**4. Conclusions**

This chapter has introduced an impulse-regime analysis of metamaterial-type transmission lines and antennas. Specifically, a novel formulation, based on Fourier transformations, has been proposed to describe pulse propagation along dispersive linear CRLH lines. The proposed theory is capable to model complex impulse-regime phenomena, such as dispersion, in a simple, accurate and fast way. Then, the method has been extended to consider CRLH leaky-wave antennas, allowing a fast and accurate analysis of the far-field radiation of these structures in time-domain. The proposed formulation has then been applied to *the development of novel phenomena and applications in the microwave domain, most of them transported from optics*. Instead of the usual magnitude engineering and filter design, a dispersion or phase engineering has been applied. In this approach, the dispersive nature and subsequent impulse-regime properties of CRLH structures have been exploited to obtain novel phenomena/applications. Each phenomenon or application proposed has theoretically been described, numerically verified, and in most of the cases, experimentally demonstrated. The shift from narrow band systems (mostly used in the past) to ultra wide band systems, required by current high date rate wireless communication systems, suggests that the

forthcoming decades will experience a major interest on this dispersive engineering approach, providing new, novel and more exciting effects and devices at microwaves.

#### **5. References**

28 Will-be-set-by-IN-TECH

in both spectrograms. On the other hand, this antenna provides an excellent time-gating trade-off, because the energy is instantaneously radiated, almost without propagation along the structure, leading to a large time resolution. Thereby, the use of a very short antenna leads to generally erroneous spectrograms, due to the wide detection of frequencies which are not part of the input pulse. Second, we modify the CRLH LWA antenna, including now a total of *N* = 20 unit cells. This configuration provides a good frequency resolution in both systems, while the temporal resolution is deteriorated in the RTSA system (due to the use of a longer antenna). The resulting spectrograms are depicted on Fig. 21(c) (FREG) and Fig. 21(d) (RTSA). As it can be observed, the FREG system provides a completely realistic spectrogram, which faithfully reproduces the input signal in terms of frequency and time (location and spreading). On the other hand, the spectrogram obtained by the RTSA has a good frequency resolution, but has some problems dealing with the temporal duration of the pulse. As previously commented, this problem is due to the propagation of the input pulse as it is being radiated, as graphically illustrated in Fig. 15. And third, we simulate the FREG and RTSA systems based on the same CRLH LWA, but composed now of *N* = 40 unit cells. The results are shown in Fig. 21(e) (FREG) and Fig. 21(f) (RTSA). The spectrogram obtained using the FREG system is quite similar to the previous FREG spectrogram (*N* = 20 unit cells), keeping the temporal characteristics but improving the frequency resolution (because a longer antenna provides higher directivity). All relevant features of the input modulated Gaussian pulse, in terms of frequency and time, can easily be extracted from this spectrogram. However, the RTSA system provides a completely wrong result. This is because of the excessive length

of the CRLH LWA, which completely destroy the temporal resolution of the system.

the fact that it is not a completely real-time system.

**4. Conclusions**

The above comparison demonstrates that the proposed FREG system presents important advantages over the RTSA system, specially in terms on temporal resolution, being able to characterize any unknown UWB input signal. Furthermore, this comparison has shown that the RTSA system can only deal with signals whose frequency and temporal characteristics are -at least overall- previously known. On the other hand, the main constrains of the FREG system are the complex equipment required, the requirement of a periodic input signal, and

This chapter has introduced an impulse-regime analysis of metamaterial-type transmission lines and antennas. Specifically, a novel formulation, based on Fourier transformations, has been proposed to describe pulse propagation along dispersive linear CRLH lines. The proposed theory is capable to model complex impulse-regime phenomena, such as dispersion, in a simple, accurate and fast way. Then, the method has been extended to consider CRLH leaky-wave antennas, allowing a fast and accurate analysis of the far-field radiation of these structures in time-domain. The proposed formulation has then been applied to *the development of novel phenomena and applications in the microwave domain, most of them transported from optics*. Instead of the usual magnitude engineering and filter design, a dispersion or phase engineering has been applied. In this approach, the dispersive nature and subsequent impulse-regime properties of CRLH structures have been exploited to obtain novel phenomena/applications. Each phenomenon or application proposed has theoretically been described, numerically verified, and in most of the cases, experimentally demonstrated. The shift from narrow band systems (mostly used in the past) to ultra wide band systems, required by current high date rate wireless communication systems, suggests that the


**3** 

Vesna Javor

*Serbia* 

**Fourier Transform Application** 

**Lightning Electromagnetic Field** 

Atmospheric discharge is one of the most interesting and powerful natural phenomenon hiding from men its undiscovered features and secrets for centuries. Lightning discharges have been studied in many theoretical and experimental ways. However, application of Fourier transform has been introduced in this research only in recent few decades. It proved

There are two main groups of problems in lightning studies that involve using Fourier transform. One deals with determining how the energy is distributed over a continuous frequency spectrum for the quantity of interest. Channel-base currents, induced voltages and currents, electric and magnetic field components, so as integrals and derivatives of the same functions, distribute components over the entire frequency range in different ways. These are non-periodic functions scattering their energy throughout the frequency spectra. Another important group of problems to be solved by Fourier transform deals with the calculation of lightning induced effects at different distances from the lightning discharge and risk assessment for buildings, various structures, people and property in an external impulse electromagnetic field. These calculations are based on experimental results for the measured lightning electromagnetic field (LEMF) and channel-base currents, which are used in different types of lightning stroke models including lossy ground effects. Lightning discharge channel is usually modeled by a thin vertical antenna at a lossy ground of known electrical parameters. Both ground and air are treated as linear, isotropic and homogeneous half-spaces. Even for such a simple approximation of the lightning channel - calculations can not be easily done in time domain, but transformation to frequency domain is used instead. Once the calculations are done in frequency domain, way back to time domain is made by

In both groups of problems an impulse function which has the analytical derivative, integral and integral transformations is very useful. New functions proposed by the author for representing lightning currents are presented in this Chapter, Section 2. These can be also used in other high voltage technique calculations. The main problem for a user of the impulse functions already given in literature to approximate some quantity is the choice of parameters so to obtain desired waveshape characteristics or values adequate to

very useful in solving many lightning research problems.

Inverse Fourier transform applied to the obtained results.

**1. Introduction** 

*University of Nis / Faculty of Electronic Engineering* 

**in the Computation of** 

