A NOVEL APPROACH FOR DESIGNING FRACTAL ANTENNAS
David C. Ni
Direxion Technology, 9F, 177-1 Ho-Ping East Road Section 1, Taipei, Taiwan, R.O.C.
Chou Hsin Chin
Department of Electro-Physics, National Chiao Tung University, Hsin Chu, Taiwan, R.O.C.
Keywords: Antenna, Fractal, Herman Ring.
Abstract: Designing fractal antennas for broadband communications, various modifications and optimisations to the
fractal patterns, such as Koch or Sierpinski, are adopted for better frequency responses. In this article, we
explore a new approach by defining a set of complex functions, z
q
ΠC
i
, where C
i
=exp(i*g
i
(z))[(z-v
i
)/(1-v
i
z)],
and then using the shapes of the solution domains of the functions directly as patterns of fractal antennas.
1 INTRODUCTION
Design of fractal antennas is currently targeted for
highly desirable characteristics such as compact size,
low profile, conformal, multi-band and broadband,
as described in (Cohen,1995), (
Gianvittorio, 2002), and
(Werner). Most of the designers adopt operations
such as translation, rotation, iterations, etc. on the
fractal generator motifs, such as Koch, Minkoski,
Cantor, Torn Square, Mandelbrot, Caley Tree,
Monkey’s Swing, Sierpinski Gasket, Julia etc. for
the creation of the self-similar shapes. To further
improve the frequency responses, they applied
modifications on the created shapes, such as in
(Puente, 2000). Recently, new approaches, such as
Generic Algorithm, are studied for handling antenna
optimisation on multi-dimensional parameters
(
Altshuler, 2002). However, these approaches do not
provide the initial conditions, namely, the original
shapes for optimisation.
In this article, we explore a novel approach based on
the methodologies used in the area of dynamic
systems in conjunction with fractal geometry as
described in (Mandelbrot, 1977), (Milnor, 2000),
and
(Falconer, 1990). We define a set of complex
functions, z
q
ΠC
i
, based on relationship of moving
and observing entities. By solving the functions for a
given domain on the complex plane, we obtain a
solution domain based on the criteria of function
convergence (Ni, 2006). Then we extract the internal
and external contours of the shapes of the solution
domains and directly use them as topologies of
antenna or antenna arrays.
Of our particular interest, we adopt fractal shapes
known as Herman Rings for the fractal antennas.
Herman Rings are characterized by fractal internal
and external contours. We observe the broadband
characteristics from these antennas.
2 FUNCTIONS
We define the function set, f = z
q
ΠC
i,
which may
have the following forms:
where z is a complex variable, q is an integer, and C
i
has following form:
here v
i
is the complex conjugate of v
i
. We propose
this form based on the following form known in the
theory of special relativity by A. Einstein:
The z
q
term in Equation (1) has implication of time
and is used to ensure that the function may converge.
The term
f = z
q
C
1
C
2
f = z
q
C
1
C
2
C
3
and so on (1)
C
i
=ex
i*
i
z
z-v
i
/
1-v
i
z
2
1/(1 – v
2
/c
2
)
1/2
(3)
exp(i*g
i
(z)) (4)
157
C. Ni D. and Hsin Chin C. (2007).
A NOVEL APPROACH FOR DESIGNING FRACTAL ANTENNAS.
In Proceedings of the Second International Conference on Wireless Information Networks and Systems, pages 157-160
DOI: 10.5220/0002148701570160
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c
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