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This dissertation, The Electromagnetic Compatibility and Multi-physics Analysis Based on the PEEC Method by Ying, Cao, 曹穎, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In this thesis, it is our biggest interest to develop full-wave based engineering friendly electromagnetic modeling approaches for coupling and radiation problems that are found in multi-physics and electromagnetic compatibility (EMC) applications. The partial element equivalent circuit (PEEC) method, a unique bridging method between electromagnetics and circuit theory, is employed and extended to address new challenges in electromagnetic analysis.Firstly, we developed the first derived equivalent circuit model of arbitrary shape graphene sheets. It is also a novel contribution to PEEC for handling dispersive and anisotropic medium. Graphene's numerical modeling is extremely cost prohibitive due to the huge contrast between its thickness and other dimensions. In this work, for the first time, the electromagnetic features of graphene are characterized by a derived equivalent circuit model from the first principle. Physical properties of the material can be conveniently obtained, such as radiation, scattering and resistance properties. Secondly, we developed the equivalent circuit model for optical electronic devices. By developing a new generalized equivalent circuit model for nanoantennas derived from the wave equation, not only material properties such as dispersivity and loss of the permittivity can be handled conveniently and efficiently, but also more physical insight of the working mechanism can be developed from the derived model.Thirdly, we developed a physics-based model size reduction (PMSR) method for key coupling analysis in the power integrity (PI) for the power distribution network (PDN) design and optimization in integrated circuit (IC), Packaging, and printed circuit board (PCB). In this thesis, thec PMSR method is applied to get the equivalent circuit model for above-ground geometries. The extracted physics-based models can be used to analyze the objective structure by parts. Lastly, we devoted great efforts in redefining the fundamental electromagnetic radiation mechanism through a distributive modeling approach. Even though radiation is being used and calculated everywhere from scientific researches, most radiation effects were successfully calculated without investigating how and why. In this thesis, by partitioning the object into pieces and extracting equivalence circuit for each piece, we derived novel formulations for both the radiated power and the transferred power between parts of the radiator. The approach can be instructively applied to EMC/EMI and other power distribution computations.Furthermore, from the global point of view which is another extreme view point of observing the radiation, we developed the PEEC based characteristic mode analysis approach. In this thesis, the characteristic mode (CM) analysis has been implemented together with the electric field integral equation (EFIE) based numerical methods to identify the trouble-makers during the radiation process. This thesis provides a guideline in discovering radiation related geometrical features, and designing methodologies for real geometries.As a summary, enlightened by the PEEC approach, we develop novel algorithms in both fundamental analysis methods for multi-physics and radiation mechanisms, and engineering methods for power integrity and coupling analysis. All above proposed algorithms have been verified and demonstrated by various examples. Compared to conventional appr

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