GENERALIZED DESIGN OF MULTI-RESONANT DIPOLE ANTENNAS USING KOCH CURVES
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GENERALIZED DESIGN OF MULTI-RESONANT DIPOLE ANTENNAS USING KOCH CURVESAbstract
Generalizations of fractal Koch curves and their use in designing multi-resonant antennas are presented in this paper. Both recursive and non-recursive generalizations of the curve are examined. Variation of the indentation angle is used for this approach. Although this variation has a direct bearing on the unfolded length of the curve, this should be considered as a primary variable since several geometries with the same unfolded length can be constructed with different permutations of indentation angles. Antenna input characteristics such as the primary resonant frequency, the input resistance at this resonance, and ratios of the first few resonant frequencies have been studied by numerical simulations. This study shows that it is possible to design multiresonant antennas using Koch curves with various indentation angles. Identifying similar parameters with other known fractal geometries would offer a viable route for designing multiband and multifunctional antennas for modern wireless applications using them.
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References
B.B. Madelbrot, The Fractal Geometry of
Nature, New York: W.H. Freeman, 1983.
H.-O. Peitgen, J.M. Henriques, L.F. Penedo
(Eds.), Fractals in the Fundamental and
ciences, Amsterdam: North
EE, vol. 81, pp. 1451-1465,
-239, 1987.
ineering, Springer, pp. 204-221, 1997.
-
Propagat., vol.
IEEE Ant.
Applied S
Holland, 1991.
G.P. Cherepanov, A.S. Balankin, and V.S.
Ivanova, “Fractal fracture mechanics,”
Engineering Fracture Mechanics, vol. 51, pp.
-1033, 1995.
J.H. Jeng, V.V. Varadan, and V.K. Varadan,
“Fractal finite element mesh generation for
vibration problems,” J. Acous. Soc. Amer.,
vol. 82, pp. 1829-1833, 1987.
A.E. Jacquin, “Fractal image coding: A
review,” Proc. IE
A. Lakhtakia, N.S. Holter, V.K. Varadan, and
V.V. Varadan, “Self-similarity in diffraction
by a self-similar fractal screen,” IEEE Trans.
Ant. Propagat., vol. 35, pp. 236
Table 4. Resonant frequencies of 3rd iterated non-recursive geometry. The innermost angle is kept
θ1= 60°. The
other angles are varied as listed.
Resonant Frequencies (MHz) Ratios of Resonant
Frequencies
θ2
θ3 Input
resistance
at fr1 fr1 fr2 fr3 fr4 fr2/fr1 fr3/fr2 fr4/fr3
20 57.5 649 1968 3281 4589 3.032 1.667 1.399
49.6 605 1815 3017 4223 3.000 1.662 1.400
38.6 537 1571 2582 3632 2.926 1.644 1.407
27.2 456 1261 1995 2848 2.765 1.582 1.428
20 55.7 638 1932 3215 4491 3.028 1.664 1.397
48.2 595 1780 2952 4129 2.992 1.658 1.399
37.1 526 1539 2523 3547 2.926 1.639 1.406
25.7 443 1229 1952 2798 2.774 1.588 1.433
20 50.4 605 1822 3018 4194 3.012 1.656 1.390
43.4 563 1677 2762 3841 2.979 1.647 1.391
33.3 497 1445 2349 3285 2.907 1.626 1.398
23.1 417 1150 1816 2586 2.758 1.579 1.424
20 42.6 553 1646 2697 3709 2.976 1.639 1.375
36.4 513 1509 2457 3380 2.942 1.628 1.376
27.8 451 1294 2077 2870 2.869 1.605 1.382
19 376 1023 1598 2234 2.721 1.562 1.398
20 33.7 489 1428 2295 3099 2.920 1.607 1.350
29.1 454 1307 2087 2818 2.879 1.597 1.350
22 397 1113 1753 2369 2.804 1.575 1.351
14.8 328 871 1335 1820 2.655 1.533 1.363
D.L. Jaggard, “Fractal electrodynamics: From
super antennas to superlattices,” in Fractals
in Eng
J. Romeu and Y. Rahmat-Samii, “Dual band
FSS with fractal elements,” Electron. Lett.,
vol. 35, pp. 702-703, 1999.
D.H. Werner and D. Lee, “Design of dual
polarised multiband frequency selective
surfaces using fractal elements,” Electron.
Lett., vol. 36, pp. 487-488, 2000.
J. Romeu and Y. Rahmat-Samii, “Fractal
FSS: a novel dual-band frequency selective
surface,” IEEE Trans. Ant.
, pp. 1097-1105, 2000.
D.H. Werner, R.L. Haupt, and P.L. Werner,
“Fractal antenna engineering: The theory and
design of fractal antenna arrays,”
Propagat. Mag., vol. 41, no. 5, pp. 37-59,
K. J. Vinoy, et al.: Generalized Design of Multi-Resonant Dipole Antennas Using Koch Curves
.L. Haupt,
erner, P.L. Werner, and A.J. Ferraro,
ctronics
ultiband
d antenna based on
, vol. 35,
branched antennas,” Electron.
ol. Lett., vol. 23, pp. 242-
P-S Inter.
rrent distribution on fractal
u, R. Pous, J.
opole: A small fractal
antennas: A compilations of
ant behavior of the
onopole antenna,” Microw.
other bent wire monopoles as
ically engineered multiband fractal
K.A. Jose, V.K. Varadan, and
the relationship between fractal
antenna elements
D.H. Werner, P.L. Werner, D.L. Jaggard,
A.D. Jaggard, C.Puente, and R
“The theory and design of fractal antenna
arrays,” in Frontiers in Electromagnetics,
D.H. Werner and R. Mittra (Eds.), New
York: IEEE Press, pp. 94-203, 1999.
D.H. W
“Frequency independent features of self-
similar fractal antennas,” IEEE AP-S Inter.
Symp. 1996, pp. 2050-2053, 1996.
N. Cohen, “Fractal antenna applications in
wireless telecommunications,” in
Professional Program Proc. of Ele
Industries Forum of New England, 1997,
IEEE, pp. 43-49, 1997.
C. Puente, J. Claret, F. Sagues, J. Romeu,
M.Q. Lopez-Salvans and R Pous, “M
properties of a fractal tree antenna generated
by electrochemical deposition,” Electron.
Lett., vol. 32, pp. 2298-2299, 1996.
C. Puente, J. Romeu, R. Bartoleme, and R.
Pous, “Fractal multiban
Sierpinski gasket,” Electron. Lett., vol. 32,
pp. 1-2, 1996.
D.H. Werner, A. Rubio Bretones, and B.R.
Long, “Radiation characteristics of thin-wire
ternary fractal trees,” Electron. Lett.
pp. 609-610, 1999.
M. Sindou, G. Ablart and C. Sourdois,
“Multiband and wideband properties of
printed fractal
Lett., vol. 35, pp. 181-182, 1999.
X. Liang and. M.Y.W. Chia, “Multiband
characteristics of two fractal antennas,”
Microw. Opt. Techn
, 1999.
C. Puente, M. Navarro, J. Romeu, and R.
Pous, “Variations on the fractal Sierpinski
antenna flare angle,” IEEE A
Symp., pp. 2340-2343, 1998.
M. Navarro, J.M. Gonzalez, C. Puente, J.
Romeu, and A. Aguasca, “Self-similar
surface cu
Sierpinski antenna verified with infra-red
thermograms,” IEEE AP-S Inter. Symp., pp.
-1569, 1999.
C. Puente-Baliarda, J. Rome
Ramis, and A. Hijazo, “Small but long Koch
fractal monopole,” Electron. Lett., vol. 34,
pp. 9-10, 1998.
C.P. Baliarda, J. Romeu, and A. Cardama,
“The Koch mon
antenna,” IEEE Trans. Ant. Propagat., vol.
pp. 1773-1781, 2000.
J.P. Glanvittorio and Y. Rahmaat-Samii,
“Fractal element
configurations with novel characteristics,”
IEEE AP-S Inter. Symp. 2000, pp. 1688-
, 2000.
S.R. Best, “On the reson
small Koch fractal monopole antenna,”
Microw. Opt. Technol. Lett., vol. 35, pp. 311-
, 2002.
S.R. Best, “On the multiband behavior of the
Koch fractal m
Opt. Technol. Lett., vol. 35, pp. 371-374,
S.R. Best, “On the performance of the Koch
fractal and
electrically small antennas,” IEEE AP-S
Inter. Symp. 2002, vol. 4, pp. 534-537, 2002.
D.H. Werner, P.L. Werner and K.H. Church,
“Genet
antennas,” Electron. Lett., vol. 37, pp. 1150-
, 2001.
D.H. Werner, P.L. Werner K.H. Church, J.W.
Culver, and S.D. Eason, “Genetically
engineered dual-band fractal antennas,” IEEE
AP-S Inter. Symp. 2001, Vol. 3, pp. 628-631,
K.J. Vinoy,
V.V. Varadan, “Resonant frequency of
Hilbert curve fractal antennas,” in: IEEE AP-
S Inter. Symp., vol. 3, pp. 648-651, 2001.
K.J. Vinoy, K.A. Jose, and V.K. Varadan,
“On
dimension and the performance of multi-
resonant dipole antennas using Koch curves,”
IEEE Trans. Antennas Propagat. Accepted
for publication (Oct 2003).
K.J. Vinoy, K.A. Jose, and V.K. Varadan,
“Multiband characteristics and fractal
dimension of dipole antennas with Koch
curve geometry,” IEEE AP-S Inter. Symp.,
K.J. Vinoy, “Fractal shaped
for wide- and multi-band wireless
applications,” Ph.D. Dissertation.
Pennsylvania State University, 2002.
ACES JOURNAL, VOL. 19, NO. 1a, MARCH 2004
H.O. Peitgen, H. Jurgens, and D. Saupe,
Chaos and Fractals: New Frontiers of
Science, New York: Springer-Verlag, 1992.


