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The Partial Element Equivalent Circuit (PEEC) method is promising numerical technique for three-dimension electromagnetic modeling across various application fields. In the framework of the PEEC method, the partial elements modeling the magnetic and electric field coupling between elementary volumes and surfaces are computed by double-folded volume and surface integrals. Assuming the quasi-static hypothesis and an orthogonal mesh, the integrals have been computed by the analytical formulas derived in literature, which significantly reduces the computational time in comparison to the numerical integration. However, the existing analytical formulas are affected by significant numerical errors for certain PEEC structural mesh necessary to model the skin and proximity effects with a higher accuracy. To utilize the full potential of the PEEC method, the calculation of partial elements has to be carefully addressed, which has not been investigated in a comprehensive way so far. Accordingly, this paper presents a systematic accuracy analysis of the existing closed-form analytical formulas and methods for calculating the self and mutual inductances between two rectangular conductors. Additionally, a new strategy to select a proper analytical formula depending on the dimensions and positions of two conductors is proposed, which allows the mutual inductance extraction with a relative error of less than 0.1 % . The new method is systematically validated on examples of 3-D dense PEEC systems using the quadruple precision arithmetic as reference., IEEE Transactions on Electromagnetic Compatibility, 63 (1), ISSN:0018-9375, ISSN:1558-187X

Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation, known as S-PEEC, requires computing quadruple integrals for each mesh patch. Several techniques have been developed to simplify the computational complexity of quadruple integrals but limited to triangular meshes as used in well-known methods such as the Method of Moments (MoM). However, in the S-PEEC method, the mesh can be rectangular and orthogonal, and new approaches must be investigated to simplify the quadruple integrals. This work proposes a numerical approach that treats the singularity and reduces the computational complexity of one of the two quadruple integrals used in the S-PEEC method. The accuracy and computational time are tested for representative parallel and orthogonal meshes., Engineering analysis with boundary elements, 134, ISSN:0955-7997

The computation of self and mutual inductances of coils is a classic problem of electrical engineering. The accurate modeling of coupled coils has received renewed interest with the spread of wireless power transfer systems. This problem has been quite well addressed for coplanar or perfectly coaxial coils but it is known that the misalignment conditions easily lead to a sharp decrease in the efficiency. Hence, it is crucial to take misalignment into account in order to properly design the overall wireless power transfer system. This work presents a study to compute analytically the mutual inductance of non-coaxial pancake coils with parallel axes. The accuracy of the proposed methodology is tested by comparison with the numerical results obtained using the tool Fast-Henry. Then, a wireless power transfer system, comprising a full bridge inverter is considered, showing the impact of the misalignment on the coupling between two pancake coils and, thus, between the source and the load.

The Partial Element Equivalent Circuit (PEEC) method is widely used to model a large variety of electrical systems ranging from interconnects to antennas and packaging. A key aspect in the development of the method is the computation of interaction integrals, namely partial inductances and coefficients of potential. In this work, a novel semi-analytical approach to the computation of the self-interaction integral over rectangular domains is proposed for the zero thickness case as it occurs in the case of the coefficients of potential and partial inductances of very thin conductors and in the surface integral equation based formulation. The proposed semi-analytical formula is verified by comparison with more standard integration schemes.

This paper presents a rigorous derivation of the dc solution of three-dimensional partial element equivalent circuit (PEEC) formulation extended to include simultaneously conductive, dielectric, and magnetic materials. The circuit interpretation of Maxwell's equations provided by the PEEC method allows to reformulate the dc modeling task in such a way that physical phenomena are fully exploited. Indeed, since the displacements currents are identically zero in dielectrics, Kirchhoff's current law is enforced in terms of charge conservation internally to dielectrics or at the interface between dielectrics and other materials. A well-posed problem is achieved by adding the charges as new unknowns and identifying the disconnected objects. Two numerical examples are presented demonstrating the accuracy of the proposed method when compared to the dc solution as extracted by the fast Fourier transform of the impulse response and a finite element method simulation.

The distortionless propagation of signals in a medium offers a way to preserve the signal integrity. There exists a condition for distortionless propagation on a transmission line known as the Heaviside condition. This paper proposes the use of the Heaviside condition to characterize and design magneto-dielectric materials that provide distortionless propagation in a specified finite frequency band. Plane wave propagation in a magneto-dielectric material is modeled by a transmission line model, thereby assuming transverse electromagnetic mode propagation. Then, the Heaviside condition is employed to derive the frequency-dependent permittivity and permeability functions of the material in rational form, so they satisfy the condition in a specified frequency interval. A procedure to design such materials is described. A numerical example of the design process is provided and an illustration of the effectiveness of modeled material in fulfilling the Heaviside condition in a specified frequency interval both in the time and frequency domains is given, indicating the validity of the approximation. The design procedure is as such a suitable preliminary design guide for deriving a realizable description of a magnetodielectric, exhibiting the distortionless property in the desired frequency interval, with certain specified requirements put on the loss, or the permeability and permittivity values satisfied. The obtained results may initiate further investigations into the bandwidth restrictions of the approximation, on closed-form design solutions, and the practical realization of such materials.

In this paper, we study the delay-rational Green’s-function-based (DeRaG) model for transmission lines. This model is described in terms of impedance representation and it contains a rational and a hyperbolic part. The crucial property of transmission lines models is to be passive. The passivity of the rational part has been studied by the authors in a previous work. Here, we extend the results to the rational part of the DeRaG model. Moreover, we prove the passivity of the hyperbolic part.

The electromagnetic compatibility (EMC) performances of a product can seriously be affected by interconnects. Interconnects can be studied by using the multiconductor transmission lines (MTLs) theory. Mathematical models of MTLs are normally validated with the aid of well-known software, such as MATLAB or PSpice. Simulink is part of the MATLAB suite but is not frequently used, and it is often underestimated both in academia and in the university education. In this paper, we briefly review the mathematical model for MTLs called DeRaG, which is a rational model based on delay extraction. Then, we propose the corresponding Simulink implementation for a 3-conductor transmission line. The Simulink has high readability, is accurate and the simulation time is remarkably faster than the corresponding model obtained in PSpice.

In wireless condition monitoring systems the antenna serves as a critical part of the data transmission link. A condition monitoring application usually pose a challenging environment for an antenna system, as they are often found in harsh machine environments. As conventional antennas usually are designed for free-space operation and for some design temperature range, the presence of additional materials and their temperature variation are commonly not accounted for. In this paper an attempt to highlight the impact of materials' temperature-dependence, in their electrical properties, on printed antenna characteristics is presented. Partial element equivalent circuit models of a common printed antenna design are developed. By incorporating temperature-dependent permittivity models of pure water, and a mixture of an industrial lubricant and water, the impact on the antenna's resonant behavior is demonstrated. The numerical examples highlight that the temperature variation in the permittivity of materials surrounding the printed antenna may impact the antenna characteristics enough to be considered in the design, if a degradation in performance is not an option.

2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), ISBN:978-4-88686-405-5, ISBN:978-1-5386-4190-3, ISBN:978-4-88686-403-1

This article presents the results of a study conducted to quantify the seasonal variation of coherence in synthetic aperture radar SAR interferograms in Kiruna, Northern Sweden. In SAR interferometry InSAR, coherence is an important concept that provides a good indication of the phase stability of the scatterers. Therefore, in this study, the degree of coherence is used as a parameter to identify the seasonal variation interferograms. For this study, 34 Radarsat-2 ultra-fine beam mode U6D images of the Kiruna area 67°51ʹN, 20°14ʹE and the improved digital elevation model DEM created by merging the Radarsat-2 DEM and ASTER DEM were used to produce 561 differential interferograms. The interferograms were arranged in three different ways for the analysis, with the first including common master interferograms with the summer master image, the second including the sequential interferograms that have the shortest temporal baseline, and the third accounting for all possible combinations of the interferograms full network of interferograms. Following this step, the variation of coherence for forest areas, urban areas, and flat waste rock areas was studied. This study shows that interferograms generated for the Kiruna region exhibit seasonal variations in coherence due to the ground snow layer in winter. Furthermore, when there is water on the ground due to the melting of the snow layer in the spring or due to rains in autumn, the coherence is reduced considerably. Another significant feature is that there is a significant change in summer-to-summer coherence for some regions even over the course of a few years. Based on this study, it is clear that the winter Radarsat-2 U6D beam mode images are not suitable for differential interferometric SAR DInSAR deformation measurements in flat waste rock regions in Kiruna. It is expected that even with winter images, PSInSAR or CTM techniques will be able to provide better deformation measurements, but, in this study, those techniques were not assessed. The next step will be to study the seasonal variations in coherence in natural or man-made targets/persistent scatterers using persistent scatter InSAR PSInSAR or coherence target monitoring CTM techniques.

During recent years anisotropic materials have received an increasing interest and found important applications in the field of shielding and antennas. The anisotropy may be due to intrinsic properties, or as a consequence of mixing. Intentionally or not, the anisotropy impacts the electromagnetic (EM) behavior of a system. Therefore, it is desirable to be able to incorporate the anisotropic effects in an EM model, to allow design tasks and analysis. In this paper, the partial element equivalent circuit (PEEC) formulation is extended to handle nondispersive linear anisotropic dielectrics. The anisotropic dielectric PEEC cell is derived and the resulting PEEC equations are developed into a descriptor system form, which is well suited for implementation in SPICE-like solvers, and for reduction by model-order reduction techniques. A verification of the model is given by a numerical example of a patch antenna situated on an anisotropic substrate and the results are in good agreement with a finite-difference time-domain implementation. The proposed PEEC model is of interest for further work, i.e., in the modeling of setups involving mixtures of materials, with an orientational alignment, and engineered materials, encountered in different EM compatibility applications.

In this paper, we investigate the distortionless conditions for multiconductor transmission lines (MTLs) with frequency-independent per-unit-length (p.u.l.) parameters. In fact, the well-known distortionless Heaviside condition is valid only for single-conductor transmission lines. The MTL is modeled using the delayed Green’s-function-based method recently proposed by the authors. In this method, the impedance matrix is described in terms of a rational part, which accounts for the low-frequency behavior, and a hyperbolic part, which determines the high-frequency response of the MTL. We find that the hyperbolic part is already distortionless at high frequency and that this property can be used to identify the p.u.l. parameters of the distortionless lossy MTL associated with the original line. To serve this purpose, the line is decoupled using a frequency-independent modal decomposition. The Heaviside condition can be enforced in the modal domain on each of the single-conductor decoupled lines. The features of the distortionless lines in the modal domain are preserved in the physical domain as a consequence of the real-valued similarity transform. The numerical results demonstrate that the new line completely characterizes the distortionless propagation of a generic MTL with frequency-independent p.u.l. parameters. The proposed formulation could be used in the optimization design process by enforcing the distortionless condition along with other design constraints.

2018 IEEE 30th International Symposium on Power Semiconductor Devices and ICs (ISPSD), ISBN:978-1-5386-2927-7, ISBN:978-1-5386-2926-0, ISBN:978-1-5386-2928-4

The simulation of mixed circuit and electromagnetic (EM) structures is of major interest in most EM applications. Many of the developed methods involve modifying a SPICE-like solver to incorporate an EM numerical method, or to extend the EM numerical method to handle the circuit components (e.g., diodes, transistors, etc.) by reimplementing their model definitions. A novel technique has been developed to simulate combined linear/nonlinear circuit and EM problems in time domain. This technique utilizes the partial element equivalent circuit method as the EM solver and employs OrCAD as the circuit solver. The link between the two solvers is established by defining the circuits connected to the EM structure as ports and approximating each port's current-voltage relations at each time point by a system of linear equations. To demonstrate the capability of the developed method, four structures are examined. Good agreement of the results shows the feasibility of the developed method to solve this type of mixed problems. Since OrCAD is used for the circuit simulations, the need to modify a SPICE-like solver or to reimplement the definitions of the circuit devices has been removed. On the other hand, by manipulating the system of equations and proper optimization techniques, an optimal solver can be achieved.

With rising frequencies involved in electronics, losses and dispersion exhibited by dielectrics become important to consider in electromagnetic modeling. The Partial Element Equivalent Circuit (PEEC) method is suitable for a mixed electromagnetic and circuit setting, forming equivalent circuits that can be interconnected with circuit elements. In this paper, a descriptor form representation of PEEC models incorporating dispersive and lossy dielectrics is developed. By representing the electrical permittivity with a Debye-Lorentz model equivalent circuits can be synthesized. The synthesized circuits for the permittivity are included in the PEEC equations by formulating the circuit equations for the additional circuit unknowns. This yields an input/output formulation that can handle an arbitrary number of finite dielectrics and be integrated by any kind of integration scheme. Furthermore, it offers a straightforward way to incorporate lossy and dispersive dielectrics into a PEEC solver compared to using recursive convolution. The proposed descriptor form representation is tested for a setup consisting of three microstrips over a ground plane, separated by a dielectric substrate. Both the ideal and the lossy and dispersive case are tested and compared. Furthermore, the proposed formulation is verified against an existing implementation in the frequency-domain. Good agreement between the proposed formulation and the existing frequency-domain PEEC formulation is obtained.

The Partial Element Equivalent Circuit ({PEEC}) method provides an electric equivalent circuit for a physical geometry. This circuit can be combined with external passive/active lumped elements, enabling the simulation of combined circuit and electromagnetic (EM) structures. The resulted circuit can be solved in dedicated solver, or equivalently can be exported to a SPICE-like solver. In this paper, the inclusion of passive and active lumped circuit elements in {PEEC} method has been studied and a combined solver has been developed. To demonstrate the capability of the solver, three structures are examined. All examples include a transmission line-PEEC model and active components. Results are compared with those from OrCAD, where an analytical model for the transmission line is used. Good agreement between the results shows the feasibility of using {PEEC} to solve this type of mixed problems. Also, comparison has been made in terms of implementation and feasibility for the aim of developing the optimal EM solver with active elements support. It is shown that SPICE is not a suitable choice to solve the PEEC models and, a specialized solver can solve the system in a much faster way. On the other hand, all the definitions and models of circuit devices e.g. transistors, MOSFETs, etc. should be implemented in the specialized solver, which raises a trade-off between the solution time and the implementation time. Validerad; 2012; 20121021 (sohsaf)

Multiconductor transmission lines have found a wide range of applications, as power lines, as high‐speed interconnects, and as on‐chip interconnects. Electromagnetic interference (EMI) can be descr ...

In electronics as well as in communications, it is highly desirable to be able to transmit a signal that is preserved from any distortions that is due to the lossy nature of the medium in which the signal travels, normally a transmission line. In this paper, we exploit the connections between the delayed Green's-function-based method from the authors and the well-known distortionless Heaviside condition. It is found that, in the method, an important results was already present but its importance not yet understood. In particular, we prove that we are able to identify the distortionless transmission line associated to a generic transmission line. We consider only 1-conductor transmission lines, with frequency-independent per-unit-length parameters. The multiconductor transmission-line case will be addressed in future works.

Ten different commercially available conductive thermoplastic materials have been tested for near- and far-field shielding effectiveness (SE). Far-field SE was tested using a modified standard measurement technique to provide results comparable with the company-provided data. Further, housings of different thermoplastic materials were constructed and equipped with an electromagnetic interference (EMI) source to model a realistic near-field SE situation. The SE data up to 1 GHz is presented. Conductive thermoplastic materials with fillings of stainless steel fibers and nickel-coated carbon fibers were the two materials that offer the best far-field shielding performance. For the near-field shielding, two materials with filling of stainless steel fibers were the best performing ones. A thermoplastic with polycarbonate (PC) base and stainless steel content of 1.5 vol% showed the best combined far- and near-field shielding results. Validerad; 2006; 20060905 (ysko)

In this paper, the transient analysis of lossy and dispersive multiconductor transmission lines is considered. The existing Green's function-based method is extended to explicitly include delays extraction, thus leading to a significant compressed time-domain state-space model. The proposed method is mainly based on poles and residues asymptotic analysis and lossless delays extraction. The resulting hybrid state-space model incorporates Dirac-combs in the input and results into a reduced number of state variables. A test case has been considered in order to clearly demonstrate the effectiveness of the proposed methodology. The results are compared with the original rational Green's function method, and with the standard inverse fast Fourier transform technique.

Cables, printed circuit boards, and VLSI interconnects are commonly modeled as multiconductor transmission lines. Models of electrically long transmission lines are memory and time consuming. In this paper, a robust and efficient algorithm for the generation of a delay-based model is presented. The impedance representation via the open-end matrix Z is analyzed. In particular, the rational formulation of Z in terms of poles and residues is exploited for both lossless and lossy cases. The delays of the lines are identified, and explicitly incorporated into the model. A model order reduction of the system is automatically performed, since only a limited number of poles and residues are included in the rational part of the model, whereas the high-frequency behavior is captured by means of closed expressions that account for the delays. The proposed method is applied to two relevant examples and validated through the comparison with reference methods. The time-domain solver is found to be more accurate and significantly faster than the one obtained from a pure-rational model.

This paper presents a new delayed model of two-conductor transmission lines with frequency-independent per-unit-length parameters. In particular, the line delay extraction problem is considered. By use of a dyadic Green's function macromodel method, the rational form of the open-end impedance matrix allows an easy identification of poles and residues, and a new technique for the extraction of the line delay in an analytical way is gained, without any impact on the complexity of the line macromodel itself. By use of Laplace and Fourier transforms, the transfer function is expressed in terms of the Dirac comb. The delay is then easily identified and directly incorporated into the system impulse response. Giving a current-controlled representation, the port voltages are evaluated. Thanks to the formulation of the transfer function by use of the Dirac comb, the convolution product is avoided, gaining accuracy and time-saving from a computational point of view. Numerical results confirm the validity of the proposed delay-extraction technique. The basic ideas for the extension of the proposed technique to the lossy case are outlined.

Highly interconnected multiprocessor systems are now performance limited by the backplane interconnection bottleneck associated with planar interconnection technologies. Smart pixel throughput capabilities are projected to exceed I Thitls/cm2 [1] and offer the promise of overcoming the bottlenecks of planar technologies for many types of interconnection-limited multiprocessor problems. Systems that use smart pixel-based free space optical interconnects (FSOI) provide two general dense interconnection capabilities: intelligent parallel data transfer and intelligent parallel data interchange. Optical imaging provides a high throughput approach to linking smart pixel planes for data transfer. In this case the high 110 density of smart pixels may provide a power consumption and size advantage over electronics [2,3]. For data interchange, FSOI provides the additional ability to perform the data partitioning and interleaving useful in space variant link interconnection patterns like the perfect shuffle (PS) [41,which are inherently difficult to implement in planar interconnection technologies. Such patterns are characterized by high BSBW [51. In multi-processor architecture design, there is a direct trade-off between minimum BSBW and latency in a network. It is therefore generally desirable to implement networks with the largest minimum BSBW that can be practically achieved to solve a given problem. The ability of optical elements to interconnect large arrays in space-variant patterns, without crosstalk in the medium, suggests that FSOI techniques are particularly promising for problems with high BSBW. For problems with greater than 1 ThitJsec BSBW (i.e., greater than the capabilities of a single chip) free space optical interconnects have a marked advantage [6,71. Therefore, globally interconnected multi-chip smart pixel based architectures have the potential to reap the full benefits of FSOI. This paper describes the experimental demonstration of a smart pixel based optical interconnection prototype currently being developed under the Free-space Accelerator for Switching Terabit tworks (FAST-Net) project, sponsored by the U.S. Defense Advanced Research Projects Agency. The prototype system incorporates 2-D arrays of monolithically integrated high-bandwidth vertical cavity surface emitting lasers (VCSELs) and photodetectors (PDs). A key aspect of the FAST-Net concept is that all smart pixels are distributed across a single multi-chip plane. This plane is connected to itself via an optical system that consists of an array of matched lenses (one for each smart pixel chip position) and a mirror. The optical interconnect system implements a global point-to-point shuffle pattern. The interleaved 2-D arrays of VCSELs and PDs in the prototype are arranged on a clustered self-similar grid pattern with a closest element pitch of 100 tm. The circular VCSEL elements have a diameter of 10 pm and the square PDs have an active region that is 50 jim wide. These arrays are packaged and mounted on printed circuit boards along with CMOS driver, receiver, and FPGA controller chips. Micro-positioning mounts are used to effect alignment that is consistent with current MCM chip placement accuracy. Shuffled optical data links between the multiple ICs have been demonstrated in preliminary evaluation of this system. These results suggest that a multi-Terabit optically interconnected MCM module is feasible.

A new technique for the reluctance method applied to the Partial Element Equivalent Circuit (PEEC) method for the time domain analysis is presented which is well suited tobe combined with acceleration techniques. In particular, taking advantage of the rank-deficiency of the magnetic and electric field couplings, a new technique for the sparsification of reluctance and capacitance matrices is adopted. Furthermore, the multiscale block decomposition technique has been applied to fast fill these matrices. Finally, the the sparse multifrontal LU factorization has been adopted to efficiently compute the global solution. Numerical results demonstrate the validity of the proposed approach. Validerad; 2014; 20140303 (jekman)

This paper presents a method to deal with the ill-posed and rank-deficient linear systems arising from sparsified partial element equivalent circuit-based electromagnetic simulations via a reluctance method. Since conventional, direct methods, cannot be used to solve these kind of problems, regularization techniques need to be employed. Among various regularization techniques, a least square-based method entitled LSQR is utilized to solve the rank-deficient problems. The proposed method is specially proper for the models where capacitive couplings can be neglected, since magnetic field is the dominating factor, like problems within power electronics. The correctness of the presented PEEC-based solver is ensured by studying bus bar models which are a part of frequency converters with application in power electronics. Godkänd; 2012; 20120422 (dan) Kretsbaserad lösare för elektromagnetisk analys av kraftelektroniksystem- Applikation mot IGBTmoduler

Photonic crystal (PhC) lenses with negative refractive index have attractedintense interest because of their application in optical frequencies. In thispaper, 2-D PhC lenses with triangular lattice of cylindrical holes in dielectricmaterial are investigated. Variant physical parameters of the lens are introducedand their effects on the lens response are studied in detail. The effect ofthe surface termination is investigated by analyzing the power flux within thePhC structure. A new lens formula has been obtained which shows a linearrelation between source distance (distance between the source and the lens)and image distance (distance between the image and the lens) for any surfacetermination of the PhC lens. It is observed that the excitation of surfacewaves does not necessarily pull the image closer to the lens. The effects of thethickness and the lateral width of the lens are also analyzed. Validerad; 2012; 20120601 (sohsaf)

This paper presents recent progress in the acceleration of PEEC based electromagnetic simulations and its impact on the design of complex bus bar structures as used in multi-level power converters. The approach presented consists of providing different dedicated acceleration methods for the different design tasks. The first acceleration technique applied is the so called reluctance matrix method for full 3D field results, reducing memory consumption by orders of magnitude and computing time by a factor 3 to 5. The second acceleration method applied is based on model order reduction techniques for port-to-port impedance extraction, reducing the computation time by several orders of magnitude and allowing wideband macro modeling for system level simulations. The paper focuses on the application of these methods showing the impact on practical bus bar design tasks Godkänd; 2012; 20120422 (dan) Kretsbaserad lösare för elektromagnetisk analys av kraftelektroniksystem- Applikation mot IGBTmoduler

The possibility to combine circuit and electromagnetic modeling in one program enable new problems to be solved and more efficient simulations to be done. In this paper, the inclusion of passive and active lumped circuit elements in the Partial Element Equivalent Circuit (PEEC) method has been studied and a combined solver has been developed. The solver uses PEEC to provide an equivalent circuit for a structure, then the external passive and active lumped elements are added, and then solves the combined system providing the potential and current distributions in the structure. To demonstrate the capability of the solver, two structures are examined. Both examples include a transmission line-PEEC model and active components. Results are compared with those from OrCAD, where an analytical model for the transmission line is used. Good agreement between the results shows the feasibility of using PEEC to solve this type of mixed problems. Godkänd; 2011; Bibliografisk uppgift: Article number 6130074; 20110906 (jekman) Full-wave electromagnetic modeling with active circuit elements, ESIS

This paper presents an efficient modeling approach for large bus bar systems in power electronic frequency converters using partial element equivalent circuit (PEEC) method and circuit-level simulations. Several acceleration methods have been applied to improve the computational speed and memory efficiency. The approach is verified against measurements, and used to analyze the impact of the stray impedance of bus bars on the electromagnetic and circuit behavior of a static frequency converter system.

Precipitation in the form of snow or rain could severely degrade the performance of large antenna arrays, in particular if knowledge about the beam shape and pointing direction in absolute numbers is necessary. In this paper, a method of estimating the far-field of each individual antenna element using the equivalent electric current approach is presented. Both a least squares estimator and a Kalman filter was used to solve the resulting system of equation and their performance was compared. Simulation results shows that the estimated far-field for one antenna element is very accurate if there is no noise on the signal. During noisier conditions the Kalman filter gives less noisy results while the systematic errors are slightly larger compared to the least squares estimator. Validerad; 2010; 20100426 (tore)

Faced with the challenges of increasing operational frequencies and switching rates of modern power electronics devices used in power systems, there is need for high frequency models (up to a few megahertz) for power components like reactors, capacitors banks and transformers. This paper presents the application of PEEC theory forthe creation of high frequency, electromagnetic models for air-core reactors. The electromagnetic field couplings are separated in mutual partial inductances and mutual coefficients of potential giving a correct solution from DC to a maximum frequency determined by the meshing. The PEEC models are validated by comparing simulation results, for both time and frequency domain analysis, against measurements and other established modeling methods, and show good agreement. The model created by PEEC theory, could be helpful in the design and diagnostics of air-core reactors and other power system components. Validerad; 2009; 20081111 (mathen) A New Method for Combined Electric and Electromagnetic Modeling of Power Distribution Systems -High frequency models for reactors

For various electrical interconnect and EMC problems, the partial element equivalent circuit (PEEC) method has proven to be a valid and fast solution method of the electrical field integral equation in the time as well as the frequency domain. Therefore, PEEC has become a multipurpose full-wave method, especially suited for the solution of combined circuit and EM problems, as found, for instance, on printed circuit board layouts, power electronics devices or EMC filters. Recent research introduced various extensions to the basic PEEC approach, for example a non-orthogonal cell geometry formulation. This paper presents a fast, flexible and accurate computational method for determining the matrix entries of partial inductances and the coefficients of potential for general non-orthogonal PEEC cell geometries. The presented computation method utilizes analytical filament formulas to reduce the integration order and therefore to reduce computation time. The validity, accuracy, and speed of the proposed method is compared with a standard integration routine on example cell geometries where the numeric results of the new method show improved accuracy, coming along with reduced computation time. Validerad; 2009; 20090327 (ysko)

This paper presents a parallel implementation of a partial element equivalent circuit (PEEC) based electromagnetic modeling code. The parallelization is based on the GMM++ and ScaLAPACK packages. The parallel PEEC solver was successfully implemented and tested on several high performance computer systems. Large structures containing over 50 000 unknown current and voltage basis functions were successfully analyzed and memory, performance, and speedup results are presented. The numerical examples are both of orthogonal and nonorthogonal type with analysis in the time- and frequencydomain. Godkänd; 2007; 20070126 (jekman)

This paper presents a partial element equivalent circuit (PEEC) model for air-core reactors modeling skin and proximity effects at higher frequencies using the volume filament approach. Modeling results are compared to measurements in both time domain and frequency domain, and show good agreement. Godkänd; 2007; 20070721 (jekman) A New Method for Combined Electric and Electromagnetic Modeling of Power Distribution Systems -High frequency models for reactors

The solution of large 3D electromagnetic models is important for the modeling of a multitude of EMC, PI and SI problems. In this paper, we explore new algorithms for the parallel solution of large time domain 3D electromagnetic problems. Our approach is to use a volume Partial Element Equivalent Circuit (PEEC) electromagnetic formulation in combination with a Waveform Relaxation (WR) algorithm. In WR, we split the system into smaller subsystems and we break weak couplings so that the problem can be solved iteratively. WR has been used to solve a multitude of different problems. It is especially suited for parallel processing due to its favorable compute time to communication ratio. We consider a specific example for the application of WR to PEEC models. Godkänd; 2007; 20070126 (jekman)

Excessive compute time is becoming a key problem for high performance system modeling as the complexity of the electromagnetic and circuit models are increasing. At the same time the PEEC models are locally becoming more complex with the increased importance of dielectric and skin-effect losses. Fortunately, parallel processing removes the restriction on the availability of compute resources. In this paper,we consider a combined approach where WR is used for the predominant weak coupling while a Gaussian matrix solver is used for the parallelization of the strongly coupled parts of the overall system. Godkänd; 2007; 20070721 (jekman)

This paper details the impact of partial element accuracy on quasi-static partial element equivalent circuit (PEEC) model stability in the time domain. The potential sources of inaccurate partial element values are found to be poor geometrical meshing and the use of unsuitable partial element calculation routines. The impact on PEEC model stability of erroneous partial element values, and the coefficients of potential and partial inductances, are shown as theoretical constraints and practical results. Projection meshing, which is a discretization strategy suitable for the PEEC method, is shown to improve calculated partial element values for the same number of unknowns, thus improving model stability. Validerad; 2006; 20061103 (ysko)

This paper characterizes the different artifacts observed within time- and frequency- domain partial element equivalent circuit based electromagnetic modeling. The main focus is on frequency domain artifacts since time domain instabilities have been treated extensively in the literature. Guidelines and examples are given on how to suppress this type of artifact by showing correlation to PEEC model geometrical meshing and PEEC model complexity reduction. Godkänd; 2004; 20060929 (ysko)

We examine the passivity and stability of quasi-static partial element equivalent circuit (PEEC) models. The impact of inaccuracies in the computed partial element values is considered as a possible source of time domain instabilities. Our analysis shows how existing partial element calculation routines, analytical and numerical, and the use of poor mesh generators can introduce large errors in partial element values. We also show how this affects the passivity and stability of the PEEC model. Theoretical constraints for passivity are derived which depend on accuracy of partial element values. The conditions are verified by performing practical PEEC model analysis. Godkänd; 2004; 20060929 (ysko)

A key use of the PEEC method is the solution of combined electromagnetic and circuit problems as they occur in many situations in todays very large scale integrated circuits (VLSI) and systems. An important aspect of this approach is the fast and accurate computation of PEEC circuit matrix elements, the partial inductances and normalized coefficients of potential. Recently, fast multipole methods (FMM) have been applied to the PEEC method in the frequency domain as a way to speed up the solution. In this paper, we consider the fast evaluation of the PEEC circuit matrix elements by two different methods, a matrix version of the (FMM) PEEC method and a method, which we call the fast multi-function (FMF) PEEC approach. In this technique, the matrix coefficients are evaluated using analytical functions approximation of the coefficients in combination with a proper choice of numerical quadrature formulas. Godkänd; 2003; 20061022 (ysko)

Electromagnetic solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for the solution of combined circuit and EM problems. The inclusion of all types of Spice circuit elements is possible. Due to this, the approach has been used in many different tools. Most of these solvers have been based on a rectangular or Manhattan representation of the geometries. In this paper, we systematically extend the PEEC formulation to nonorthogonal geometries since many practical EM problems require a more general formulation. Importantly, the model given in this paper is consistent with the classical PEEC model for rectangular geometries. Some examples illustrating the application of the approach are given for both the time and frequency domain. Validerad; 2003; 20060929 (ysko)

There exists a technology suited for dealing with the unique constraints of the 3D stacked processor environment; free space optical interconnects (FSOI). This technology uses VCSEL's, vertical cavity surface emitting lasers, as a communications medium. FSOI has been proven to work in a two dimensional matrix format that would be optimal for communications between stacks.

The close environment of railway tracks is heavily polluted by electromagnetic noise from the railway system itself. The reliability of railway signalling, communication, and control systems depends on good immunity to electromagnetic noise. There are sometimes false detector signals indicating non-existing flat wheels and ghost trains. A possible reason for detector failures is interference by transient voltage peaks in the detector system. Thus characterisation has been made of the electromagnetic environment around the detector system located at the track. The investigation shows that the typical electromagnetic environment is a combination of broadband low-level noise, and rare fast transients of potentially harmful amplitudes. Validerad; 2006; 20060905 (ysko) Electromagnetic compatibility issues in the Swedish railway system