**5. Conclusion**

80 Fourier Transform Applications

Fig. 21. Vertical and radial electric field of the antenna *h*=300m at the lossy ground, for

Fig. 22. Vertical electric and azimuthal magnetic field at the ground surface (*z*=0) for *r*=500m

function with parameters *Im*=11kA, *tm*=0.5826μs, *a*=1.5 and *b*=0.02, and for NCBC function with parameters *Im*=11kA, *tm*=0.472μs, *a*=1.1, *b*1=0.16, *c*1=0.34, *b*2=0.0047, and *c*2=0.66, and two different decaying constants λ=2000m and λ=4500m, the results are compared to the results from (Nucci, 1990) calculated for perfectly conducting ground using the same Modified Transmission Line Model with Exponential Decay (MTLE) with the decaying

channel having height *H*=2600m and radius *a*=0.05m. For the same *v*, *H* and *a*, for the distributed resistance *R*'=0.1Ω/m along the antenna, driven by a Dirac delta current source connected across a 3.25m gap, the results are presented also for the perfectly conducting ground (Shoory et al., 2005). Shoory et al., 2005, used the electromagnetic model and a similar procedure to here presented: EFIE type equation, Method of Moments (MoM), method of images for the approximate solution of Sommerfeld's integrals (another

108m/s and the

constant λ=2000m (Nucci et al., 1990), the same return-stroke speed *v*=1.3.

ε*r*1=10 and σ1=0.01S/m for *f*=3MHz, as the functions of distance

Fourier transform proved to be very successful in lightning research. It enables calculations in frequency domain which are more suitable for including lossy ground effects than in time domain. It also provides information about frequency spectra of the quantities of interest in lightning research. For antenna modeling of a lightning stroke in frequency domain, Sommerfeld's integral is calculated efficiently using Two-image approximation.

Fourier Transform Application in the Computation of Lightning Electromagnetic Field 83

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Results are in good agreement with the results from literature for various ground electrical parameters, heights of vertical dipoles above ground, in the near and far field. Based on these results, it can be concluded that the effects of lossy ground are greater on horizontal than on vertical electric field, and that specific conductivity influences more than electrical permittivity. Fourier transform application has to be further investigated in terms of optimal choice of FFT parameters in order to reduce computing time which can be important in antenna modeling of lightning discharge channels and in analysis of lightning electromagnetic fields.
