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An effective method for extracting parameters of a Debye or a Lorentzian dispersive medium over a wideband frequency range using a genetic algorithm (GA) and a transmission-line model is presented. Scattering parameters (S-parameters) of the transmission-line sections, including a parallel plate, microstrip, and stripline, are measured. Wave equations for TEM/quasi-TEM mode with a complex propagation constant and a frequency-dependent wave impedance are used to evaluate the corresponding S-parameters in an analytical model. The discrepancy between the modeled and measured S-parameters is defined as the objective function in the GA. The GA is used for search of the dispersive-medium parameters by means of minimizing the objective function over the entire frequency range of interest. The reconstructed Debye or Lorentzian dispersive material parameters are corroborated by comparing the original measurements with the FDTD modeling results. The self-consistency of the proposed method is demonstrated by constructing different test structures with an identical material, i.e., material parameters of a substrate extracted from different transmission-line configurations. The port effects on the material parameter extraction are examined by using through-reflection-line calibration. Index Terms--Electromagnetic propagation in dispersive media, finite-difference time-domain (FDTD) methods, genetic algorithms (GAs), scattering parameters, transmission lines.

Reverberation chambers are attractive electromagnetic compatibility test facilities, both economically and technically. Careful design and analysis of these facilities are important, if the results obtained are to be treated with a high level of confidence. Numerical modeling is an important part of the process of reverberation chamber design and analysis. Hence, it is important that the modeling techniques to be used are appropriately validated. Much of the published work to date takes either a statistical or a deterministic view of validation. This paper provides validation evidence for a low-resolution transmission line matrix (TLM) model of a reverberation chamber in a manner approximating the way in which the chamber is used, i.e., validating based on the effects of a simple device under test. A variety of statistical and heuristic approaches have been used to quantify the level of agreement, intending to set the likely lower bound for the quality of comparisons between simulations and measurements. While not drawing any 'universal' conclusions about the veracity of the TLM technique, the paper concludes that a relatively simple model of a reverberation chamber provides a useful analysis of the chamber with close comparisons between modeled and measured data. Index Terms--Mode-stirred chamber, reverberation chamber, test facilities, transmission line matrix (TLM), validation.

A 'simulation program with integrated circuit emphasis' (SPICE) model for the evaluation, in frequency and time domain, of the coupling of a bundle of shielded coaxial cables with an external electromagnetic source such as a bulk current injection clamp, is developed. The proposed equivalent circuit takes into account the presence of the transfer impedance and the presence of the transfer admittance, and it does not need the subdivision in elementary cells. Intermediate results are validated by comparing the exact numerical solutions with the output of the SPICE circuit, and the final results are validated by means of comparison with measurements carried out on an experimental setup. The feature selective validation (FSV) technique is used as a measure of the comparisons. Index Terms--Bundles, coaxial cables, feature selective validation (FSV), simulation program with integrated circuit emphasis (SPICE) model, transfer admittance, transfer impedance.

A goal for the validation of computational electromagnetics (CEM) is to provide the community with a simple computational method that can be used to predict the assessment of electromagnetic compatibility (EMC) data as it would be undertaken by individuals or teams of engineers. The benefits of being able to do this include quantifying the comparison of data that has hitherto only been assessed qualitatively, to provide the ability to track differences between model iterations, and to provide a means of capturing the variability and range of opinions of groups and teams of workers. The feature selective validation (FSV) technique shows great promise for achieving this goal. This paper presents a detailed analysis of the FSV method, setting it firmly in the context of previous comparison techniques; it suggests the relationship between validation of graphically presented data and the psychology of visual perception. A set of applicability tests to judge the effectiveness of computer-based CEM validation techniques is also proposed. This paper is followed by a detailed comparison with visual assessment, which is presented in Part II. Index Terms--Computational electromagnetics (CEM), feature selective validation (FSV), validation.

The feature selective validation (FSV) method has been proposed as a technique to allow the objective, quantified, comparison of data for inter alia validation of computational electromagnetics. In the companion paper 'Feature selective validation for validation of computational electromagnetics. Part I--The FSV method,' the method was outlined in some detail. This paper addresses two specific issues related to the implementation of the FSV method, namely 'how well does it produce results that agree with visual assessment?' and 'what benefit can it provide in a practical validation environment?' The first of these questions is addressed by comparing the FSV output to the results of an extensive survey of EMC engineers from several countries. The second is approached via a case study analysis. Index Terms--Computational electromagnetics (CEM), feature selective validation, validation.

This paper presents a new technique for the transient analysis of long lossy cables. The proposed model represents an improvement of the standard ladder network approximation of transmission lines for two reasons: First, the propagation delay time is preliminarily extracted so that the lossy phenomena are modeled as minimum delay lossy cable, and second, a model order reduction (MOR) is applied to the lossy line via the analytical calculation of poles and residues of the half-T ladder network approximating the delayless lossy cable. The combination of such two techniques allows us to achieve a significant reduction of the computational efforts in simulating long lossy cable while preserving the modeling accuracy. Numerical tests are performed that demonstrate the robustness and accuracy of the proposed method. Index Terms--Frequency-dependent losses, lossy multiconductor transmission lines, model-order reduction, shielded cables, transient analysis.

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 in-accurate 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. Index Terms--Partial element equivalent circuit (PEEC).

Frequency-modulation techniques have been used to reduce electromagnetic interference (EMI) produced by the clock of digital systems working in the range of hundreds of megahertz. The working principle consists of modulating the original constant clock frequency in order to spread the energy of each single harmonic into a certain frequency band, thus reducing the peak amplitude of EMI at harmonic frequencies. Nowadays, the switching frequency of power converters has increased up to values that make interesting the application of such techniques to reduce EMI emissions due to switching of power circuits. This paper presents the theoretical principles of frequency modulation using deterministic profiles for the modulating function. It shows the effectiveness of such methods in terms of EMI reduction for different modulation profiles and other parameters. The method is compared with other methods using random modulation. Tests carried out on a buck converter are presented for experimental validation of the method. A short discussion on optimal modulation profiles and parameters is also included. Index Terms--Electromagnetic interferences (EMI), power converters, switching frequency modulation, spread spectrum frequency modulation (SSFM).

This paper considers the case of a wide-band Lorentzian (WBL) algorithm in the finite-difference time-domain (FDTD) modeling of dispersive media. It is shown herein that the WBL model is a physically meaningful and practically useful case of the frequency behavior of materials along with the Debye and narrow-band Lorentzian (NBL). The recursive convolution algorithms for the finite-difference time-domain technique for NBL and WBL models differ. The Debye model, which is suitable for comparatively low-frequency dispersive materials, may not have sufficient number of parameters for describing the wide-band material, especially if this material exhibits pronounced absorption at higher frequencies. It is shown that the Debye model can be used, if the Q-factor of the linear circuit analog corresponding to the Lorentzian model of the material is less than approximately 0.8. If the quality factor is in the limits of about 0.8 < Q [less than or equal to] 1, then the WBL model is appropriate. For Q > 1, the NBL model must be applied. The NBL model is suitable for dielectrics exhibiting resonance effects in the microwave frequency range. The WBL model is typical for composites filled with conducting fibers. Index Terms--Debye model, dispersive media, finite-difference time-domain (FDTD) technique, Lorentzian model, recursive convolution.

A SPICE circuit model is developed for the evaluation in frequency and time domain, of the common and differential mode voltages at the terminals of a two-parallel-wires shielded cable during a current injection test. The proposed circuit is an exact equivalent of the model's governing multiconductor transmission line equations without the need of any subdivision in elementary cells and takes into account the presence of both transfer impedance and admittance. Index Terms--SPICE model, transfer admittance, transfer impedance, two-wires shielded cable.

A SPICE circuit model for the evaluation of the effects of the bulk current injection test on coaxial shielded cables is developed. The proposed equivalent circuits do not need the usual subdivision of the circuits in elementary cells, it is valid in both frequency and time domain and is based on the exact solution of the equations stemming from a lossless transmission line model. The intermediate and final results are validated by means of comparison with others, evaluated by independent methods. Index Terms--Bulk current injection (BCI) test, coaxial cable, equivalent circuit, shielded cable.

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. Index Terms--Circuit modeling, partial element equivalent circuit (PEEC) method, full-wave analysis.

The statistical analysis of the magnetic flux density due to sinusoidal steady-state 50- (or 60-Hz) currents in conductor pair randomly placed inside a conduit is carried out by means of a suitable developed computation model. From the statistics of the field, an equivalent deterministic model is derived. This model allows one to estimate the magnetic flux density levels without knowing the exact position of the conductors. The results are compared with those measured in two laboratory experimental setup. Index Terms--Magnetic fields, statistical model.

This paper proposes a numerical procedure, based on a mixed circuit-field approach to compute the transient and spatial potential distributions inside vessels containing flammable liquids, induced by a direct lightning strike. The circuit model is used to simulate the metallic vessel as an equivalent electrical network, which is solved by the SPICE simulator. In this way, it is possible to compute the transient potential distribution on the external vessel walls. These potential values are the boundary conditions of the partial differential equation system, valid at the inner of the container, which is solved by the finite-difference time-domain method. The model takes into account the transient and nonuniform volume charge density inside the liquid and the temporal accumulation of charges at the air/liquid interface. A validation of the proposed method, in the absence of liquid, is furnished. The transient and spatial distributions of the potential in the container are analyzed in order to detect possible hazards. Index Terms--Direct lightning stroke, flammable liquids, metal containers, mixed circuit-field approach.

Frequency- and time-domain expressions for the transfer impedance of single conductor shielded cables are proposed. The time-domain convolution needed for the evaluation of the distributed longitudinal voltage induced on the internal conductor of the cable is directly evaluated by means of an equivalent SPICE circuit that can be incorporated in already existing shielded coaxial cables circuit models. Index Terms--Equivalent circuit, recursive convolution, shielded cables, transfer impedance, transient impedance.

A novel frequency-domain distributed-parameter circuit model of the setup for the measurement of conducted emissions (CE) in three-conductor systems is developed in order to predict the effects that an electrically-long power cord connecting the equipment under test (EUT) to the line-impedance stabilization network (LISN) plays on CE levels. To this end, a three-conductor lossless and uniform transmission line model is adopted for the description of the power cord, and modal decomposition of the line voltages and currents to common- and differential-mode voltages and currents is used to derive new closed-form expressions of the CE at the LISN ports. Suitable EUT-to-LISN matrix transfer functions are introduced and it is shown that CE measured at the entrance of the power outlet (i.e., at the LISN ports) may differ significantly from those flowing out of the EUT mains ports, due to propagation and coupling along the power cord. The role played by the mains cable cross section on CE propagation and conversion is investigated, and upper/lower bounds for the power cord effects on CE are derived analytically by applying an asymptote plot analysis to the magnitude of the EUT-to-LISN transfer functions. Direct numerical solution of the transmission line model is used to validate the obtained literal expressions of CE and related bounds, as well as to give explicit indications about the impact of long-cable effects on CE. Index Terms--Common and differential modes, conducted emissions, modal analysis, upper and lower bounds.

A method for simulating the eye pattern of high-speed digital signals propagated on printed circuit boards using multi-conductor transmission-line modeling is proposed in this paper. The approach takes into account the frequency-dependent properties of the dielectric materials of the board and of the conductors. The validation is performed by comparing the modeling with measurements taken from the literature, and directly performed on test boards specially design for this study. Index Terms--Dielectric constant, dissipation factor, frequency-dependent dielectric, signal integrity.

The search for the best configuration of the lightning protection system (LPS) that maximizes the regions inside the building, in which the values of the field are less than the specified threshold levels is an important topic of the LPS design. In this paper, we propose the use of a constrained decision planning tool to optimize the field profile in the regions where the high susceptible equipment will be placed. The induced magnetic flux is evaluated by time-domain simulation. The concepts of 'safe area' and 'connectivity index' are presented and used as measures of this procedure. Index Terms--Electromagnetic compatibility, EMP radiation effects, lightning, time-domain analysis.

Noise on a dc power bus that results from device switching, as well as other potential mechanisms, is a primary source of many signal integrity (SI) and electromagnetic interference (EMI) problems. Surface mount technology (SMT) decoupling capacitors are commonly used to mitigate this power-bus noise. A critical design issue associated with this common practice in high-speed digital designs is placement of the capacitors with respect to the integrated circuits (ICs). Local decoupling, namely, placing SMT capacitors in proximity to ICs, is investigated in this study. Multilayer PCB designs that employ entire layers or area fills for power and ground in a parallel plate structure are considered. The results demonstrate that local decoupling can provide high-frequency benefits for certain PCB geometries through mutual inductive coupling between closely spaced vias. The associated magnetic flux linkage is between the power and ground layers. Numerical modeling using an integral equation formulation with circuit extraction is used to quantify the local decoupling phenomenon. Local decoupling can effectively reduce high-frequency power-bus noise, though placing capacitors adjacent to ICs may limit routing flexibility, and tradeoffs need to be made based on design requirements. Design curves are generated as a function of power-bus layer thickness and SMT capacitor/IC spacing using the modeling approach to quantify the power-bus noise reduction for decoupling capacitors located adjacent to devices. Measurement data is provided to corroborate the modeling approach. Index Terms--DC power-bus design, decoupling capacitor location, high-speed digital design, local decoupling, mutual inductance, SMT decoupling capacitors.

It is shown that the resistance and internal inductive reactance of a conductor of rectangular cross section are not equal when skin effect is well developed, i.e., when the cross-sectional dimensions are much larger than a skin depth, unlike the case of a conductor of circular cylindrical cross section. Hence, the high-frequency internal inductance cannot be determined from the resistance and must be computed separately. Also, the widely used time-domain representation of the internal impedance B [square root of s] is not valid. Numerical results are given for conductors of various cross-sectional aspect ratios and dimensions. Index Terms - Impedance, inductance, printed circuit boards, skin effect.

Power conversion systems and, in particular, power drives, are now present in a large number of applications and environments. The switching operations of power drive systems (PDS's) are sources of radiated and conducted EMI's that give rise to problems of electromagnetic compatibility (EMC) with other systems. This paper proposes an efficient numerical technique to evaluate the radiated emissions due to a PDS, taking into account the radiation from intentional apertures (i.e., those for ventilation). The power section of the PDS is simulated by a combination or' radiating dipoles in which the current is known. The radiated electromagnetic (EM) field induces on the PDS metallic cage surface currents that, in turn, radiate outside the cage. These currents are computed by an efficient numerical method known as Partial-Element Equivalent Circuit technique. The proposed prediction model is, hence, able to predict the total radiated emission from a PDS in its design stage in order to fulfill the EMC requirements called for by the international standards. Index Terms - Electromagnetic compatibility, electromagnetic interferences, power electronics.

The complexity of electronic systems for RF and digital applications is ever increasing, and the corresponding compliance analysis for ensuring the required specifications in terms of performances, signal and power integrity is a challenging task often accomplished by relying on commercial circuit simulators. The modeling of multiport devices involves the assembly of electrical networks usually described in terms of S‐parameter. This work proposes a new single‐step algorithm that computes the global S‐parameter matrix for a cascade of multiple networks with multiple ports without the need of any S‐parameter transformation in T‐parameters and their inverse transformation. The proposed method involves the construction of a large matrix filled with all S‐parameters of all networks, and the subsequent evaluation of only one matrix expression. The proposed method is shown to be very efficient and reliable, since it can be easily automated without the need of a manual connections of tens or even hundreds of ports of the multiple blocks, which is an action that needs to be performed within a typical circuit simulator environment. Also, the proposed method overcomes the limitation of the standard method based on S‐to‐T parameter transformation since it is of general applicability to networks with different number of input and output ports. Examples involving the cascade of multiple 2‐ports and multiports networks are considered, and the results are validated and compared with the reference results obtained from a commercial circuit simulator. The proposed method is shown to be effective and fast compared to its counterpart based on the T‐parameters. [ABSTRACT FROM AUTHOR]

Ferromagnetic grids are becoming more and more popular for electromagnetic shielding applications in avionics, satellite design, and power electronic systems. This paper presents an equivalent homogeneous but anisotropic model of a planar ferromagnetic grid. The nonlinear characteristic and the hysteresis of the material are taken into account. The field source is a low frequency magnetic dipole placed in the proximity of the grid. Both grid and source models are given in the form of multiconductor transmission line (TL) equations. They are solved, in the time domain, by the circuit simulator SPICE.

A hybrid method is presented for incorporating general terminations into the solution of lossy multiconductor transmission lines (MTL's). The terminations are characterized by a state-variable formulation which allows a general characterization of dynamic as well as nonlinear elements in the termination networks. The method combines the second-order accuracy of the finite difference-time domain (FDTD) algorithm for the MTL with the absolutely stable, backward Euler discretization of the state-variable representations of the termination networks. A compact matrix formulation of the recursion relations at the interface between the MTL and the termination networks allows a straightforward coding of the algorithm. Skin effect losses of the line conductors as well as the effect of an incident field are easily incorporated into the algorithm. Several numerical examples are given which contain dynamic and nonlinear elements in the terminations. These examples demonstrate the validity of the method and show that the temporal and spatial step sizes can be maximized, thereby minimizing the computational burden.

Since the efficiency of switched mode power supplies (SMPS) is much higher than that of linear power supplies, this type of supply has gained favor among designers and manufacturers. Switching frequencies extend from tens to hundreds of kilohertz with the result that radiation from circuits carrying switched current is becoming more of a problem. This paper addresses the modeling of the converter section of an SMPS in order to calculate the current distribution and the radiated electromagnetic field. The inhomogeneities in the circuit are treated by equivalent electrical parameters and a technique is introduced to take into account the fictitious effects on radiation due to the electrostatic terms in the dipole equations. The global approach is validated by comparison of the computed results with those measured for a simple and clearly arranged SMPS experimental setup.

This paper deals with the induced transient voltages on nonlinearly terminated metallic loops inside a building due to an indirect lightning strike. The conductive parts of the building (such as reinforcing bars in walls and floors, metallic beams), the lightning protection system, and the loops are simulated by an electric field integral equation in time domain, with the nonlinear loads by a system of nodal equations. These two sets of equations allow a solution to be determined completely in time domain. The proposed technique is validated by comparison with other referenced numerical techniques. Some results which show the effects of the conductive structural elements of the budding on the induced transients are presented.

A lightning stroke to the protection system of the control building of an industrial plant can produce various effects such as transient voltages induced in feed cables, in measuring, protection and control cables, and in components of electrical equipment within the building, as well as transient voltages between down conductors and metal bodies often characterized by high peak values. These effects can give rise to operating anomalies in the equipment which may sometimes be damaged, and can also constitute a hazard to human life. This paper reports the results of a frequency-analysis study of effects connected with point values of the electromagnetic field generated within the building (e.g., the impact on field-effect transistor, etc.) or due to the presence of radiation fields, namely fields whose harmonic components, characterized by small wavelengths compared to the dimensions of the 'victim' circuit, assume not negligible values. The best way of calculating these effects is through a procedure based on a field approach [1]-[3]. Characterization of the electromagnetic field is therefore ensured by a numerical procedure that permits simultaneous simulation of the protection system and analysis of the electromagnetic field by means of the Method of Moments used by various authors [5]-[8] for the study of direct lightning strokes into thin-wire structures. Two distinct points of impact of the lightning stroke to the protection system are considered and the ensuing results are compared.

The feature-selective validation (FSV) method is proving itself to be a robust and helpful technique to quantify visually complex measurement sets, such as those resulting from computational electromagnetic validation exercises or experimental repeatability studies. This paper reports on an enhancement to this technique that includes data related to the level of dc difference (i.e., offset) between two sets of results, hitherto disregarded within the method. This offset difference measure (ODM) contributes to the amplitude difference measure (ADM) and ensures that the ADM and global difference measure values reflect the level of disagreement between the two traces even if this is the only difference between the two. The paper describes the background to this development and provides details of the selection and implementation of the ODM measure. Index Terms--Feature-selective validation (FSV), numerical modeling, repeatability, validation.