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The partial element equivalent circuit (PEEC) method provides an electromagnetic model of interconnections and packaging structures in terms of standard circuit elements. The surface-based PEEC (S-PEEC) formulation can reduce the number of unknowns compared to the standard volume-based PEEC (V-PEEC) method. This reduction is of particular use in the case of high-speed circuits and high-switching power electronics, where the bandwidth extends from low frequencies to the GHz range. In this article, the S-PEEC formulation is revised and cast in a matrix form. The main novelty is that the interaction integrals involving the curl of the magnetic and electric vector potentials are computed through the Taylor series expansion of the full-wave Green's function, leading to analytical forms that are rigorously derived. Therefore, the numerical integration is avoided, with a consequent reduction of the computation time. The proposed formulas are studied in terms of the frequency, size of the mesh, and distance between the basis function domains. Three examples are presented, confirming the accuracy of the proposed method compared to the V-PEEC method and surface-based numerical methods from literature. [ABSTRACT FROM AUTHOR]

The method of auxiliary sources (MAS) is an established technique for the numerical solution of electromagnetic shielding and scattering problems exhibiting an increasing interest for the simulation of various electromagnetic compatibility (EMC) applications. In previous works, it was shown that for the problem of transverse magnetic illumination of a perfect electric conducting cylinder by an electric current filament, it is possible for large numbers N of auxiliary sources that the MAS currents diverge and oscillate, while the generated MAS field converges to the exact solution. In this article, we further analyze the convergence issues and oscillations encountered in the MAS by considering the transverse electric case due to excitation by a magnetic current filament. We demonstrate analytically that the convergence/divergence phenomena of the currents and fields also occur in this problem and then study the nature of this divergence in detail. In particular, we prove a large-N asymptotic formula for the divergent MAS currents, which captures accurately the important characteristics of the associated inherent oscillations. Numerical results for noncircular shapes are also presented. The discussed effects must be carefully taken into account in EMC simulations pertaining to cylindrical conductors. [ABSTRACT FROM AUTHOR]

Source reconstruction using equivalent dipole moments to replace the original noise source is widely used in radio frequency interference. The conventional reconstruction methods only work well in the cases of free space or with a large ground plane. In this article a new method is proposed for source reconstruction over an arbitrarily shaped ground plane. It uses the field below the ground plane to eliminate the arbitrary ground effect. Comparing to the method of solving surface integral equation, it is simple and does not need the ground geometric information. The new method is validated in the full-wave simulations. [ABSTRACT FROM AUTHOR]

In this article, direct characterization of the wide-band input impedance of grounding system buried in multilayer soil is presented. The problem is formulated by mixed-potential integral equations solved by the method of moments (MoM). The method accommodates both delta-gap voltage and impressed-current excitations. The input impedance is then directly obtained from the MoM matrix. The proposed method does not rely on the integration of the electric field on the ground surface. Hence, the calculated input impedance is unique and path-independent. The accuracy of the proposed method is evaluated for the case of vertical ground electrodes buried in homogeneous soil. The cases of vertical grounding electrode buried in multilayer soil as well as square and circle-plates buried in homogeneous soil are studied. It is shown that for plate-shape grounding systems, the total surface area determines the grounding system input impedance and the effect of plate geometry is negligible. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To avoid numerical inaccuracy of the transient solution by the time-domain solvers or frequency-domain solvers, a simultaneous extrapolation approach reconstructing of the wide-band frequency spectrum using low-frequency and early-time data by the local linear basis functions is presented. The basic idea is transforming the transient integral equations into the analytical-form matrix equation, which can be solved using basis functions with a local support. By means of the early-time and low-frequency data, the matrix equation is solved by the method of singular value decomposition to obtain the wide-band spectrum. The proposed approach is validated by several numerical examples and applied in calculating the transient horizontal electric field of a lightning channel. The major advantage of the presented approach is an efficient and stable algorithm that can be generalized to apply to other transient scenarios when frequency- and time-domain-based transient analysis are involved. [ABSTRACT FROM AUTHOR]

For the modeling of wire structures in rectangular metallic enclosures, a Foster-type partial-element equivalent circuit model is presented. The model is based on the electric field integral equation of the wire structures. The integral equation is converted to a circuit network adopting the method of moment and the Kirchhoff's voltage law. The dyadic Green's functions for a three-dimensional (3-D) rectangular cavity are used. The circuit elements and the controlled sources are realized by the Foster-type circuit model. Application examples validate the accuracy and efficiency of the presented model. [ABSTRACT FROM AUTHOR]

An efficient method is proposed to determine the shielding effectiveness of an axi symmetric multilayered composite enclosure by using a generalized transition matrix. In this method, each layer is approximated with a generalized transmission line and the interface between two consecutive layers is modeled by an equivalent two-port network. The method of moments (MoM) solution of the governing surface integral equations at each layer is elucidated in detail to determine the parameters of the respective network and the transmission operator relating the neighboring layers. The resultant cascaded network is used to relate the tangential components of the transferred fields to the tangential components of the incident field, enabling one to compute the shielding properties of the enclosure. The main feature of the proposed method is its remarkable high computation speed as compared to the conventional methods wherein the layers and their respective interfaces are treated simultaneously, causing the size of the impedance matrix in the MOM to become excessively large. The efficiency of the proposed model is demonstrated by comparing the simulation results of several case studies with those available in the literature and obtained using a commercial finite integration technique code. [ABSTRACT FROM AUTHOR]

The most popular approximate models for the analysis of vertical and horizontal wires within a conducting half-space are based on image theory. However, their accuracy is often confined within some low-frequency (LF) range. Such models are often based on the integral equation technique with the so-called “traditional” choice of potentials. In this letter, a new LF approximation is derived from an alternative choice of potentials, i.e., “formulation B.” The accuracy of the proposed approximation and the traditional image approximations is evaluated by comparison with the electromagnetic simulation software FEKO for different wire geometries and different values of earth resistivity in a frequency range up to 10 MHz. It is shown that the new LF approximation is consistently more accurate in all analyzed cases, which widens its applicable frequency range in relation to the image approximations based on the traditional choice of potentials. [ABSTRACT FROM AUTHOR]

This paper presents the partial element equivalent circuit formulation of electromagnetic systems with moving objects. The motion of portion of the system generates two effects: additional specific electromotive forces related to the speed and magnetic flux density and time-varying partial elements. The proposed formulation is presented in a general context including conductors, dielectrics, and magnetic materials. Exploiting Galerkin's testing procedure, additional contributions to the electric field integral equation that are proportional to electrical currents and magnetization appear. Three numerical examples are presented to support the theoretical analysis. [ABSTRACT FROM AUTHOR]

A zero-order integral equation method (IEM) in our former report was introduced to simulate the high-altitude electromagnetic pulse (HEMP). The planar gamma source model was employed and results of the zero-order IEM matched those of the outgoing wave method (OWM). In this paper, a second-order IEM is introduced for the calculation of the HEMP. The point gamma source model is employed and the modified space and basis function decomposition are introduced. The partial derivatives of the current densities are calculated by the least square method. The results show that the fields and currents calculated by the OWM and the second-order IEM are in good agreement. Both the first-order IEM and the second-order IEM are converged. The second-order IEM is more complicated but more accurate than the OWM. [ABSTRACT FROM AUTHOR]

The main difference between the application of the method of moments (MoM) to grounding system and antenna analysis is the shunt energization by the injection of current. There is no consensus on the modeling of such energization, which is also crucial for the definition of quantities that characterize grounding system time and frequency behavior. The contributions of this paper are as follows: The presentation of a simple and unified approach to model all important cases of energization based on a generalized network representation of the grounding electrodes; the demonstration that the mesh current method, whose matrix equation is identical to that of the MoM, leads to straightforward procedures in the analysis of all cases of energization; and the approach enables the computation of uniquely defined impedances to ground and transfer impedances at arbitrary points at the grounding electrodes (required for N-port representation) by simple matrix manipulations. The proposed approach is general since it allows for a rigorous full-wave and an approximate quasi-static modeling, depending on the choice of Green's functions. [ABSTRACT FROM AUTHOR]

A time-domain discontinuous Galerkin Poggio–Miller–Chang–Harrington–Wu integral equation method, which is based on marching-on-in-degree (MOD) scheme, is proposed to simulate electromagnetic pulse (EMP) responses of arbitrarily shaped dielectric objects, where half Rao–Wilton–Glisson basis functions are chosen as the spatial basis ones. Both electric and magnetic current continuities between adjacent elements are guaranteed by introducing additional interior penalty terms. Therefore, three-dimensional dielectric structures with either conformal or nonconformal meshes can be treated. Meanwhile, the weighted Laguerre polynomials are chosen as the temporal basis functions and implemented for the MOD scheme, and stable EMP responses can be captured. Since our method is based on the surface integral equation with the objects’ surface meshed, the number of unknowns are significantly reduced in comparison with that of the volume integral equation method. Some numerical examples are presented to validate both stability and accuracy of the developed algorithm. [ABSTRACT FROM AUTHOR]

We propose a new channel-base current model, which is particularly well suited for lightning-induced voltage calculations. We will show that this new proposal meets a significant number of characteristics required to these applications, and favorably compares to existing solutions. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient method for extracting the coupling capacitance between through-silicon via (TSV) and the adjacent redistribution layer (RDL) interconnections based on the scalar potential integral equation and cylindrical accumulation mode basis functions. As the numerical integration of capacitance is very complicated, we employed an approximation based on the use of double-exponent transformation and the segmentation method to improve the calculation efficiency. The maximum deviation is less than 5%. The scalability of the proposed model is verified by performing parametric studies on different physical design parameters; the results show good agreement between the proposed model and the numerical simulation. Additionally, we studied several different structures of TSVs with and without RDLs to explain the influence of the coupling capacitance between TSVs and RDLs on crosstalk noise. [ABSTRACT FROM AUTHOR]

An efficient simulation of shielding effectiveness of some metallic cabins or enclosures is performed using an improved Calderón preconditioner-based time-domain integral equation method. During its implementation, Rao–Wilton–Glisson and Buffa–Christiansen functions are used as the spatial basis functions for solving the Calderón preconditioned time-domain electric field integral equation, which generate a set of well-conditioned system matrices irrespective of the mesh density. Moreover, a set of approximate prolate spheroidal wave functions is chosen as the temporal basis functions; therefore, both late-time stability and accuracy are improved significantly for simulating electromagnetic pulse responses in some typical cabins. Numerical results are validated in comparison with those obtained by some commercial software. These results are useful for further evaluating electromagnetic environment effects in some complex systems. [ABSTRACT FROM AUTHOR]

Reconstruction of the electromagnetic (EM) fields inside a dielectric object is investigated in order to develop a noninvasive specific absorption rate measurement. The proposed reconstruction method is based on the boundary integral equation (BIE) derived from the surface equivalence theorem that relates the equivalent EM currents on the surface enclosing the primary source to the radiated external fields. The EM currents are reconstructed by solving the discretized BIE using the field data sampled on the surface surrounding all of the target objects that consist of the dielectric phantom and radiating antenna. The field distribution inside the dielectric object is obtained from the reconstructed currents. A probe correction technique is also proposed to enable the application of this method to practical probe measurements. As the first step to the practical applications, the validity and usefulness of the proposed method are demonstrated numerically and experimentally using lossless and lossy homogeneous dielectric objects located near a dipole antenna, respectively. It is shown that the accuracy tends to deteriorate in the case of the lossy phantom, but this can easily be improved without significant modification of the proposed method. [ABSTRACT FROM AUTHOR]

This work proposes a formulation to overcome some of the numerical challenges of a full-wave model of a lossy single-phase overhead line or a bare underground conductor without significant loss of accuracy. This approach is defined as a quasi full-wave approximation which consists to a non-iterative approach to avoid solving the integral equation associated with a full-wave model. For the sake of comparison, four possibilities are considered in the evaluation, namely: full-wave, quasi-full-wave, quasi-transverse-electromagnetic and image approximations. The results show that the loss of information of the proposal approach is minimal and it can be used for a suitable evaluation of the electromagnetic fields associated with the overhead line or buried conductor. [ABSTRACT FROM AUTHOR]

A broad-band Huygens surface method requiring only the measurement of the magnetic field for near-field to near-field transformations is presented. The proposed method is valid down to near dc and supports arbitrary shaped Huygens surfaces. The method relies on an augmented-integral equation formulation that is used to predict the electric field on the Huygens surface. The proposed formulation is discretized using a high-order locally corrected Nyström method. The surface magnetic and electric fields can then be used to compute external electric and magnetic fields. The method is validated using electromagnetic fields radiated by a three-phase motor showing excellent results over several Fourier harmonics of the motor fields, including the zeroth harmonic. The method is also validated at high frequency for a dipole antenna array. [ABSTRACT FROM PUBLISHER]

In previous studies, high-frequency approximation (HFA) and outgoing wave methods (OWM) were used in calculating the high-altitude electromagnetic pulse (HEMP) generated by the high-altitude nuclear explosion. Maxwell's equations were reduced to ordinary differential equations. Here, an integral equation method (IEM) based on the HFA is employed to solve Maxwell's equations in the HEMP environment. A space and basis function decomposition is developed to improve the calculation performance. The IEM and the OWM are found identical in calculating both the transverse and the radial electric field. They are found to be of the first-order accuracy during the calculation of the transverse radiation field and the radial electric field. The saturation effects of both the transverse and the radial electric field are also discussed in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient time-domain technique is introduced for transient analysis of a rectangular metallic enclosure with arbitrary-shaped apertures. The surface equivalent theorem is applied to divide the problem into two separated regions. Then, assuming the magnetic current density on the apertures surface as the unknown of the problem, the governing mixed potential integral equation (MPIE) is derived. Here, to solve the resultant MPIE, we use a marching-on-in-degree (MOD) scheme with the weighted Laguerre polynomials as the entire-domain temporal basis functions. As well, in order to treat the arbitrary-shaped apertures, Rao–Wilton–Glisson spatial basis function is applied. In addition, to improve the efficiency of the proposed method, we apply some accelerating techniques that make the developed MOD method more efficient than the well-known Computer Simulation Technology finite integration technique, even for highly resonating enclosures. [ABSTRACT FROM PUBLISHER]

In this paper, a multiscale compressed and spliced Sherman–Morrison–Woodbury algorithm (MSCS-SMWA), based on the characteristic basis function method (CBFM), has been presented to accelerate direct solutions of electromagnetic scattering. The impedance matrix or reduced matrix can be compressed into block diagonal matrices with the adaptive cross approximation (ACA) and easily obtained the matrix inverse with this method. The MSCS-SMWA method is combined with a multiscale compressed ACA and a multiscale spliced singular value decomposition (SVD). The numerical results of several perfect electric conducting (PEC) objects are validated to demonstrate the performance of this method. Compared with the conventional methods, SMWA with the ACA and CBFM, the simulation results of the proposal method have been shown that the computation time and storage requirements have reduced about 10.77% and 44.22%, for the sphere with 10λ radius. Also, it costs 49.16% less CPU time and 1.54% less memory than the conventional method with SVD. [ABSTRACT FROM PUBLISHER]

The pulsed electromagnetic coupling to a narrow perfectly electrically conducting strip is analyzed using the concept of external impedance. For postulated spatial electric-current distributions, the problem is reduced to an integral equation of the time-convolution type that is, under the narrow-strip assumption, solved numerically via a marching-on-in-time scheme. Illustrative numerical examples concerning the impulsive plane-wave incidence demonstrate the space-time behavior of the induced electric-current density. [ABSTRACT FROM PUBLISHER]

An efficient algorithm based on the contour integral method (CIM) is presented in this letter for the modeling of lossy multiconductor transmission lines. Different from the volume integral equation, the CIM only discretizes the contour of the cross section of each conductor, which significantly reduces the number of unknowns in the resultant system equations. The solution of the CIM is accelerated by the hierarchical-matrix ( \mathcal H-matrix) algorithm for the extraction of the per-unit-length resistance and inductance parameters of massively coupled transmission lines. The procedures for the \mathcal H-matrix-based solution are optimized to keep its optimal computational complexity. The numerical results from the proposed method agree well with those from the commercial software. The complexities of CPU time and memory cost for the construction of the \mathcal H-matrices are both $O(N\log {}N)$, and the complexity of the solution for parameter extraction is $O(N\log ^2{}N)$. [ABSTRACT FROM AUTHOR]

The China high-speed trains use cable trays to neatly arrange the cables running through the distributed systems. On one hand, they protect cables against external electromagnetic interference and reduce external radiation from the cables. On the other hand, the cable trays create waveguide structures that affect the coupling among cables inside the cable trays. To simplify coupling analysis for cables going through a cable tray, a lumped circuit model was built using admittance blocks extracted from a mixed-potential integral equation (MPIE) formulation. In the MPIE formulation, either the half-free space or the waveguide dyadic Green's function was used depending on the region where the cables were. A test case was investigated. Results by the proposed circuit model were validated by measurement and full-wave simulation results. [ABSTRACT FROM PUBLISHER]

This paper characterizes the frequency domain near-field coupling effects from complicated three-dimensional transmission lines, monopole/dipole radiators, and printed circuit boards (PCBs) located in a metallic rectangular cavity with an efficient iterative fast Fourier transform-accelerated integral-equation method. The simulation method combines the rectangular-cavity Green's functions with the frequency-domain electric field integral equation, which is further accelerated by the extension of adaptive integral method for rectangular cavities. By using this method, the near-field coupling effects and internal field distributions are captured and compared with independent references for various structures, including transmission lines, monopole/dipole radiators, and PCBs in rectangular cavities. Numerical results show that strong couplings do appear at multiple resonant frequencies of the structures. In addition, this method can be further employed to mitigate and suppress near-field coupling effects in the optimization of electromagnetic compatibility/interference designs. [ABSTRACT FROM PUBLISHER]

The $N$-port equivalent Thévenin representation of a power-ground structure is constructed using the Lorentz reciprocity theorem of the time-convolution type. It is shown that the introduced multiport Kirchhoff-circuit representation offers a number of alternative routes to determining the pulsed electromagnetic radiated emissions of a power-ground structure from its response to an electromagnetic disturbance in the receiving situation. Moreover, the result may serve as an important check on the validity of numerical solutions to related electromagnetic radiation problems. An illustrative example that validates the equivalent-circuit representation is given. [ABSTRACT FROM PUBLISHER]

An accurate modeling technique is proposed to solve the problem of the penetrated transient field through a perforated metallic shield. In this technique, the method of moments (MoMs) is adopted to treat the governing time-domain electric field integral equation for the unknown electric current density on the metallic surface of the shield. The weighted Laguerre polynomials are used as entire-domain temporal basis functions in the MoM-based technique to set the solution approach by the marching-on-in-degree (MOD) method. To examine the accuracy of the proposed modeling technique, simulated results are presented for a finite and an infinite perfect electric conductor (PEC) plates as well as for a metallic box illuminated by a modulated/unmodulated incident wave. The accuracy of the proposed technique is demonstrated by comparing the simulated results with those obtained using the well-known Computer Simulation Technology (CST) finite integration technique and FEKO frequency-domain MoM. [ABSTRACT FROM PUBLISHER]

This paper proposes an efficient time-domain method to solve the method-of-moments-formulated integral equation pertinent to electromagnetic coupling through an aperture into a parallel plate waveguide (PPW) filled with a lossy and dispersive dielectric. The proposed method utilizes a fast Fourier transform-accelerated marching-on-in-time algorithm as a solution framework. Appropriate numerical procedures are introduced to avoid the adverse numerical effects associated with frequency-domain windowing and time-domain aliasing when convolving the time-domain Green's function of PPW with the derivative and integral of the respective temporal basis functions. The accuracy of the proposed method is confirmed by comparing the results of a circular, multiple square-shape apertures and a square aperture with those obtained using a commercial finite integration technique and a frequency-domain solver. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient mesh-free method (MFM) is introduced to evaluate the shielding effectiveness of a metallic enclosure with aperture. To this end, equivalent magnetic current densities and their relative electrical vector potentials are assumed on both sides of the aperture. Magnetic current of each side is related to its vector potential, using an integrating operator including proper Green's functions. Then, the electromagnetic field at each side is obtained by a differential operation on its respective electrical vector potential. Enforcing the continuity of the tangential magnetic and electric fields on the aperture leads to two decoupled differential and integral equations that are solved together by using proper shaping functions for the assumed magnetic currents and electrical vector potentials at the defined nodes. The proposed method is validated by the commercial software FEKO and measurements. In addition, it is shown that the proposed MFM is very efficient compared to two similarly formulated efficient method-of-moments-based methods. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient method for the evaluation of impedance/admittance matrix elements in time-domain integral equation analysis of uniformly meshed planar structures. In this method, the computation time related to the numerical integration of the required double surface integrals is remarkably reduced by discretizing the integration surfaces in equally spaced quadrature points and using the spatial translation invariant characteristic of the Green's function. It is shown that the computational burden of the proposed method scales as O(N_q ), where $N_q $ is the number of the quadrature points in one integration patch. This feature will remarkably improves the computation time when compared to O({N_q^2 }) offered by the conventional quadrature rules. The simulation results of the two cases of a circular aperture located on a parallel plate waveguide and a doubly periodic perfectly conducting structure residing in free space demonstrate the efficiency of the proposed method over its rivals. The accuracy of the proposed method will also be confirmed by comparing the results with those obtained using a commercial finite integration technique and a frequency-domain solver. [ABSTRACT FROM PUBLISHER]

It is common practice in the engineering analysis process to use an approximate image method for the computation of the current in buried horizontal conductors (in the literature, this is often referred to as the “modified image” or “reflection coefficient” method). According to this approach, the earth/air interface is replaced by a positive mirror image of the charge and current in the conductor, and its field is multiplied by a suitable reflection coefficient. Different opinions on the validity of this approximation have been expressed in published debates, but more systematic analysis of the error introduced by this approach is not available in the literature. To establish the amount of error, we compare the computation results of the image model with the rigorous Sommerfeld integral method for a wide range of parameters. Contrary to widespread opinion, our results suggest that the modified image (or reflection coefficient) method in EFIE-based solutions (e.g., the Pocklington equation) leads to a large error (larger than 20%) in the low-frequency range for the computation of the current distribution in conductors longer than 10 m. In such a case, MPIE-based methods are preferred for use to achieve a smaller error (approximately 5%). Guidelines for the application of image models related to the conductor, earth and excitation parameters, upper frequency limit, and modeling method are presented. [ABSTRACT FROM AUTHOR]

In the framework of a high-frequency transmission-line theory for nonuniform lines (TLST), new reflection and transmission coefficients are derived using generalized definitions of equivalent quantities from the classical transmission-line theory. This leads to local and frequency-dependent reflection and transmission coefficients expressed in terms of matrizant elements. These quantities are needed to describe networks of nonuniform radiating transmission lines. A comparison between the currents calculated in the approach of TLST and those calculated with the aid of the new transmission and reflection coefficients shows an excellent agreement. [ABSTRACT FROM AUTHOR]

A hybrid approach is proposed to signal integrity analysis of trace and vias in plate pair with an infinitely large dimension. By using the domain decomposition method, trace domain and via domain are divided from the plate domain. Each individual domain of via and trace structure is modeled by the 3-D full-wave tool HFSS as a multimode network composed of TEM mode waveguide ports at top/bottom antipad interfaces and vertical lumped ports on the segmentation interfaces. The plate domain is dominated by TMZ0 modes and network parameters are solved by boundary integral method. Connection of network of each domain enforces the field continuity conditions along the segmentation interfaces and yields the final S parameter of trace and via as well as trace/via to trace/via coupling. Once the via pattern and trace routing are determined, the coupling can be efficiently modeled by the proposed hybrid approach and the layouts of via structures and trace routing in a plate pair are efficiently optimized. [ABSTRACT FROM AUTHOR]

In this paper, two models for the calculation of geomagnetically induced electric fields near the shoreline are compared. The first is an analytic model which requires the solution of an integral equation at each frequency, and the second is a simplified model that only requires Fourier transforms. The mechanism responsible for the differing results is determined, and it is suggested that one of the features of the analytic model should be included in the simplified model. This modification can be made without reducing the computational advantages of the second model. We also show the relative effect of the shoreline enhancement on the voltage impressed on cables for two different ground conductivities. [ABSTRACT FROM AUTHOR]

The incorporation of dispersive behavior of power-ground structures in the time-domain contour integral method is investigated. It is shown that material dispersion can be accounted for with the help of a numerical method for the inverse Laplace transform. The proposed technique is very versatile and allows for the incorporation of the general (causal) dielectric-relaxation model. In this paper, conduction-loss and Debije's dielectric-relaxation models are closely studied. Numerical examples are validated using the feature selective validation analysis. [ABSTRACT FROM AUTHOR]

A very efficient boundary-element method for the calculation of the quasi-static port inductances of vertical interconnections within parallel-plate structures is developed. It requires only a one-dimensional discretization along the contour of the plate pair and can be applied to arbitrary geometries. The algorithm is validated by the exact analytical solution for the circular geometry. The low-frequency response of an arbitrary multiport structure can be directly analyzed by the coupled port-inductance network together with the plate capacitance. As examples a circular-shaped and two irregularly shaped plane pairs are considered. The comparison with exact analytical solutions and three-dimensional-full-wave field simulation shows a very good agreement. [ABSTRACT FROM AUTHOR]

This paper presents a computationally efficient method for solving automotive low-frequency electromagnetic compatibility (EMC) problems by using integral equations. We consider the interaction of magnetic fields with thin, finite, conducting 3-D metallic structures, obtaining the fields radiated by these structures by using single- and double-layer equivalent currents. Our proposed numerical solution is unique in its representation of equivalent currents as the sum of solenoidal and nonsolenoidal components found using the method of moments (MoM) in two steps: first, the solenoidal currents are found using loop basis functions, after which the nonsolenoidal currents are found. Decomposing the equivalent currents into solenoidal and nonsolenoidal components provides a total solution that is computationally efficient for problems dominated by magnetic fields. We validated this numerical electromagnetic solution against semianalytical solutions and measured data and illustrated its applicability by analyzing three practical automotive problems. We then analyzed the magnetic fields generated by a power cable inside a car, suggested a methodology for optimizing the locations of antennas for smart-entry systems, and studied the EMC implications of an inductive-charging system in an electric vehicle. [ABSTRACT FROM AUTHOR]

In this paper, we present an incremental multilevel matrix filling and sparsification scheme for the method of moment (MoM) solution of the electric field integral equation at low and very low frequencies. The proposed scheme allows a strong reduction of the memory requirements without a loss in accuracy. Numerical results show the method performance in terms of memory requirements, CPU time and accuracy with respect to the standard MoM, the multilevel fast multipole algorithm, and the adaptive cross approximation. [ABSTRACT FROM AUTHOR]

The partial element equivalent circuit (PEEC) method has been widely used in different industrial and scientific fields for electromagnetic analysis. PEEC-based solvers have been optimized and accelerated in order to be able to solve larger and more complex problems that arise in industry. In power electronic system simulations, PEEC models are often simplified by neglecting electric field couplings and using quasi-static model. The simplified system can be further accelerated using reluctance technique and then sparsified up to high levels without degrading the accuracy of the solution. In previous work, the sparse system was solved using sparse direct solution, while in this study, an iterative approach is employed which resulted in lower time complexity of the solution. However, since matrices achieved from PEEC equations are severely ill-conditioned, regularization techniques need to be applied to avoid numerical instabilities. The regularization is done mathematically and can be interpreted as adding a frequency-dependent pseudocapacitor to each node in the PEEC model. Because the pseudocapacitors are frequency dependent, hence frequencies close to dc are not covered in this study and have left as future work. The new sparse and regularized system can then be solved using a Schur complement technique together with iterative solvers with a novel preconditioning approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is the definition of an equivalent two-port model of a transmission line that is able to take into account high frequency radiation effects. Such a model is particularly useful when one has to represent the line into a more complex power system, modeled in a lumped way. To reach this goal, it is necessary to produce a reliable and computationally effective solution to the problem of the high-frequency electromagnetic field coupling with a terminated transmission line. From a mathematical standpoint, this problem can be presented by means of an integral equation whose solution can be achieved with regularization procedures for linear inverse problems. In order to obtain a computationally efficient result, the unknown current is first developed in a Fourier series and then the Landweber iterative algorithm is applied to identify the series coefficients. The proposed method is then tested taking as reference the numerical results obtained using the Numerical Electromagnetics Code (NEC-2), reaching a good agreement. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient modeling technique for transient electromagnetic analysis of a rectangular metallic enclosure with multiple apertures, using the surface equivalent principle (SEP) and integral equations. The SEP is used to replace the apertures by perfect electric conductor surfaces while introducing appropriate magnetic current densities on both sides of the apertures. As a result, the problem is reduced to two independent regions. The first region is outside the enclosure for which the free-space Green's function with the aid of image theory can be used to obtain the total fields in it. The second region is the inside of the enclosure and a closed-form expression is then derived for its time-domain dyadic Green's function. Finally, the governing time-domain magnetic field integral equation (TD-MFIE) for the structure is derived by enforcing the continuity of the tangential magnetic field at the apertures. To eliminate the late time instabilities in solving the resultant TD-MFIE, an unconditionally stable marching-on-in degree scheme is used. A new accelerated algorithm is proposed for the internal problem that relies on the separation of time and space in the cavity Green's function. The validity of the proposed method is confirmed by comparing the simulation results of several case studies with those obtained using the frequency-domain methods and CST microwave studio. [ABSTRACT FROM AUTHOR]

We propose a novel doubly hierarchical method of moments for the analysis of large and multiscale structures. A reciprocal multilevel matrix compression method (rMLMCM) is combined with the multilevel fast multipole algorithm (MLFMA), and they are used for the small-scale and large-scale cluster interactions, respectively. The resulting system is preconditioned following the hierarchical multiresolution-incomplete LU approach, which has proven successful for solving multiscale complex structures. The proposed method is applied to electromagnetic compatibility analysis of the real life, complex structures. Numerical results demonstrate the proposed preconditioned rMLMCM/MLFMA is effective also for large structures with strongly nonuniform discretization. [ABSTRACT FROM AUTHOR]

The method of manufactured solutions (MMS) is introduced here for the verification of the method-of-moment (MoM) codes. The selection of appropriate manufactured solutions is investigated. The numerical integration of the electric field integral equation is discussed and the effect thereof on the utility of the MMS for the MoM is considered. General convergence rates of the MoM are discussed and the computation of the relevant norms is explained. Several examples are shown, highlighting the power of the MMS for different aspects of the code verification process. [ABSTRACT FROM PUBLISHER]

This paper describes the approach developed in order to model the electromagnetic response of a cable bundle, part of the electrical wiring interconnection system of a real aircraft, submitted to an external electromagnetic excitation. The aim of this study is to highlight the main challenges in the synthetic modeling and validation of a fully real setup, from the electromagnetic compatibility point of view. Both conducted and radiated excitations have been considered in the electromagnetic global model. The solution is obtained through a cooperative simulation approach involving one 3-D full-wave solver and a multiconductor transmission line solver. The results are compared with measurements and specific tools, such as feature selective validation and integrated error against log frequency, are used to assess the adequacy of the results. [ABSTRACT FROM PUBLISHER]

In this study, an experimental method has been investigated for efficient assessments of whole-body specific absorption rates (SAR) from radio base station antennas. Using surface amplitude measurements of the electric field components together with an integral equation technique, a method is obtained which is not biased to specific antenna designs or phantom shapes. For realistic material parameters, it has been found that only the amplitude of the tangential field components over the phantom boundary is needed to accurately assess whole-body SAR, which makes the proposed method well suited for integration with commercially available SAR measurement systems. The method has been validated with simulations and measurements. Compared with a volumetric scan, and for the cases investigated, the measurement time was reduced with a factor larger than 3 while keeping the relative error smaller than 8%. [ABSTRACT FROM AUTHOR]

Thin-wire antenna model of the human body exposed to the transient excitation is presented in the paper. The analysis is based on the solution of the corresponding integral equation and it is carried out directly in the time domain (TD). The integral equation is handled via the TD Galerkin-Bubnov scheme of the boundary element method. Numerical results are presented for the time-harmonic and transient exposures. Index Terms--Antenna model, Hailen integral equation, human body, transient exposure.

In this paper, electromagnetic effects arising from high intensity radiated fields (HIRF) within realistic aircraft structures are investigated using the method of moments (MoM) and experimental tests. This study focuses on simulation-to-measurement correlation, where two potential error sources are investigated: Accuracy of the numerical techniques and the generation of numerical models. It is shown that the conventional mixed potential electric field integral equation may lead to inaccurate results regarding the field penetration through apertures. An alternative integral equation is introduced which splits the computational domain into an interior and an exterior domain, improving the results for aperture problems. To analyze the accuracy and the range of applicability for these integral equations, a generic aircraft structure is investigated, both numerically and experimentally. Thereby, various modeling aspects required for a meaningful simulation of aircraft are discussed. Following these observations, a real aircraft is analyzed in a broad frequency range from 10 kHz to 1 GHz. It is demonstrated that accurate numerical techniques are as important as modeling and appropriate simplification of the considered structures. [ABSTRACT FROM PUBLISHER]

One effective method, based on time-domain PMCHW (Poggio, Miller, Chang, Harrington, and Wu) integral equation, is presented for studying on time- and frequency-domain electromagnetic responses of some composite structures. A set of derived equations is solved by an adaptive marching-on-in-order (MOO) procedure. During its implementation, dielectric parts of the composite structure are described by the PMCHW equations, and its metallic parts are governed by the time-domain electric field integral equations, where temporal basis of the Laguerre polynomials are employed for both of them. As an example of composite microstrip patch structure, its dielectric- metallic junction is handled using an appropriate combination of the full RWG basis functions so as to obtain high computational accuracy, and one MOO acceleration scheme is employed for accelerating the temporal convolution effectively. Numerical results are given to demonstrate efficiency as well as accuracy of our proposed method used for capturing electromagnetic responses of some typical composite structures, with their transient current responses, far-field distributions, radar cross sections, and directivities predicted successfully. [ABSTRACT FROM PUBLISHER]

This paper presents the analysis of radiated immunity of flex cable with ground plane using transmission line equations. The conformal mapping transformation technique and the integral equations are employed to extract the equivalent RLCG parameters for canonical types and complicated types of structures, respectively. The external electromagnetic field sources are modeled as equivalent voltage and current sources in the transmission line equations. After the equivalent circuit is obtained, the induced voltage is computed via the SPICE solver. Validation with case studies shows that the approach is capable of efficiently modeling the radiated electromagnetic interference to evaluate the immunity level of devices under test. [ABSTRACT FROM PUBLISHER]