Model order reduction of coupled circuit‐device systems

We consider model order reduction of integrated circuits with semiconductor devices. Such circuits are modeled using modified nodal analysis by differential‐algebraic equations coupled with the nonlinear drift‐diffusion equations. A spatial discretization of these equations with a mixed finite element method yields a high dimensional nonlinear system of differential‐algebraic equations. Balancing‐related model reduction is used to reduce the dimension of the decoupled linear network equations, whereas the semidiscretized semiconductor model is reduced using proper orthogonal decomposition. Because the computational complexity of the reduced‐order model through the nonlinearity of the drift‐diffusion equations still depends on the number of variables of the full model, we apply the discrete empirical interpolation method to further reduce the computational complexity. We provide numerical comparisons that demonstrate the performance of the presented model reduction approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of the short‐open calibration technique to vector finite element method for analysis of microwave circuits

A novel numerical de‐embedding scheme called the short‐open calibration (SOC) technique, in conjunction with the vector finite element method (FEM), has been developed to characterize two‐port network of arbitrarily shaped, three‐dimensional discontinuities in microwave circuits. This SOC technique is effectively implemented into the FEM for boundary truncation of the unbounded circuit structures. In such a manner, fast convergence of iterative solver for large‐sparse linear matrix equations from FEM is achieved. The SOC technique is used to remove parasitic effects brought by the approximation of the impressed voltage source and also the problem of resulting consistency between the two‐ and three‐dimensional simulations. Scattering parameters of discontinuous sections are constructed from the definition of port voltages and currents. Numerical solutions are well compared with those published in the available literatures. It is demonstrated that the features of the SOC technique are advantageous when combined with FEM for electromagnetic problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Computer‐aided design and simulation of optical microring resonators

This paper contains results of the three‐dimensional full‐vectorial finite element (3D FEM) frequency‐domain simulations of microring silicon resonators intended for the add/drop multiplexing, switching, and sensor applications. The second‐order edge elements are used, and the computational domain is closed using the standard perfectly matched layer. The calculations are performed for add‐drop and all‐pass configurations in a wide spectral range covering the first and the second telecommunication windows. Although computationally very demanding, the three‐dimensional full‐vectorial finite element offers designers a feasible and efficient way to design and simulate complex integrated optical components containing microring resonators, especially in the case when the radii of rings are too small to approximate that theories were valid. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐domain sensitivity analysis of planar structures using first‐order one‐way wave‐equation boundaries

An efficient adjoint variable method technique is developed for time‐domain sensitivity analysis of planar structures with transmission‐line modeling complemented by a first‐order one‐way wave‐equation absorbing boundaries. A backward‐running adjoint simulation is derived and solved. The validity of the technique is illustrated through three microstrip circuits. The examples demonstrate the efficiency and accuracy of the technique in comparison with the classical finite‐difference approaches to the estimation of the response sensitivities. Copyright © 2007 John Wiley & Sons, Ltd.     

Algebraic multigrid Laplace solver for the extraction of capacitances of conductors in multi‐layer dielectrics

This paper describes the development of a robust multigrid, finite element‐based, Laplace solver for accurate capacitance extraction of conductors embedded in multi‐layer dielectric domains. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. In particular, a new, node‐based agglomeration scheme is proposed to speed up the process of agglomeration. Several attributes of this new method are investigated through the application of the Laplace solver to the calculation of the per‐unit‐length capacitance of configurations of parallel, uniform conductors embedded in multi‐layer dielectric substrates. These two‐dimensional configurations are commonly encountered as high‐speed interconnect structures for integrated electronic circuits. The proposed method is shown to be particularly robust and accurate for structures with very thin dielectric layers characterized by large variation in their electric permittivities. More specifically, it is demonstrated that for such geometries the proposed node‐based agglomeration systematically reduces the problem size and speeds up the iterative solution of the finite element matrix. Copyright © 2007 John Wiley & Sons, Ltd.     

A new parallelization strategy for solving time‐dependent 3D Maxwell equations using a high‐order accurate compact implicit scheme

With progress in computer technology there has been renewed interest in a time‐dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second‐order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high‐order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd‐order accurate explicit scheme for approximation of spatial derivatives with the 4th‐order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl‐based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three‐dimensional time‐dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Complementary split rings resonators (CSRRs): Towards the miniaturization of microwave device design

In this paper, it is demonstrated that complementary split rings resonators (CSRRs), a new type of planar resonators recently introduced by some of the authors, are key elements for the miniaturization of microwave devices implemented in planar technology, such as filters and diplexers. These devices essentially consist on a host transmission medium (microstrip line) to which the CSRRs are electrically coupled, and additional microstructure in order to achieve the required device performance. From the analysis and numerical simulations of the equivalent circuit model of the basic device cell, as well as electromagnetic simulations of actual structures, it is confirmed that CSRRs are useful resonators for the synthesis of planar microwave filters where dimensions, out-of-band performance and bandwidth can be simultaneously optimized. The simultaneous fulfillment of these aspects is a relevant advantage of the proposed structures. The possibility to implement band pass filters with wide bandwidth and high performance, the small electrical size of CSRRs, as well as their potential applications in other microwave devices, make these particles of actual interest in microwave engineering.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.     

Calculation of iron loss in rotating machines by direct consideration of eddy currents in electrical steel sheets

A method for calculation of iron loss in rotating machines is proposed. The calculation employs the finite element method while taking into consideration the eddy currents in electrical steel sheets. First, the electromagnetic field distribution and iron loss of several types of electrical steel sheets are calculated by the proposed method, formulated as a one‐dimensional model. The results are compared with those of experiments and the conventional method in order to verify the validity of the proposed method. The influence of the skin effect and magnetic saturation in the electrical steel sheets on the iron loss characteristics is also investigated. Next, the proposed method formulated as a three‐dimensional model is applied to several types of rotating machines. It is shown that the skin effect is significant in the case of high‐frequency harmonic fields and that direct consideration of eddy currents by the finite element method is indispensable in such cases. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 176(3): 69–80, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21053     

Positive‐real property of passive fractional circuits in W‐domain

Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Fractional circuits constitute a new challenge for the analysis and synthesis methods of traditional circuits theory. Passivity is the fundamental property of traditional circuits (integer order electric circuits). As is known to all, passivity is equivalent to positive realness in traditional linear circuits. However, this equivalence is broken down by introducing fractional elements into electrical networks in s‐domain. To address this issue, on the basis of s‐W transformation, we study the passive criteria of fractional circuits with rational order elements in this paper. Definitions of positive‐real (matrix) function in W‐domain are given, and the equivalence conditions of positive realness are derived. In addition, a conclusion is proposed in which the immittance (matrix) function of passive fractional circuits with rational order elements is positive real in W‐domain. The applications of passive criteria in circuit synthesis are shown.     

Least squares spectral element method for 2D Maxwell equations in the frequency domain

We propose a high order numerical method for the first order Maxwell equations in the frequency domain, defined in media with arbitrary complex shape. Our approach is based on the combination of the least squares approach with the spectral element method. The former frees the solution from spurious modes, that can be found sometimes in classical finite element simulations. Many examples of such non‐physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements are a numerical technique for solving partial differential equations which can be regarded as an extension of finite elements: they merge the flexibility of finite elements in dealing with complex geometries, and the better accuracy of spectral methods. Convergence to exact solution is improved by increasing (at run time) the polynomial degree, with no changes on the computational grid: this provides a significant advantage in respect to low order finite element, which necessarily have to resort to grid refinement. In the authors opinion this approach can be successfully used for the treatment of large scale electromagnetic problems or, alternatively, for applications where higher precision is required. We present a few numerical experiments which prove the capability of the method in object. Copyright © 2004 John Wiley & Sons, Ltd.     

Three‐dimensional finite element eddy current analysis by using high‐order vector elements

Sets of high‐order basis functions of a tetrahedral element are systematically constructed and applied to finite element analysis of eddy current problems. A polynomial space is divided into a lot of subspaces assigned on the edges, faces, and a volume of the tetrahedral element. Lagrange‐type vector basis functions of the subspaces are presented. The effect of the high‐order vector elements is investigated by a cubic conductor model located in AC steady‐state magnetic fields. In the calculations using the fundamental and second‐order elements, no convergent value of the eddy current power loss can be obtained in spite of fine meshes because the eddy current shifts to the surface of the conductor. The higher‐order vector elements give the convergent solutions in the coarse meshes. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(4): 60–67, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10306     

Relationship of fast‐scale and slow‐scale instabilities in switching circuit with multiple inputs

Power converter circuits, such as current‐controlled or voltage‐controlled converters and inverters often have multiple inputs in the controller. The multiple inputs cause high‐frequency and low‐frequency oscillations. In earlier studies, the characteristics of circuits in fast‐scale and slow‐scale dynamics have been investigated. However, in many cases, circuits with multiple inputs have three or more dimensional topology which makes detailed analysis difficult. In this paper, we analyze a simple interrupted electric circuit in order to understand essential characteristics of fast‐scale and slow‐scale dynamics. The advantage of this simple interrupted circuit is that it is possible to derive a 1‐dimensional map, which facilitates rigorous studies. Based on the structure of the return map and the characteristic multiplier, we explain the characteristics of the system. We report the occurrence of pitchfork, period doubling, and border collision bifurcations in slow scale, and period doubling bifurcation in fast scale. We found that local bifurcation, which appears in fast‐scale dynamics, does not significantly affect the global behavior of the system while instabilities in the slow‐scale dynamics strongly affect the system behavior. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of cylindrical resonators by wave concept iterative process in cylindrical coordinates

The purpose of this study is the formulation of a wave concept iterative process for the analysis of the microwave planar circuits printed between two dielectric mediums in a cylindrical metallic box. This method is based on the transverse wave formulation. It also uses the Hankel Transform to express the integral relation in a spectral domain. An example of circular patch has been studied and the obtained results validate the new approach. The good agreement between the simulation results and the experimental published data justifies the design procedure and validates the present analysis approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance Evaluation of an Axial‐Type Magnetic‐Geared Motor

This paper first proposes an axial‐type magnetic‐geared motor that uses permanent magnets only in the high‐speed rotor. The operating principle of this motor is described and the torque–speed characteristics are computed by using three‐dimensional finite element method analysis. In order to increase the torque density, a novel axial‐type magnetic‐geared motor with permanent magnets on the high‐speed rotor and stator is also proposed. The torque–speed characteristics are compared to the original model with permanent magnets only on the high‐speed rotor. Finally, the computed torque–speed characteristics are verified against measurements on a prototype.     

Multilayered transformer utilizing Mn‐Zn ferrite and its application to a forward‐type DC–DC converter

This paper describes the electrical characteristics of a multilayered transformer composed of a Mn‐Zn ferrite core, and primary and secondary conductors positioned alternately not only in the vertical direction but also in the horizontal direction. In order to elucidate the operating characteristics of the two types of transformers, one was given the conventional planar winding structure and the other the new winding structure described above, and a two‐dimensional finite element method that took account of the two conditions and a constant input voltage and load current was introduced. The coupling coefficient of the conventional multilayered transformer deteriorated with increasing load current. But the coupling coefficient of the proposed multilayered transformer was independent of the load current. A forward‐type DC–DC converter using the new multilayered transformer had higher efficiency than a converter using the conventional multilayered transformer. © 2001 Scripta Technica, Electr Eng Jpn, 135(4): 1–8, 2001     

汽轮机叶片三维有限元模型前处理

该文采用了先将整体结构分成子块进行剖分、后组合成整体的思路，并提出了整数空间坐标系的概念，成功地解决了子块之间的联接和边界条件处理等难点，建立了一套适合于三维结构的有限元前处理方法．并研制了汽轮机叶片有限元前处理程序，成功地应用于叶片三维有限元分析．图９参５     

Cellular non‐linear networks for minimization of functionals. Part 1: Theoretical aspects

A method for the definition of cellular non‐linear networks able to find approximate minima of rather a large class of continuous functionals is proposed and discussed from a theoretical point of view. The method is based on the spatial discretization of continuous functionals and on the theory of potential functions for resistive circuits. The discretization of the continuous functionals is obtained by resorting to the finite difference method or to the finite element method. The spatial discretization converts a functional into a function of a finite set of variables. By exploiting the theory of potential functions for resistive circuits, from such a function one can derive a lumped circuit that makes it possible to find an approximate minimum of the given functional. Copyright © 2001 John Wiley & Sons, Ltd.     

基于棱单元法计算爪极发电机负载特性

本文用四面体棱单元三维有限元方法计算一台28V,35A汽车用爪极发电机负载特性.用迭代的方法计算出发电机负载不同转速时的输出电流.棱单元有限元法比节点元有限元法对内存的需求少,计算时间少,因此适合计算爪极发电机负载特性.样机的实验结果与棱单元法计算结果的一致性验证了计算结果的正确性.本文对爪极发电机负载性能和参数的计算以及爪极发电机的优化设计具有一定的理论参考意义.     

On the efficient simulation of electrical circuits with constant phase elements: The Warburg element as a test case

The constant phase Element (CPE) concept naturally emerges as a model for describing a range of electrical phenomena where ionic diffusion is involved. We suggest a new method for modelling the transient behavior of electrical circuits that contain CPE elements. Without loss of generality, we study the Warburg element to demonstrate the method, but the method can be easily extended to any CPE. Transient simulations of such elements require the numerical evaluation of a computationally expensive convolution integral that links the voltage drop across the element, with the current that passed through it. In our work we suggest a new method for reducing the computational cost of the numerical evaluation of the convolution integral. We show that the computational cost can be reduced by one order of magnitude.