146 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 47, NO. 1, FEBRUARY 2005 Far-Field–Current Relationship Based on the TL Model for Lightning Return Strokes to Elevated Strike Objects José Luis Bermudez, Member, IEEE, Farhad Rachidi, Senior Member, IEEE, Marcos Rubinstein, Wasyl Janischewskyj, Life Fellow, IEEE, Volodymyr O. Shostak, Senior Member, IEEE, Davide Pavanello, Jen Shih Chang, Senior Member, IEEE, Ali M. Hussein, Senior Member, IEEE, Carlo Alberto Nucci, Senior Member, IEEE, and Mario Paolone Abstract—New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike ob- ject, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed , the speed of light in vacuum , and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electro- magnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level , these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground. Manuscript received September 9, 2003; revised May 25, 2004. This work was supported by the Swiss National Science Foundation under Grant 20-56862.99 and Grant 2000-068147 and by the Canadian Natural Sciences and Engineering Research Council. J. L. Bermudez, F. Rachidi, and D. Pavanello are with the Ecole Polytech- nique Fédérale de Lausanne (Swiss Federal Institute of Technology), CH-1015 Lausanne, Switzerland (e-mail: Farhad.Rachidi@epfl.ch). M. Rubinstein is with the University of Applied Sciences of Western Switzer- land, CH-1401 Yverdon, Switzerland. W. Janischewskyj is with the Universityof Toronto, Toronto, ON M5S 3G4, Canada. V. O. Shostak is with the Kyiv Polytechnic Institute, Kyiv, 03056 Ukraine. J. S. Chang is with McMaster University, Hamilton, ON L8S 4M1, Canada. A. M. Hussein is with Ryerson University, Toronto, ON M5B 2K3, Canada. C. A. Nucci and M. Paolone are with the University of Bologna, Bologna 40136, Italy. Digital Object Identifier 10.1109/TEMC.2004.842102 Index Terms—Electromagnetic fields, elevated strike objects, lightning, lightning location systems, lightning return stroke modeling. I. INTRODUCTION T HE determination of the peak return stroke current from remotely measured electric or magnetic fields consider- ably facilitates the collection of data on the lightning return stroke current without having to instrument towers or trigger the lightning artificially and without the inherent relative inef- ficiency associated with those methods. This is especially true nowadays because of the widespread use of lightning location systems. Indeed, such systems are already used to also provide estimates of lightning current parameters using regression equa- tions (e.g., [1]–[3]). The theoretical estimation of return stroke currents from remote electromagnetic fields depends on the adopted return stroke model. Expressions relating radiated fields and return stroke channel base currents have been derived for various “en- gineering” return stroke models (e.g., [4]). For rocket-triggered cloud-to-ground lightning events, Willet et al. compared the predictions obtained using one of these engineering models, namely the transmission line (TL) model, to experimental data sets consisting of simultaneously measured current, electric field, and return stroke speed, and they reported reasonable agreement [5]. Based on the TL model, for an observation point at ground level, the radiated (far) electric and magnetic fields produced by a vertical lightning channel terminated directly at ground are simply proportional to the channel base current [6] (1) (2) in which is the channel base current, is the return stroke speed, and is the distance from the channel base to the obser- vation point. Equations (1) and (2) are derived assuming that the return stroke is initiated at ground, which makes their use rea- sonable to a certain extent, also for triggered lightning, as in [5]. On the other hand, experimental observations at tall telecom- munication towers, such as the 553-m-high Canadian National 0018-9375/$20.00 © 2005 IEEE