Abdolhamid Shoory

Analysis of lightning-radiated electromagnetic fields in the vicinity of lossy ground

An antenna theory (AT) approach in the frequency domain is presented to compute electromagnetic fields radiated by a lightning return stroke. The lightning channel is modeled as a lossy-wire monopole antenna (a wire antenna with distributed resistance) energized by a current source at its base, and the ground is modeled as a lossy half-space. The method of moments is used for solving the governing electric field integral equation (EFIE) in the frequency domain. The resultant current distribution along the channel is used to calculate electromagnetic fields at different distances from the channel. All field components are evaluated using a rapid but accurate procedure based on a new approximation of Sommerfeld integrals. In contrast with the previous models, the approach proposed here is characterized by a self-consistent treatment of different field components in air or on the surface of a lossy half-space. It is shown that the omission of surface wave terms in the general field equations, as done in the perfect-ground approximation, can strongly affect model-predicted field components.

Validity of Simplified Approaches for the Evaluation of Lightning Electromagnetic Fields Above a Horizontally Stratified Ground

We review in this paper simplified analytical expressions derived by Wait using the concept of attenuation function for the analysis of the propagation of lightning radiated electromagnetic fields over a horizontally stratified ground. Considerations regarding the use of these formulations as well as their domain of applicability are given. For the case, where the upper ground layer has a lower conductivity than the lower layer, the magnitude of the attenuation function can take values greater than unity. Time-domain waveforms of the vertical electric field along a horizontally stratified ground, obtained using the simplified formulations feature, an oscillatory behavior in their early-time response. The peak value of the field is also found to be larger than that corresponding to the case of a perfect ground. The accuracy of the Waits formulations is examined taking as reference full-wave simulations obtained using the finite-difference time domain (FDTD) technique. FDTD simulations confirm the oscillatory waveform of the far field above a horizontally stratified ground (with an upper layer characterized by a lower conductivity than that of the lower layer), as well as the enhancement of the field peak compared to the case of a homogeneous, perfectly conducting ground.

Lightning electromagnetic radiation over a stratified conducting ground: 2. Validity of simplified approaches

In the first part of this paper, the rigorous theory describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground was presented and the exact expressions for the lightning electromagnetic fields were developed and discussed. In this part of the paper, the theory along with its time domain numerical evaluation algorithm is used for the assessment of the validity of simplified approaches proposed in the literature for the vertical electric and horizontal magnetic field components. The simplified approaches are based on the concept of ground surface impedance and its corresponding attenuation function. It is shown that the results obtained using the simplified approaches are in excellent agreement with exact results in both near (50 m) and intermediate (1000 m) distance range. However, since the vertical electric and azimuthal magnetic field components are not appreciably affected by the ground finite conductivity, they can also be evaluated assuming the ground as a perfectly conducting ground. On the other hand, the horizontal electric field above a horizontally stratified ground is very much affected by the ground electrical parameters. Its waveform is characterized by an early negative excursion due to the currents flowing into the ground followed by a late time positive excursion which is due to the elevation of the observation point from the ground level. The magnitude of the negative peak is sharper for subsequent return strokes than first return strokes and is higher for lower conducting grounds. A new formula is proposed for the evaluation of the horizontal electric field at a given height above the air-ground interface. The formula can be viewed as the generalization of the Cooray-Rubinstein formula for the case of a two-layer ground. We show that the new formula is able to reproduce in a satisfactory manner the horizontal electric field above a two-layer ground. The proposed formulation is, however, less accurate at distances as close to 10 m from the channel base and for very poor ground conductivity (0.0001 S/m).

Lightning electromagnetic fields at very close distances associated with lightning strikes to the Gaisberg tower

In this paper we present and discuss measurements of electric (vertical and radial) and magnetic fields from leaders and return strokes associated with lightning strikes to the 100 m tall Gaisberg tower in Austria obtained in 2007 and 2008. The fields were measured at a distance of about 20 m from the tower. Simultaneously, return stroke currents were also measured at the top of the tower. The data include, for the first time at such close distances, simultaneous records of vertical and horizontal electric fields. The vertical electric field waveforms appeared as asymmetrical V-shaped pulses. The initial, relatively slow, negative electric field change is due to the downward leader, and the following, fast, positive electric field change is due to the upward return stroke phase of the lightning discharge. The horizontal (radial) electric field due to the leader phase has a waveshape similar to that of the vertical electric field. However, the horizontal field due to the return stroke is characterized by a short negative pulse of the order of 1 mu s or so, starting with a fast negative excursion followed by a positive one. The return stroke vertical electric field changes appear to be significantly smaller than similar measurements obtained using triggered lightning. This finding confirms the shadowing effect of the tower, which results in a significant decrease of the electric field at distances of about the height of the tower or less. The vertical and horizontal E field changes due to the return stroke were also found to be larger on average than the leader electric field changes. In a significant number of cases (33%), the vertical electric field waveforms due to the return stroke were characterized by a first peak exceeding the typical late-time flattening due to the electrostatic term. This is in contrast with similar measurements related to triggered lightning which do not exhibit such a first peak. About one quarter of the measured vertical electric field waveforms (18 pulses out of 76) featured an unusual waveform characterized by a positive leader field change followed by a bipolar return stroke field change with a zero crossing time of about 60 mu s.

On the Measurement and Calculation of Horizontal Electric Fields From Lightning

In this paper, we discuss two issues related to the measurement and calculation of the horizontal electric fields from lightning. On the one hand, there is an inherent difficulty in measuring the horizontal electric field component from lightning because of the overshadowing effect of the vertical electric field component which, depending on the distance to the lightning channel, the ground conductivity, and the height of the observation point can be one to two orders of magnitude larger than the horizontal electric field component. Consequently, even a small tilt of the measuring antenna would result in a noticeable contamination of the measured horizontal waveform. This may explain the fact that data on horizontal electric fields are very scarce. Numerical simulations show that, for a ground conductivity of 0.0025 S/m, the resulting error for a one-degree sensor tilt in the field peak is about 20% for distances ranging from 60 to 500 m. For strikes to a 100-m-tall tower, the resulting errors are found to be slightly smaller (about 10% to 15% for the first peak). The second issue dealt with in this paper is the computation methods of the horizontal electric field. In this regard, some authors have emphasized the importance of taking into account the so-called conduction current in the calculation of nearby horizontal electric fields. We show in this paper that the conducted contribution is automatically taken into account when using the general solutions of Maxwells equations or obtained by exact numerical simulations. In this case, there is no need to consider separately any other contributions because the solution yields the total horizontal electric field, taking into account both the radiation from the channel and the current flowing into the ground. However, a “conducted contribution” needs indeed to be taken into account separately when high-frequency approximate solutions are used for the evaluation of the electric field. At very close distances to the lightning strike location, the current distribution in the ground may be highly nonuniform because of surface arcing and plasma channel formations. Given the random nature of these phenomena, it is virtually impossible to gain detailed knowledge of the current distribution and, hence, to evaluate the resulting horizontal electric field near the strike point. Based on the results and discussion presented in this paper, we recommend taking special care when measuring the horizontal electric field from lightning to minimize the contaminating effect of the vertical electric field. It is important that both components (vertical and horizontal) be measured simultaneously to evaluate possible contamination of the horizontal field.

Lightning electromagnetic radiation over a stratified conducting ground: Formulation and numerical evaluation of the electromagnetic fields

The formulation describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground is presented in this paper. The derivation of the Greens functions required to solve the problem is first discussed in detail, and the expressions for the lightning electromagnetic fields are determined. Afterward, an efficient method for the numerical evaluation of the electromagnetic field is proposed. The proposed method is based on a suitable modification of a previously developed model for the evaluation of the fields in the presence of a lossy but homogeneous soil. Particular attention is devoted to the soil reflection coefficient properties, both from a physical and from a mathematical point of view. In part 2 of the paper, the developed approach and numerical algorithms will be used to evaluate the effect of the soil stratification on the radiated fields and to perform the validity assessment of simplified approaches proposed in the literature.

On the Mechanism of Current Pulse Propagation Along Conical Structures: Application to Tall Towers Struck by Lightning

We discuss in this paper the propagation of lightning current pulses along conical tall structures. Although the dominant mode of an infinitely long conical transmission line is transverse electric and magnetic (TEM), such a structure can also support higher order TE and TM modes which display a gradual cutoff frequency variation with height. Recently, Baba and Rakovs finite-difference time domain numerical analysis revealed that for a perfectly conducting conical structure, while the current pulses suffer no attenuation as they travel from the cones apex to its base, the attenuation is significant when pulses propagate from the base to the apex. Adopting an analysis method using 1) the COMSOL Multiphysics simulation environment based on the finite element method and 2) the partial equivalent element circuit method, we study the same reduced-scale structure analyzed by Baba and Rakov. The obtained results confirm the conclusions drawn by Baba and Rakov. We also perform simulations for the case of a 100-m tall tower considering different tower-base radii. It is shown that the upward current pulses are affected by a strong attenuation resulting from the field scattering near the discontinuity at the tower base, followed by a weaker attenuation resulting from the propagation along the cone from its base to the apex. A simple way to modify the engineering lightning return stroke models to account for the attenuation of the upward current pulses is suggested. Finally, we report on experiments to study the current pulse propagation along a 1/582 reduced scale model of the Toronto, CN, tower. The obtained experimental data support the numerical simulations.

Application of the Cascaded Transmission Line Theory of Paul and McKnight to the Evaluation of NEXT and FEXT in Twisted Wire Pair Bundles

The cascaded transmission line theory of Paul and McKnight is used in this paper to predict near-end crosstalk (NEXT) and far-end crosstalk (FEXT) in a bundle of twisted wire pairs. The approach is validated using the CST Cable Studio commercial software and experimental data. NEXT and FEXT along twisted pair bundles are then evaluated using a pure deterministic approach for the electromagnetic coupling while taking into account the random distribution of victim and aggressor pairs in the bundle. The results obtained using the presented approach are compared with available simplified empirical expressions (ANSI/FSAN). It is shown that the simplified expressions are able to predict the overall trend of the power sum loss. However, they do not always provide the worst case values. The presented theory can find important applications in the design of data transmission systems for which accurate crosstalk modeling is a vital task. It can be used for example as a replacement for the experiments in obtaining the parameters of simplified models for NEXT and FEXT.

Time-Domain Generalized Telegrapher's Equations for the Electromagnetic Field Coupling to Finite Length Wires Above a Lossy Ground

In this paper, a time-domain variant of the generalized telegraphers 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.

Relativistic Doppler effect in an extending transmission line: Application to lightning

We present in this paper a thorough analysis of current wave propagation with arbitrary speed along an extending transmission line. We derive rigorous analytical equations in the time and frequency domains expressing the reflections of the current wave occurring at the extending end of the line. The derived equations reveal that it is not possible to represent current reflections occurring at the extending end of a transmission line using a constant, frequency-independent reflection coefficient, as previously done in the literature. The reflected wave from the extending end of the line is shown to be affected by the Doppler frequency shift. In other words, the reflected wave from an extending transmission line suffers distortion, the amount of which depends on the incident wave form, its frequency content, and the speed of the extending end of the line. The derived expression is in agreement with the relativistic Doppler effect and is consistent with the Lorentz transformation. Finally, engineering models for return strokes are generalized and closed-form analytical expressions are derived for the spatial-temporal distribution of the current along the channel accounting for reflections at ground and at the return stroke wave front taking into account the Doppler effect.