With increasing complexity of microwave integrated circuits and tendency towards building integrated modules, real estate in printed circuit boards becomes more at premium. On the other hand, building MIC's on a single semiconductor substrate such as GaAs has other drawbacks as substrate requirements for different components are sometimes contradictory. This has motivated researchers to consider multi-layer and stacked designs. Multi-layer planar circuits offer advantages that cannot be equaled by traditional single layer designs. In this respect, a new class of planar structures, based upon a multi-layered stack of dual-mode stripline or microstrip patches is becoming increasingly popular. In the new stacked design coupling between planar circuits separated by a ground plane is accomplished through coupling apertures in the common ground plane. <br ><br /> This thesis is about developing a new approximate multiport network model for fast analysis of multi-layered planar structures with ground plane slots. To extend applicability of multiport network model (MNM) to the class of planar structures containing ground plane slots, a generalized network formulation for aperture problems is combined with traditional MNM to account for the presence of the slot. To this end, the slot is replaced by an unknown equivalent surface magnetic current. Slot ports are defined in terms of electric and magnetic fields over the slot in accordance with the generalized network formulation for aperture problems. While traditional MNM for planar circuits is based on generalized impedance matrices, we adopt a hybrid matrix approach for multi-layer structures. The hybrid matrix consists of four sub-matrices that relate terminal voltages and currents of edge and slot ports. The same generalized impedance matrix in the absence of the slot can be used to relate terminal voltages and currents of edge ports when the slot ports are short-circuited. Open circuit voltage at edge ports due to terminal voltages at slot ports and terminal currents at slot ports due to input currents at edge ports are represented by two transfer matrices. Both these transfer matrices can be calculated from 2D analysis which only considers <em>TM^z</em> modes. <br ><br /> Interaction among slot ports, represented by a generalized admittance matrix, however, requires considering both <em>TM^z</em> and <em>TE^z</em> modes. This generalized admittance matrix is obtained from tangential component of the magnetic field over the slot due to the equivalent surface magnetic current and relates terminal voltages and currents of slot ports. Full modal expansion consisting of both <em>TM^z</em> and <em>TE^z</em> modes is used to compute the generalized admittance matrix of a slot in a regularly shaped planar cavity. For irregularly shaped patches, modal expansion is not available. Instead, a new contour integral equation for magnetic field, derived for the first time in this thesis, is combined with complex images method for calculation of generalized admittance matrix of a slot radiating in a planar cavity of arbitrary shape. <br ><br /> Once the hybrid matrix representation of a planar circuit on a ground plane containing a slot is derived, it can be connected to the hybrid matrix of any other planar circuit on the other side of the ground plane. This can be done by enforcing network equivalent of continuity of tangential fields across the slot. This leads to a generalized impedance matrix for the multi-layer structure relating terminal voltages and currents of edge ports of both planar circuits. <br ><br /> To show the accuracy of the proposed method of analysis, several proof-of-concept structures have been analyzed by both this method and ANSOFT HFSS full-wave simulator as a reference. In most cases excellent agreement is achieved in predicting the return loss and radiation patterns of these multi-layer structures which proves the validity of the proposed approach for fast analysis and design of multi-layer planar structures.

With increasing complexity of microwave integrated circuits and tendency towards building integrated modules, real estate in printed circuit boards becomes more at premium. On the other hand, building MIC's on a single semiconductor substrate such as GaAs has other drawbacks as substrate requirements for different components are sometimes contradictory. This has motivated researchers to consider multi-layer and stacked designs. Multi-layer planar circuits offer advantages that cannot be equaled by traditional single layer designs. In this respect, a new class of planar structures, based upon a multi-layered stack of dual-mode stripline or microstrip patches is becoming increasingly popular. In the new stacked design coupling between planar circuits separated by a ground plane is accomplished through coupling apertures in the common ground plane. <br ><br /> This thesis is about developing a new approximate multiport network model for fast analysis of multi-layered planar structures with ground plane slots. To extend applicability of multiport network model (MNM) to the class of planar structures containing ground plane slots, a generalized network formulation for aperture problems is combined with traditional MNM to account for the presence of the slot. To this end, the slot is replaced by an unknown equivalent surface magnetic current. Slot ports are defined in terms of electric and magnetic fields over the slot in accordance with the generalized network formulation for aperture problems. While traditional MNM for planar circuits is based on generalized impedance matrices, we adopt a hybrid matrix approach for multi-layer structures. The hybrid matrix consists of four sub-matrices that relate terminal voltages and currents of edge and slot ports. The same generalized impedance matrix in the absence of the slot can be used to relate terminal voltages and currents of edge ports when the slot ports are short-circuited. Open circuit voltage at edge ports due to terminal voltages at slot ports and terminal currents at slot ports due to input currents at edge ports are represented by two transfer matrices. Both these transfer matrices can be calculated from 2D analysis which only considers <em>TM^z</em> modes. <br ><br /> Interaction among slot ports, represented by a generalized admittance matrix, however, requires considering both <em>TM^z</em> and <em>TE^z</em> modes. This generalized admittance matrix is obtained from tangential component of the magnetic field over the slot due to the equivalent surface magnetic current and relates terminal voltages and currents of slot ports. Full modal expansion consisting of both <em>TM^z</em> and <em>TE^z</em> modes is used to compute the generalized admittance matrix of a slot in a regularly shaped planar cavity. For irregularly shaped patches, modal expansion is not available. Instead, a new contour integral equation for magnetic field, derived for the first time in this thesis, is combined with complex images method for calculation of generalized admittance matrix of a slot radiating in a planar cavity of arbitrary shape. <br ><br /> Once the hybrid matrix representation of a planar circuit on a ground plane containing a slot is derived, it can be connected to the hybrid matrix of any other planar circuit on the other side of the ground plane. This can be done by enforcing network equivalent of continuity of tangential fields across the slot. This leads to a generalized impedance matrix for the multi-layer structure relating terminal voltages and currents of edge ports of both planar circuits. <br ><br /> To show the accuracy of the proposed method of analysis, several proof-of-concept structures have been analyzed by both this method and ANSOFT HFSS full-wave simulator as a reference. In most cases excellent agreement is achieved in predicting the return loss and radiation patterns of these multi-layer structures which proves the validity of the proposed approach for fast analysis and design of multi-layer planar structures.

L'étude de la susceptibilité électromagnétique de circuits électroniques nécessite l'utilisation d'un outil de simulation rapide, précis et suffisamment flexible pour intégrer les dernières innovations technologiques. La méthode itérative basée sur le concept d'onde (notée WCIP pour Wave Concept Iterative Procedure) initialement proposée par H. Baudrand est particulièrement adaptée pour la modélisation numérique de circuits multicouches à plusieurs niveaux de métallisation. Pour ce type de circuits, elle se révèle être l'une des méthodes qui utilise le plus petit nombre d'inconnues pour atteindre une précision donnée. Néanmoins, la WCIP n'est pas adaptée à la prise en compte des diélectriques inhomogènes et des trous d'interconnexion. L'objectif de la thèse est de s'affranchir de ces limitations par un couplage avec des méthodes numériques volumiques. En premier lieu, l'hybridation a été mise en œuvre avec une méthode basée sur la théorie des lignes de transmission pour des raisons de correspondance de maillages. Par la suite, le couplage avec une technique d'éléments finis de type Galerkin Discontinu (notée GD) Hybridée permet d'atteindre des objectifs de précision et de rapidité car GD apporte une flexibilité dans la discrétisation. En effet, c'est une méthode d'éléments finis non conforme qui permet notamment de faire varier d'un élément à l'autre l'ordre polynomial d'approximation. On a ainsi développé une nouvelle méthode numérique hybride couplant la WCIP avec des méthodes volumiques qui offrent plus de souplesse pour la prise en compte des milieux complexes. Enfin, une stratégie de résolution par décomposition de domaines est également abordée à la fin du manuscrit. / Electromagnetic susceptibility study of electronic circuits requires the use of a simulation tool which is fast, accurate and flexible enough to incorporate the latest technological innovations. The Wave Concept Iterative Procedure (WCIP) initially proposed by H. Baudrand is particularly adapted for numerical modeling of multilayered circuits with multilevel metallization. For this kind of circuits, it turns out to be one of the methods that uses the smallest number of unknowns to reach a given accuracy. However, the WCIP is not appropriate for inhomogeneous dielectric substrates and metallized via holes. The aim of this PhD thesis is to overcome these limitations coupling the WCIP with volume numerical methods. First, hybridization is carried out with the Frequency Domain Transmission Line Matrix (denoted FDTLM) assuming matching meshes at the interface between computational domains of both methods. Subsequently, the coupling with a finite element technique like a Hybridized Discontinuous Galerkin (denoted DG) method is considered to achieve the objectives of accuracy and speed because DG brings flexibility in the discretization. Indeed, it is a nonconforming finite element method which allows in particular changing the polynomial approximation order from one element to another. Therefore, a new hybrid method is developed coupling the WCIP with volume numerical methods which offer more flexibility for dealing with complex environments. Finally, a domain decomposition solution strategy is also discussed at the end of the manuscript.