Skin-Effect Loss Models for Time- and Frequency-Domain PEEC Solver

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Heterogeneous Integration of RF and Microwave Systems Using Multi-layer Low-Temperature Co-fired Ceramics Technology

[eng] The aim of this work is the development of a modelling methodology for the fast analysis of non-radiative multilayer RF passive components without compromising solution accuracy. Instead of following a compact model approach, oftenly used in integrated technologies, the method is based on a specialized quasi-static partial element equivalent circuit (PEEC) numerical solver. Besides speed and accuracy, the solver can be embedded in circuit simulators; thus, models are already available in the schematic entry. Using this framework, model scalability is enhanced in terms of geometry, substrate cross-section, material properties, topology and boundary conditions. The dissertation starts showing the actual performance of the obtained solver and the motivations beneath its development. Then, the description about solver development is splitted in three parts, but all of them are interrelated. First, the PEEC formulation is adapted according to relevant electromagnetic behaviour of the component. It is worth stressing that a different perspective related to the principle of virtual work is used in this formulation. The second part deals with the evaluation of partial elements, the core of the solver. It is carried out using analytical space-domain close-form solutions of the Green’s function (GF) of the substrate. Partial elements are then assembled into a mesh. Therefore, the importance of the mesh up on solution accuracy is discussed in the last part and a basic layout aware mesh generator is proposed. Practical application of the methodology includes the implementation of a library of RF passives for multilayer substrate. For validation, the chosen substrate is a low temperature co-fired ceramics (LTCC) technology. Different set of devices have been fabricated, characterized and compared against model prediction. In addition, the obtained results are also verified using state-of-the-art electromagnetic solvers.[spa] El objetivo de este trabajo es el desarrollo de una metodología de modelado para el análisis rápido, pero sin comprometer la precisión de la solución, de componentes pasivos no radiativos de RF en substratos multicapa. El método se basa en el algoritmo numérico cuasi-estático de los elementos parciales de circuito equivalente (PEEC). Éste puede ser incorporado en simuladores de circuitos; por tanto, los modelos ya están disponibles en la entrada de esquemático de forma transparente para el diseñador de circuitos. Utilizando este marco, la escalabilidad del modelo se mejora en términos de la geometría, la definición del corte tecnológico, las propiedades del material, la topología del componente y las condiciones de contorno electro-magnéticas. Esta disertación comienza mostrando las motivaciones que han llevado a su desarrollo y la capacidad real del método de resolución obtenido. A partir de aquí, se realiza la descripción de todo el desarrollo del marco numérico que se divide en tres partes que están interrelacionadas. En primer lugar, la formulación PEEC se adapta según el comportamiento electromagnético real del componente. Vale la pena subrayar que en esta formulación se utiliza una perspectiva diferente a la habitual y que está relacionada con el principio de los trabajos virtuales de d’Alembert. La segunda parte trata de cómo se evalúan los elementos parciales y constituye el núcleo principal del algoritmo. Se lleva a cabo utilizando soluciones analíticas de la función de Green (GF) del sustrato en el dominio espacial. Los elementos parciales, que forman la malla numérica del modelo, se ensamblan en la matriz del sistema siguiendo un procedimiento de análisis nodal modificado (MNA). En la última parte, se discute la importancia de la malla sobre la precisión de la solución y se propone un generador de malla basado en la física del componente y no sólo en la descripción de la geometría. Como aplicación práctica de la metodología, se realiza la generación de una biblioteca de componentes pasivos RF para sustratos multicapa

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

Power distribution network inductance calculation, transient current measurement and conductor surface roughness extraction

The first part in the thesis discussed the modeling of the mid-frequency inductance for Zpp type plane pairs in power distribution networks (PDN). It is a key step for the placement of the decoupling capacitors. This paper gives an efficient approach for the calculation of the inductance for different capacitor placements. The PEEC based formulations takes advantage of the opposite currents in the planes. This leads to compute time reductions and memory savings for both the element calculation and the matrix solve step. A formulation is used where placement of capacitors leads to only small changes in the circuit matrix. Comparisons with other models are made to validate our results. In the second part, the application of GMI probe to measure IC switching current. IC switching current is the main noise source of many power integrity issues in printed circuit boards. Accurate measurement of the current waveforms is critical for an effective power distribution network design. In this paper, using a giant magneto-impedance (GMI) probe for this purpose is studied. A side-band detection and demodulation system is built up to measure various time-domain waveforms using an oscilloscope. It is found that the GMI probes are potentially suitable for this kind of time-domain measurements, but probe designs and measurement setups need further improvements for this application. In the third part, the new Sigma rule to evaluate parameters of copper surface roughness in PCB layers is presented. This approach is based on taking SEM images of PCB cross-sections. The approach is automat [sic] zed [sic] by applying image processing tools and Matlab code to evaluate average roughness amplitude and period of roughness function. This information could be used in numerical and analytical modeling, as well as in the DERM method to separate rough conductor loss from dielectric loss --Abstract, page iv

Entire domain basis function expansion of the differential surface admittance for efficient broadband characterization of lossy interconnects

This article presents a full-wave method to characterize lossy conductors in an interconnect setting. To this end, a novel and accurate differential surface admittance operator for cuboids based on entire domain basis functions is formulated. By combining this new operator with the augmented electric field integral equation, a comprehensive broadband characterization is obtained. Compared with the state of the art in differential surface admittance operator modeling, we prove the accuracy and improved speed of the novel formulation. Additional examples support these conclusions by comparing the results with commerical software tools and with measurements

Model order reduction techniques for PEEC modeling of RF & high-speed multi-layer circuits.

by Hu Hai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references.Abstracts in English and Chinese.Author's Declaration --- p.iiAbstract --- p.iiiAcknowledgements --- p.viTable of Contents --- p.viiiList of Figures --- p.xiList of Tables --- p.xivChapter Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Overview of This Work --- p.2Chapter 1.3 --- Original Contributions in the Thesis --- p.3Chapter 1.4 --- Thesis Organization --- p.4Chapter Chapter 2 --- PEEC Modeling Background --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.2 --- PEEC Principles --- p.6Chapter 2.3 --- Meshing Scheme --- p.10Chapter 2.4 --- Formulae for Calculating the Partial Elements --- p.12Chapter 2.4.1 --- Partial Inductance --- p.12Chapter 2.4.2 --- Partial Capacitance --- p.14Chapter 2.5 --- PEEC Application Example --- p.15Chapter 2.6 --- Summary --- p.17References --- p.18Chapter Chapter 3 --- Mathematical Model Order Reduction --- p.20Chapter 3.1 --- Introduction --- p.20Chapter 3.2 --- Modified Nodal Analysis --- p.21Chapter 3.2.1 --- Standard Nodal Analysis Method Review --- p.22Chapter 3.2.2 --- General Theory of Modified Nodal Analysis --- p.23Chapter 3.2.3 --- Calculate the System Poles Using MNA --- p.27Chapter 3.2.4 --- Examples and Comparisons --- p.28Chapter 3.3 --- Krylov Subspace MOR Method --- p.30Chapter 3.4 --- Examples of Krylov Subspace MOR --- p.32Chapter 3.5 --- Summary --- p.34References --- p.35Chapter Chapter 4 --- Physical Model Order Reduction --- p.38Chapter 4.1 --- Introduction --- p.38Chapter 4.2 --- Gaussian Elimination Method --- p.39Chapter 4.3 --- A Lossy PEEC Circuit Model --- p.44Chapter 4.3.1 --- Loss with Capacitance --- p.44Chapter 4.3.2 --- Loss with Inductance --- p.46Chapter 4.4 --- Conversion of Mutual Inductive Couplings --- p.47Chapter 4.5 --- Model Order Reduction Schemes --- p.50Chapter 4.5.1 --- Taylor Expansion Based MOR Scheme (Type I) --- p.51Chapter 4.5.2 --- Derived Complex-valued MOR Scheme (Type II) --- p.65Chapter 4.6 --- Summary --- p.88References --- p.88Chapter Chapter 5 --- Concluding Remarks --- p.92Chapter 5.1 --- Conclusion --- p.92Chapter 5.2 --- Future Improvement --- p.93Author's Publication --- p.9

Fast Numerical Model of Power Busbar Conductors Through the FFT and the Convolution Theorem

[EN] Skin and proximity effects can cause a non-uniform current distribution in the electrical conductors used in alternating current (ac) busbar systems, which increases resistance, decreases internal inductance, and causes asymmetries in the electromagnetic fields and forces. As no explicit solution for the ac resistance or the ac internal inductance of a rectangular conductor has been found, numerical methods are needed to obtain the distribution of the currents inside the busbars. In this paper, a novel numerical approach, based on the fast Fourier transform (FFT) and the convolution theorem, is proposed to model the rectangular conductors of the busbar system, based on the subdivision of the conductor in filamentary subconductors. This technique is know to lead to a dense, huge inductance matrix, that must be multiplied by the current vector, which limits its practical application. The proposed method replaces this matrix-vector multiplication with a simple element-wise vector product in the spatial frequency domain. The FFT speed makes the proposed method very fast and easy to apply. This approach is theoretically explained and applied to an industrial busbar system.This work was supported in part by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU), in part by the Agencia Estatal de Investigación (AEI), and in part by the Fondo Europeo de Desarrollo Regional (FEDER) in the framework of the Proyectos I+D+i - Retos Investigación 2018, under Project Reference RTI2018-102175-B-I00 (MCIU/AEI/FEDER, UE).Martinez-Roman, J.; Puche-Panadero, R.; Sapena-Bano, A.; Burriel-Valencia, J.; Terrón-Santiago, C.; Pineda-Sanchez, M.; Riera-Guasp, M. (2022). Fast Numerical Model of Power Busbar Conductors Through the FFT and the Convolution Theorem. IEEE Transactions on Power Delivery. 37(4):1-11. https://doi.org/10.1109/TPWRD.2021.312626511137