gap etched on the external top metal layer of a SIW cavity resonator. This solution enables component fabrication to be fully compatible with single-layer low-cost PCB fabrication. Specifically, in [6] the feasibility of the CSIW topology was proved by designing and testing an X-band resonator. Furthermore, an X-band three-pole narrow-band BPF was designed, fabricated, and tested showing good miniaturization degree and spurious-free band performance in [9]. On the other hand, by using a multi-layer process, embedded CSIW resonators and filters were first proposed in [4] and then demonstrated in [5; 10; 11] at lower frequency bands, such as L-band. In particular, two-pole and three-pole narrow-band BPFs were designed for UMTS/LTE-2100 applications (i.e., 2110-2170 MHz), being characterized for an improved compactness. Such a result has been achieved by implementing very high embedded coaxial loading capacitances between inner layers of a multi-layer LTCC stack-up. This topology has been recently implemented by using the PCB manufacturing in [12; 13] for the design of fourth-order narrow-band BPF in X- and L-band, respectively, showing a good compromise between compactness and loss. This work deals with the design of embedded CSIW filters in multi-layer LTCC technology with widened filtering responses, which means overcoming a typical problem of combline filters implemented in SIW technology.