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This paper deals with an analytical solution of the time domain Pocklington integro-differential equation for the transient current flowing along the horizontal grounding electrode of finite length. The electrode is excited with an equivalent current source representing the lightning strike current. Presence of the earth–air interface is taken into account through the formulation, via simplified reflection coefficient arising from the modified image theory. The analytical solution is carried out using the Laplace transform and the Cauchy residue theorem, respectively. Results obtained by the analytical solution are compared to those calculated using numerical solution of the corresponding frequency domain Pocklington equation in conjunction with the Inverse Fast Fourier Transform. The results obtained via different methods agree satisfactorily. [ABSTRACT FROM PUBLISHER]

The calculation of the high-altitude electromagnetic pulse (HEMP) fields resulting from a nuclear explosion is dependent on the modeling of secondary electrons generated by the high-energy Compton electrons. In this paper, we discuss different modeling procedures used for this task and show how modeling a delay in the formation of the conductivity resulting from the low-energy electrons affects the HEMP electric fields at the surface of the ground. [ABSTRACT FROM AUTHOR]

In this paper, a time-domain variant of the generalized telegrapher's equations for transient electromagnetic field coupling to a finite-length wire above a lossy half-space is derived. The approach is fully based on the thin-wire antenna theory. The lossy ground effects are taken into account by means of the reflection coefficient approximation. The obtained equations are handled numerically via the Galerkin–Bubnov indirect boundary element method. Computational examples are presented for the case of a single-wire line excited by an electromagnetic pulse excitation source. The obtained results for the induced current along the line are compared with those obtained using 1) the method of moments solution of the electric field integral equation implemented in the numerical electromagnetics code (NEC-4), and 2) the transmission line (TL) theory. It is shown that the results obtained by the proposed method are in excellent agreement with those of NEC-4. It is also shown that the TL approximation yields in general results which are in reasonably good agreement with the full-wave results, especially for the early time response and even beyond the limits of the accuracy of the TL theory. The TL theory can, however, give accurate results only for times before the arrival of the first reflection from the TL terminations and it fails to reproduce accurately the dispersion effects occurring after the first reflection. [ABSTRACT FROM AUTHOR]

This paper presents the calculation results of lightning-induced voltages on overhead lines using two different formulations for the horizontal electric field at the earth surface. The first one is a time-domain equation equivalent to the surface impedance contained in the Cooray–Rubinstein formula, while the second one is an improved equation that provides more accurate results in the vicinity of lightning. The induced voltages are calculated for a strike in the vicinity of the line (50 m) and the results show that, for good-conducting earth, the two formulations are equivalent. However, for poor-conducting earth, the second expression provides a higher and longer induced voltage. Based on the calculation results, a limiting condition for the use of these equations is proposed. [ABSTRACT FROM PUBLISHER]

The calculation of voltages induced by external electromagnetic fields on multiconductor transmission lines (MTLs) has been the subject of several studies. In this paper, discrete equations for MTLs exposed to incident fields are derived based on the time-domain finite-element method and the backward differentiation formula. Based on these equations, a value-delivery table characterizing the MTLs is presented. Combining this table with modified node analysis formulation, it is convenient for analyzing the responses of transmission lines composed of complex termination networks or complex transmission-lines networks. The validity and efficiency of the proposed algorithm is demonstrated using several examples. Finally, a 1-km 35 kV overhead line above an imperfectly conducting ground is studied, and the influences of ground wire and a metal-oxide arrester to the lightning-induced voltage are both discussed. [ABSTRACT FROM PUBLISHER]

A subcell model for thin wires in the finite-difference time-domain (FDTD) method using modified telegraphers equations has been developed by Holland et al. Edelvik has previously presented an extension of their algorithm, which allows for arbitrarily located and oriented wires with respect to the Cartesian grid. This is important to be able to accurately model wires that cannot be aligned to the Cartesian grid, e.g., tilted wires and circular loop wires. Recently, a dual set of equations has been proposed for modeling of thin slots. In this paper, we show that using a similar algorithm as for thin wires we can also handle slots of arbitrary location in Cartesian planes. Previous thin slot models have been susceptible for instabilities. We show that a symmetric coupling between field and slot yields a stable time-continuous field-slot system and that the fully discrete field-slot system is stable under a generalized Courant-Friedrich-Lewy (CFL) condition. The proposed method is demonstrated for scattering from a finite-length slot in an infinite conducting wall and a shielding enclosure including a slot. The results are in good agreement with published experimental data. [ABSTRACT FROM AUTHOR]

In this correspondence, we propose a supplementary spatial correlation function used to amend a simplification made in an earlier published paper in which a semianalytic solution of field-to-wire coupling in an electrically large cavity was first proposed. It can be shown that the horizontal and vertical components of the incident field are correlated in most cases. Without neglecting the correlation between the field components, the supplementary function can help to give more accurate results. It is demonstrated by two numerical simulation examples in which the semianalytic results are compared with the Monte Carlo results and/or the analytic solution. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence and error evaluation of the distributed analytical representation and iterative technique (DARIT-field) which is a new approach for the analysis of field coupling to multiconductor transmission lines. The DARIT-field method has the advantage of high computational efficiency over the other methods. In order to know the convergence speed and the error at each iteration step of DARIT-field, an analytic expression of iterative error is derived by combining the two telegrapher's equations into a matrix equation and using the euclidean norm to explore its upper bound. The expression shows that the convergence speed is mainly influenced by three parameters, namely coupling factor (CF), terminal loads, and the line length to excitation field wavelength ratio $(d/\lambda)$. The convergence speed is a function of CF, terminal loads, and the line length to excitation field wavelength ratio $(d/\lambda)$. These results allow the users to make a compromise between computational cost and accuracy by selecting the number of iterations. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for modeling of electrically thin conductive shields in the finite-difference time-domain (FDTD) method. The method is based on representation of the relation between the fields at two faces of the shield as an impedance boundary network condition (INBC) in the frequency domain. The INBC includes frequency-dependent self and mutual impedances which are approximated by series of partial fractions in terms of real or complex conjugate pole-residue pairs. A discrete time-domain INBC at the shield is generated, which is then incorporated within the FDTD method. The primary advantages of the proposed approach are: 1) the convolution equations are not used in the formulation, 2) the approximation applied for discretizing the Maxwell equation has second-order accuracy in time and first-order of accuracy in space, and 3) the stability of the method is governed by the classical Courant Friedrichs Lewy stability condition. Numerical examples are presented to validate the new method and to demonstrate its efficiency and accuracy. [ABSTRACT FROM PUBLISHER]

A procedure to synthesize a suitable biphasic composite material from the given Shielding effectiveness (SE) specifications is proposed herein. In particular, this paper presents an analytic approach for calculating parameters of a Debye-like equivalent homogeneous material, which meets the SE requirements in given frequency range. Establishing the relationship of the SE with the intrinsic material and morphological properties of a composite will make it possible to effectively find an equivalent homogeneous lossy Debye-like material model, starting from the given SE frequency characteristic. The Maxwell Garnett mixing rule is used to synthesize a composite made by aligned cylindrical inclusions. A few examples of how this procedure works are presented; validation by time domain numerical simulations is provided. [ABSTRACT FROM PUBLISHER]

In this paper, a nonorthogonal locally 1-D finite difference time-domain (LOD-NFDTD) method is presented for electromagnetic (EM) scattering involving curvilinear coordinate system. Formulations of scattered field and convolutional perfectly matched layer absorbing boundary condition in generalized nonorthogonal grids for LOD-NFDTD are also presented. The nonorthogonal grids are used to fully mesh the computational domain which leads to efficient computation. Moreover, the proposed technique requires fewer arithmetic operations than the alternating direction implicit NFDTD method leading to a reduction of CPU time. The numerical dispersion of the proposed method as a function of Courant-friedrich-lewy number (CFLN) is also presented. Computational results for EM scattering from 2-D conducting, dielectric, and coated cylinders as well as overfilled dielectric and bent cavity structures are presented. [ABSTRACT FROM PUBLISHER]

This paper provides an efficient iterative solution in the frequency domain for electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) based on distributed analytical representation of the exciting sources and iterative technique originated from waveform relaxation. The method consists of two kinds of iterations, the first is that the incoming EMP wave couples to each conductor while the effects of neighboring conductors were neglected; the second is that each conductor will be not only subject to the illumination of the EMP wave, but also influenced by the virtual sources which are the induced voltages and currents of the neighboring conductors at the previous iteration. The key highlights of the proposed method are that the induced voltage and current at each iteration are considered as the virtual distributed exciting sources for next iteration, and the integrals were solved analytically by the Baum–Liu–Tesche equation, leading to a pretty good efficiency and quick convergence for most real cases. The validation results over a wide range show that the proposed method could efficiently handle EMP coupling to MTLs with a large number of conductors and the accuracy of the solutions is closely related to the number of iterations allowing the flexibility to choose between the accuracy and the time cost. [ABSTRACT FROM AUTHOR]

With the complex-frequency-shifted perfectly matched layer (CFS-PML) implemented based on both the stretched coordinates and the bilinear transform method as the absorbing boundary condition (ABC), a novel unified finite-difference time-domain (FDTD) algorithm is developed for general FDTD spatial schemes and general media. The proposed FDTD-PML algorithm employs a general expression for the permittivity of arbitrary linear dispersive media and also takes the nonlinear effects into account. The bilinear transform used in this paper has better accuracy than the frequently used forward, backward, and central difference schemes. Compared with the recursive convolution implementation of the CFS-PML, the bilinear transform implementation involves much simpler FDTD expressions and has better absorbing performance with the same computational cost. Several two-dimensional (2-D) and 3-D simulations involving the anisotropic media, the Debye media, the Drude media, and the Kerr nonlinear media have been done to validate the presented algorithm, and indicate the advantages of the bilinear transform implementation of the CFS-PML. A simulation involving the Lorentz media calculated with the proposed algorithm adopting the wavelet-based high-order FDTD scheme is also included to validate the accuracy and effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

In this paper, an efficient approach is used to evaluate the stochastic variations of the bulk permittivity for complex periodic composite material. This method is based on the stochastic collation method together with a periodic 3-D finite-difference approach. Based on the proposed method, the influence of the input uncertainties (e.g., mixture inclusion permittivity, conductivity, volume fraction, and host cell periodicity) on the complex bulk permittivity is discussed. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for modeling nonuniform lossy transmission lines. The proposed technique is based on the concept of Green’s function of the differential problem represented by the Telegrapher’s equations. The Green’s function of nonuniform one-dimensional problems is expanded in terms of the eigenfunctions of the uniform problem, yielding a rational macromodel that has a simple representation in the time-domain. The use of global basis functions also addresses the problem of space dependence of the per-unit-length parameters, completely avoiding to resort to any discretization technique. Several examples of single and coupled nonuniform lines are presented and the accuracy of the method is verified by comparison with reference results. [ABSTRACT FROM AUTHOR]

In this paper, an unconditionally stable finite-difference time-domain algorithm is presented for analysis of lossy nonuniform multiconductor transmission line (MTL). The results of the proposed algorithm are confirmed by those of the Leap-Frog algorithm. The unconditionally stable algorithm alone cannot decrease the time consumption, especially when the MTL is excited by modulated signals. The complex phasor transformation approach is used to separate the modulating signal from the carrier signal when an MTL is excited by a modulated signal. A new set of equations is generated using this approach. The new equations are based on the modulating signal, and the carrier signal is eliminated in these equations. The derived equations are solved by Leap-Frog algorithm, and the results confirm the accuracy of these equations. Finally, the proposed equations are solved by the unconditionally stable algorithm at several temporal step sizes. The results indicate that this method has much lower CPU time compared with the conventional method and also has a very good accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a general domain expression is developed to calculate the horizontal electric field at the ground surface. The expression satisfies stricter conditions than the Cooray–Rubinstein (C-R) and Wait formulae. We proved that the new expression can be reduced into the first approximation of the C-R and Wait formulae. An evaluation that utilized the numerical results obtained by the three formulae was conducted to investigate the error caused by the assumptions made in the C-R and Wait formulae. Finally, the approximate method proposed by Caligaris, Delfino, and Procopio was utilized to evaluate the new formula and the C-R formula through comparison with the results obtained conventionally using the C-R formula. [ABSTRACT FROM PUBLISHER]

This paper describes a block-latency insertion method (LIM) for the fast transient simulation of the large networks with many coupling elements. First, the basic formulation of LIM is reviewed. Next, the block-LIM formulation for the network with many coupling elements, such as the mutual inductance, the mutual capacitance, and controlled sources is described. Then, the block-LIM algorithm is applied to the tightly coupled transmission lines, which are connected to each other by a number of mutual inductors and capacitors. Finally, some numerical results are shown, and it is confirmed that the proposed technique is useful and efficient for the simulation of the tightly coupled transmission lines. [ABSTRACT FROM AUTHOR]

Near-electric-field and magnetic-field probes are used for a wide variety of applications. Accurate measurement of the fields, however, requires an accurate model of the receiving characteristic of the probe. The receiving characteristic for a reciprocal near-field probe can be calculated from its transmitting characteristic. This receiving characteristic can be used to evaluate the quality of the probe and to compensate for the effect of the probe on the measured field, thereby allowing the electric and magnetic fields to be found accurately from the measurements. In the following paper, methods of evaluating near-field probes using reciprocity are derived and are applied to a typical loop probe in order to compensate near-field measurements over a device under test. [ABSTRACT FROM AUTHOR]

The time-domain counterpart of the Okoshi’s contour integral method is formulated with the aid of the reciprocity theorem of the time-convolution type. A numerical procedure for solving the time-domain reciprocity relation is proposed and validated using an analytical solution based on the eigenfunction expansion and the finite-integration technique. For the former, the time-domain counterpart of the classical double-summation formula for a rectangular power-ground structure is found and evaluated. [ABSTRACT FROM PUBLISHER]

We derive equations to calculate the number of samples (tuner positions) required to achieve a certain inhomogeneity for the maximum of a rectangular field strength component with given confidence in reverberation chambers. Perfect and limited reverberation are investigated. The results are in good agreement with unreferenced values found in reverberation standards, e.g., IEC 61000-4-21. They can be used to a priori predict the required number of independent samples from the quality factor and the chamber volume only. Evidence is given that current homogeneity limits in standards (3 dB, IEC 61000-4-21) are inconsistent with the minimum number of samples to use (namely 12) at high frequencies. [ABSTRACT FROM AUTHOR]

Based on the transmission line theory, modal transformation is applied to a balanced two-conductor line connected to a signal source and a load, which yields an equivalent circuit expressed in differential and common modes. This newly developed equivalent circuit clearly shows that the common-mode currents on a balance two-conductor line are generated by 1) direct injection of the common-mode current by a connected RF source; 2) multiple mode conversions by the source and load; and 3) multiple reflections of the modal currents at the source and load. The effects of branch lines connected to the feeder line are also investigated, focusing on generation of the common-mode current. It is concluded that the common-mode currents are also generated by 4) series connection of a branch line. Particularly, in the case of a switching branch line, the connection of a feeder line makes the branch line imbalanced, resulting in the common-mode current in the branch line. The aforementioned theoretical findings are compared with computer simulation using the method of moments with the numerical electromagnetic code (NEC2). [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]

We infer peak currents from radiation electric field peaks of 48 positive return strokes acquired in Gainesville, FL, USA, from 2007 to 2008. In doing so, we use the transmission line model, National Lightning Detection Network (NLDN) -reported distances, and assumed return-stroke speed. From a similar analysis of negative subsequent strokes, it appears that the implied return-stroke speed in the NLDN field-to-current conversion equation is 1.8 × 10^8 m/s (the NLDN peak current estimation algorithm is calibrated for negative subsequent strokes). The NLDN uses the same field-to-current conversion procedure (and hence the same implied return-stroke speed) for positive return strokes. However, NLDN-reported peak currents for positive return strokes differ from peak currents predicted by the transmission line model with an assumed return-stroke speed of 1.8 × 10^8 m/s. The discrepancy between regression equations for negative and positive return strokes suggests that the NLDN procedure to compensate for field propagation effects and find the average range-normalized signal strength (RNSS) works differently for these two groups of strokes. We find that the difference can be explained by the bias toward NLDN sensor reports from larger distances for positive strokes combined with the higher relative sensor gain (the ratio of sensor's peak current estimate to the NLDN-reported peak current) at larger distances. [ABSTRACT FROM PUBLISHER]

An exact analytical solution for the via-plate capacitance in multilayer printed-circuit board (PCB) structures is presented. The formulation is based on Laplace's equation for the static electric potential within the via-plate region, which is electrically small for a large frequency range. The potential distribution is determined by the separation of Laplace's equation in cylindrical coordinates for the three subdomains: via barrel and pad, antipad, and the plate region. It is shown that the unknown via-plate capacitance is determined by only one single coefficient of the resulting linear equation system. The influence of additional via pads is readily included. The results are compared with previously published approaches and validated by 2-D static, as well as by 3-D full-wave numerical simulations. [ABSTRACT FROM AUTHOR]

An improved multiple scattering method is developed for an irregular plate pair where via pad/antipad radius is electrically small and the spacing between any two vias is relatively large so that the axially anisotropic parallel plate modes can be neglected. The plate-pair impedance matrix, widely used as an important parameter in power integrity analysis and also a critical part for via coupling in the intrinsic and the physics-based via models, is found to be related to the addition theorems of the zero-order axially isotropic propagating modes. As the impedance matrix of an irregular plate pair can be calculated by many analytical and numerical methods, the relationship between the plate-pair impedance matrix and the addition theorems of the zero-order axially isotropic propagating modes enables the handling of both the mutual coupling among vias and the reflection from plate-pair edges. Thus, the conventional multiple scattering method, restricted to either an infinitely large or a finite circular plate pair, can be extended to irregular plates for the via structures described earlier. The assumptions of the method are discussed and several numerical examples are provided to validate the proposed improved method. [ABSTRACT FROM AUTHOR]

A new subcell finite-difference time-domain model is presented to solve shielding problem. The field penetration through the nonperfectly conductive shield is modeled by two-port network equations in terms of frequency-dependent admittances which are rationalized by the vector fitting procedure. The resulting equations are used to synthetized an equivalent linear time invariant circuit which is analyzed directly in time domain without using convolution equations. This important aspect is the main novelty of the proposed procedure. [ABSTRACT FROM AUTHOR]

The early time (E1) nuclear high altitude electromagnetic pulse electric field calculated with the code CHAP is compared with the field given by an integral solution of Maxwell's equations, also known as the Jefimenko equation, to aid our current understanding on the factors that affect the time dependence of the electromagnetic pulse (EMP). For a fair comparison the CHAP current density is used as a source in the Jefimenko equation. At first, the comparison is simplified by neglecting the conduction current and replacing the standard atmosphere with a constant density air slab. The simplicity of the resultant current density aids in determining the factors that affect the rise, peak and tail of the EMP electric field versus time. The explicit 3-D approach of the Jefimenko equation confirms the importance, as described in the high-frequency approximation, of sources off the line-of-sight and the time dependence of the time derivative of the current density in shaping the EMP electric field time dependence. This conclusion also holds when the conduction current and the standard atmosphere are properly accounted for. Comparison of the CHAP electric field with the Jefimenko electric field is also another way to validate the equations developed under the high-frequency/outgoing wave approximation. [ABSTRACT FROM PUBLISHER]