## Motivation

In the last decades, the saturation of the electromagnetic spectrum, the increasing demand for devices that are more and more compact and the characteristics of the new broadband radiocommunications services, have forced the use of ever higher frequency bands, where enough spectrum is available. Electronics at so high frequencies requires new concepts and faces difficulties quite different from the ones found below 1 GHz. This has brought the increase in research in the synthesis and development of semiconductor devices able to work at microwave and millimeter frequencies, which could substitute the traditional microwave components. Therefore, the aim is to develop low cost technologies, with high performance, adequate for mass production and which are also able to achieve a significant volume, weight and consumption reduction of the telecommunication systems. In fact, there is a variety of applications recently proposed in the frequency range between 60 GHz and 90 GHz whose success mainly depends of the availability of that low-cost technology, suitable for mass production: wireless networks [DH07], automotive radars [Fle08], imaging sensors [YSM03] and biomedical devices [MWW+07], among others.
Conventional waveguides (see Fig. 1.1), the first generation of microwave guiding structures, have an excellent performance: electromagnetic shielding (totally eliminating radiation losses), low insertion loss, high power carrying capacity and high Q-factor. However, they are not suitable for mass production, and they are also bulky and voluminous and difficult to integrate with planar technology.
The alternative to the guided technology is the planar technology or printed circuits (see Fig. 1.2). These strip-like or slot-like planar printed transmission lines used in Microwave Integrated Circuits (MICs) are the second generation of microwave guiding elements. The intrinsic advantages of the planar circuits are numerous: low cost, low weight, small size and manufacturing processes relatively simple, economic and accurate, and adequate for mass production. However, the electromagnetic field singularities cause high current densities in the conductor edges producing high conductor losses, which increase as the frequency increases. So we could say that planar circuits lack the high power carrying capacity and the high Q-factor of the conventional waveguides. In addition, in structures with high density integration some coupling problems appear, and although the manufacturing cost of the circuits is very reduced, they need to be packaged and sometimes the package costs more than the circuit itself.

Rectangular waveguide

Planar printed transmission lines: Microstrip line

Planar printed transmission lines: Coplanar waveguide (CPW)

Furthermore, the transitions between both technologies (see Fig. 1.3) mean a great reduction of bandwidth, and they are usually quite sophisticated, involving mechanic problems as well as an additional increase of the cost.

Simple design examples of microstrip to rectangular waveguide transitions: probe type.

Simple design examples of microstrip to rectangular waveguide transitions: ridge type.

To bridge the gap between MIC structures and conventional waveguides, in early 2001, doctors Dominic Deslandes and Ke Wu developed an ingenious and revolutionary concept that, without any doubt, has given rise to a new generation of integrated circuits for high frequency applications. They are the “Substrate Integrated Circuits” (SICs). Their emergence has meant a breakthrough comparable to the invention of the MICs in the 1950s. This new technology concept consists of integrating each individual component in a single platform, thus eliminating the assembly process and drastically reducing the undesirable effects due to the electric connections and mechanical transitions among the different elements forming any communication system. It also allows a significant reduction of the global volume and production cost of entire telecommunication systems. The principle of operation of SIC is to build artificial channels within the substrate to guide the waves. Inside this big family of integrated circuits, the Substrate Integrated Waveguide (SIW) technology [DW01a] is a mixed technology between waveguide and printed circuit that solves the problems associated to both previous technologies, integrating a rectangular waveguide in a planar substrate (see Fig. 1.4). It consists of an “artificial” waveguide synthesized by two parallel rows of via holes embedded in a dielectric substrate, which is covered with conducting sheets on the top and bottom sides (see Fig. 1.5). Figure 1.4: Substrate integrated waveguide. As one of the “divine innovations”, the SIW has been recently selected as one of the “10 Technologies Changing the Future of Passive and Control Components” [Vye11]. Moreover, the future of this technology is very promising as high precision PCB manufacturing techniques –including LTCC– should support passive component design using SIW structures to extend up to the 100 GHz range, while advanced micro-fabrication techniques, such as photo-imaging, micromachining, CMOS process, and others, have the potential to push the design of substrate integrated structures up to the hundreds GHz and THz range. Furthermore, it is possible to use this new technology for making many devices, such as antennas [LK13,Wu13], filters [CSW09,CSH+09,MSR10], mixers, power dividers [KB13] and multiplexers [AMV11], and to integrate many substrate integrated waveguide circuits into a single-board subsystem. This low cost realization of the traditional waveguide circuit inherits the merits from both the planar technology for easy integration and the waveguide for low radiation loss. Moreover, it has an intrinsic flexibility for implementing any kind of geometries and forms that the traditional waveguide does not have. Figure 1.5: Scheme of a SIW filter.

## State of the art

In this section, the state of the art regarding SIW technology and, in particular, its analysis and design is going to be carefully studied. A significant effort has been devoted to the research and development of SIW technology in the last few years: this widespread research activity has produced novel modeling techniques for SIW components, a number of new technological solutions, as well as SIW circuits and systems with outstanding performance. The increasing number of scientific publications on SIW technology confirms the growing interest of the scientific community (Fig. 1.6). Some publications [XW05,HA98,DW06a] provide some design rules or equations relating the radius of the via holes, the separation of the post walls, etc. so that the field leakage is minimum or for avoiding bandgaps in the working bandwidth. However, to study a general substrate integrated waveguide circuit, a fullwave analysis is required. For these reasons, the efficient analysis of SIW devices becomes a new challenge that is the object of intense research in the last few years. Figure 1.6: Number of SIW-related publications in IEEE journals [BPWA09]. Some recent contributions for the accurate and efficient analysis of SIW circuits are based upon the well-known Boundary Integral - Resonant Mode Expansion (BI-RME) method [BPW07,BPW08a,MSBG07,MSC+09], which provides the generalized admittance matrix of the SIW circuit in polar form with a reduced number of frequency dependent computations. Also various numerical techniques such as finite element method (FEM), finite difference time domain (FDTD), finite-difference frequency-domain (FDFD), transmission line method (TLM), and 2D multiport method have been developed to analyze the structure under consideration [XZH+03,XWH06,AA08,AMS10,AAB12]. Other recent contributions to this field are hybrid techniques based on mode-matching and the method of moments [RMS10] that can be used to analyze any device that is fed through canonical waveguides. In general, those hybrid techniques are formulated by applying the equivalence theorem [Sch36, Bal89], so that the ports are replaced by a pair of unknown electric and magnetic current densities. A hybrid proposal that uses this pair of currents to achieve the equivalence [WK08,WK07] has been successfully applied to the analysis of several SIW devices [DW01a,DW03a,DW06a]. In [WK08], the metalized holes comprising the substrate integrated waveguide are characterized by means of cylindrical emergent spectra, implying an important computational advantage. Other techniques, although efficient, are just able to analyze the resonances in a SIW cavity [AABIS13]. However, more efforts on increasing the numerical efficiency of these hybrid modal analysis methods can still be developed, specifically by considering other generalized matrix formulations (i.e. the one based on scattering parameters) together with fast frequency sweep schemes. Moreover, in the analysis and design of SIW structures, it is necessary to keep in mind that there are three mechanisms of loss in a substrate integrated waveguide [BPPW07]. Two of them are related to the finite conductivity of the metal and to the loss tangent of the dielectric medium. However, there is a third mechanism of loss due to the possible leakage through the gaps: the radiation loss. Although the issue of radiation losses has been discussed in a number of papers [XW05,DW06b], most of the SIW analysis methods found in the literature [BPW08b,WK08, CSEM12] neglect its contribution, assuming that the design rules that permit to minimize the radiation leakage [XW05,CDWC08] are fulfilled in the device under analysis.