FRACTAL ANTENNAS

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FRACTAL ANTENNAS: :

FRACTAL ANTENNAS:

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OVERVIEW Introduction Antenna Definition Antenna Parameters Fractals The Geometry Of Fractals Fractal Dipole Antennas-Koch Fractal Fractal Loops Koch Loop Minkowski Loop Sierpinski Sieve Applications Of Fractal Antennas Advantages & Disadvantages Conclusion References

INTRODUCTION :

INTRODUCTION In today world of wireless communications, there has been an increasing need for more compact and portable communications systems. Just as the size of circuitry has evolved to transceivers on a single chip, there is also a need to evolve antenna designs to minimize the size. Currently, many portable communications systems use a simple monopole with a matching circuit. However, if the monopole were very short compared to the wavelength, the radiation resistance decreases, the stored reactive energy increases, and the radiation efficiency would decrease. As a result, the matching circuitry can become quite complicated. As a solution to minimizing the antenna size while keeping high radiation efficiency, fractal antennas can be implemented. The fractal antenna not only has a large effective length, but the contours of its shape can generate a capacitance or inductance that can help to match the antenna to the circuit. Fractal antennas can take on various shapes and forms. For example, a quarter wavelength monopole can be transformed into a similarly shorter antenna by the Koch fractal.

Antenna Definition:

Antenna Definition An antenna is a device use to transfer guided electromagnetic waves to radiating waves in an unbounded medium usually free space and vice versa

Antenna Parameters :

Antenna Parameters Input Impedance:- For an efficient transfer of energy, the impedance of the radio, of the antenna and of the transmission cable connecting them must be the same Bandwidth:- The bandwidth of an antenna refers to the range of frequencies over which the antenna can operate correctly Directivity:- Directivity is the ability of an antenna to focus energy in a particular direction when transmitting, or to receive energy better from a particular direction when receiving.

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Gain:- The amount of energy radiated in that direction compared to the energy an isotropic antenna would radiate in the same direction when driven with the same input power. Radiaion Lobe:- Portion of the radiation pattern bounded by regions of relatively weak radiation intensity.

Fractals:

Fractals Fractals are complex geometric designs that repeat themselves, or their statistical properties on many scales, and are thus “self similar.” The geometry of fractals is important because the effective length of the fractal antennas can be increased while keeping at total area same.The shape of the fractal antenna can be formed by an iterative mathematical process, called as Iterative function systems (IFS).

THE GEOMETRY OF FRACTALS:

THE GEOMETRY OF FRACTALS The geometry of fractals is important because the effective length of the fractal antennas can be increased while keeping at total area same. The shape of the fractal antenna can be formed by an iterative mathematical process, called as Iterative function systems (IFS).

FRACTAL DIPOLE ANTENNAS- KOCH FRACTAL :

FRACTAL DIPOLE ANTENNAS- KOCH FRACTAL The expected benefit of using a fractal as a dipole antenna is to miniaturize the total height of the antenna at resonance, where resonance means having no imaginary component in the input impedance. The geometry of how this antenna could be used as a dipole is shown in Fig 1. Fig. 1 - Geometry of Koch dipole

FRACTAL LOOPS :

FRACTAL LOOPS Loop antenas are well understood and have been studied using a variety of Euclidean geometry. The have distinct limitations, howeever. Resonant loop antennas require a large amount of space and small loops have very low input resistance. A fractal island can be used as a loop antenna to overcome these drawbacks. Two possible fractals fed as loop antennas are depicted in Fig. Fig. 4 -Two possible fractal loop antennas

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Fractals loops have the characteristic that the perimeter increases to infinity while maintaining the volume occupied. This increase in length decreases the required volume occupied for the antenna at resonance. For a small loop, this increase in length improves the input resistance. By raising the input resistance, thye antenna can be more easily matched to a feednig transmission line.

KOCH LOOP :

KOCH LOOP The starting pattern for the Koch loop that is used as a fractal antenna is a triangle. From this starting pattern, every segment of the starting pattern is replaced by the generators. The first four iterations are shown in Fig. 5. The starting pattern is Euclidan and, therefore, the process of replacing the segment with the generator constitutes the first iteration.

KOCH LOOP :

KOCH LOOP The starting pattern for the Koch loop that is used as a fractal antenna is a triangle. From this starting pattern, every segment of the starting pattern is replaced by the generators. The first four iterations are shown in Fig. 5. The starting pattern is Euclidan and, therefore, the process of replacing the segment with the generator constitutes the first iteration . First four iterations of Koch loop

MINKOWSKI LOOP :

MINKOWSKI LOOP Minkowski loop (Fig. 7) can be used to reduce the size of the antenna by increasing the efficiency with which it fills up its occupied volume with electrical length. A Minkowski fractal is analyzed, where the perimeter is near one wavelength. Several iterations are compared with a square loop antenna to illustrate the benefits of using a fractal antenna. Fig. 7 - First three iterations of Minkowski loop

SIERPINSKI SIEVE :

SIERPINSKI SIEVE So far, only the space saving benefits of fractal antennas have been exploited. There is another property of fractals that can be utilized in antenna construction. Fractals have self-similarity in their geometry, which is a feature where a section of thfractal appears the same regardless of how many times the section is zoomed in upon. Self-similarity ithe geometry creates effective antennas of different scales. This can lead to multiband characteristicantennas, which is displayed when an antenna operates with a similar performance at various frequencies. The generation of the fractal is howFig. 10. A Sierpinski sieve dipole can be easily compared to a bowtie dipole antenna, which is thgenerator to create the fractal. The middle third triangle is removed from the bowtie antenna, leaving three equally sized triangles, which are half the heighof the original bowtie. The process of removing tmiddle third is then repeated on each of the new triangles. For an ideal fractal this process goes on for an infinite no. of times.

APPLICATIONS OF FRACTAL ANTENNAS :

APPLICATIONS OF FRACTAL ANTENNAS Theree are many applications that can benefit fromfractal antennas. Discussed below are several ideas where fractal antennas can make an real impact. The sudden growin the wireless communication area has sprung a need for compact integrated antennas. The space saving abilities of fractals to efficiently fill a limited amount of space create distinct advantage of using integrated fractal antennas over Euclidean geometry. Examples of these types of applicatiinclude personal hand-held wireless devices such as cell phones and other wireless mobile devices such as laptops on wireless LANs and networkable PDAs. Fractal antennas can also enrich applications that include multiband transmissions. This area has many possibilitieranging from dual-mode phones to devices integrating

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communication and location services such as GPS,the global positioning satellites. Fractal antennas also decrease the area of a resonant antenna, which could lower the radar cross-section (RCS). This benefit can be exploited in military application the antenna is a very crucial parameter.

Advantages of fractal antenna technology are: :

Advantages of fractal antenna technology are: minituratization • better input impedance matching wideband/multiba instead of many) frequency independent (consistent performance over huge frequency range) reduced mutual coupling in fractal array antennas

Didvantages of fractal antenna technology are: :

Didvantages of fractal antenna technology are: gain loss complexity numerical limitations The benefits begin to diminish after first few iterations

CONCLUSION :

CONCLUSION Many variations of fractal geometries have been incorporated into the design of antennas. Further work is required to get an understanding of the relationship between the performance of the antenna and the fractal dimension of the geometry that is utilized in its construction. This requires two curses of action. The first course of action requires that many more examples of fractal geometries are applied to antennas. The second crucial course of action is to attain a better understanding of the fractal dimension of the geometries such that correlations can be drawn about this dimension and the performance of the antenna. Also important is that the design of the antenna approaches an ideal fractal as much as possible. Several iterations can be studied to understand the trends that govern the anteena to better understand the physics of the problem.

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REFERENCES http://library.thinkquest.org/3493/frames/fractal.html http://www.ccs.neu.edu/home/fell/COM1201/PROGRAMS/RecursiveFractals.html http://en.wikipedia.org/wiki/Fractal http://www.math.lsa.umich.edu/mmss/coursesONLINE/chaos/chaos7/index.html www.fractus.com www.fractenna.com Best, S, (2003). "A Comparison of the Resonant Properties of Small Space-Filling Fractal Antennas" . IEEE Antennas and Wireless Propagation Letters 2 (1): 197-200. http://www.physics.princeton.edu/~mcdonald/examples/EM/best_ieeeawpl_2_197_03.pdf . FRACTAL ANTENNAS Mircea V. Rusu, Physics Faculty, Bucharest University, Roman Baican, Adam Opel AG. Russelheim, Germany , Ioana ENE, University "Politehnica" Bucharest, Romania 9. Generalized Sierpinski Fractal Multiband Antenna Jordi Romeu and Jordi Soler IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 8, AUGUST 2001 10. Performance characteristics of Minkowski curve fractal antennas M.Ahmed and others journal of engineering and sciences, 2006 11. Fractal antennas literature study by Philip Felber