Fractal antennas and fractal resonators

Details Fractal antennas and fractal resonators Fractal antennas and fractal resonators

1995-08-09

2002-09-17

Wilmer, Michael C. (Department: 2821)

Communications: radio wave antennas

Antennas

With radio cabinet

C343S792500

Reexamination Certificate

active

06452553

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to antennas and resonators, and more specifically to the design of non-Euclidian antennas and non-Euclidian resonators.
BACKGROUND OF THE INVENTION
Antenna are used to radiate and/or receive typically electromagnetic signals, preferably with antenna gain, directivity, and efficiency. Practical antenna design traditionally involves trade-offs between various parameters, including antenna gain, size, efficiency, and bandwidth.
Antenna design has historically been dominated by Euclidean geometry. In such designs, the closed antenna area is directly proportional to the antenna perimeter. For example, if one doubles the length of an Euclidean square (or “quad”) antenna, the enclosed area of the antenna quadruples. Classical antenna design has dealt with planes, circles, triangles, squares, ellipses, rectangles, hemispheres, paraboloids, and the like, (as well as lines). Similarly, resonators, typically capacitors (“C”) coupled in series and/or parallel with inductors (“L”), traditionally are implemented with Euclidian inductors.
With respect to antennas, prior art design philosophy has been to pick a Euclidean geometric construction, e.g., a quad, and to explore its radiation characteristics, especially with emphasis on frequency resonance and power patterns. The unfortunate result is that antenna design has far too long concentrated on the ease of antenna construction, rather than on the underlying electromagnetics.
Many prior art antennas are based upon closed-loop or island shapes. Experience has long demonstrated that small sized antennas, including loops, do not work well, one reason being that radiation resistance (“R”) decreases sharply when the antenna size is shortened. A small sized loop, or even a short dipole, will exhibit a radiation pattern of 1/2&lgr; and 1/4&lgr;, respectively, if the radiation resistance R is not swamped by substantially larger ohmic (“O”) losses. Ohmic losses can be minimized using impedance matching networks, which can be expensive and difficult to use. But although even impedance matched small loop antennas can exhibit 50% to 85% efficiencies, their bandwidth is inherently narrow, with very high Q, e.g., Q>50. As used herein, Q is defined as (transmitted or received frequency)/(3 dB bandwidth).
As noted, it is well known experimentally that radiation resistance R drops rapidly with small area Euclidean antennas. However, the theoretical basis is not generally known, and any present understanding (or misunderstanding) appears to stem from research by J. Kraus, noted in Antennas (Ed. 1), McGraw Hill, New York (1950), in which a circular loop antenna with uniform current was examined. Kraus' loop exhibited a gain with a surprising limit of 1.8 dB over an isotropic radiator as loop area fells below that of a loop having a 1 &lgr;-squared aperture. For small loops of area A<&lgr;
2
/100, radiation resistance R was given by:
R
=
K
·
(
A
λ
2
)
2
where K is a constant, A is the enclosed area of the loop, and &lgr; is wavelength. Unfortunately, radiation resistance R can all too readily be less than 1 &OHgr; for a small loop antenna.
From his circular loop research Kraus generalized that calculations could be defined by antenna area rather than antenna perimeter, and that his analysis should be correct for small loops of any geometric shape. Kraus' early research and conclusions that small-sized antennas will exhibit a relatively large ohmic resistance O and a relatively small radiation resistance R, such that resultant low efficiency defeats the use of the small antenna have been widely accepted. In fact, some researchers have actually proposed reducing ohmic resistance O to 0 &OHgr; by constructing small antennas from superconducting material, to promote efficiency.
As noted, prior art antenna and resonator design has traditionally concentrated on geometry that is Euclidean. However, one non-Euclidian geometry is fractal geometry. Fractal geometry may be grouped into random fractals, which are also termed chaotic or Brownian fractals and include a random noise components, such as depicted in
FIG. 3
, or deterministic fractals such as shown in FIG.
1
C.
In deterministic fractal geometry, a self-similar structure results from the repetition of a design or motif (or “generator”), on a series of different size scales. One well known treatise in this field is
Fractals, Endlessly Repeated Geometrical Figures,
by Hans Lauwerier, Princeton University Press (1991), which treatise applicant refers to and incorporates herein by reference.
FIGS. 1A-2D
depict the development of some elementary forms of fractals. In
FIG. 1A
, a base element
10
is shown as a straight line, although a curve could instead be used. In
FIG. 1B
, a so-called Koch fractal motif or generator
20
-
1
, here a triangle, is inserted into base element
10
, to form a first order iteration (“N”) design, e.g., N=1. In
FIG. 1C
, a second order N=2 iteration design results from replicating the triangle motif
20
-
1
into each segment of
FIG. 1B
, but where the
20
-
1
′ version has been differently scaled, here reduced in size. As noted in the Lauwerier treatise, in its replication, the motif may be rotated, translated, scaled in dimension, or a combination of any of these characteristics. Thus, as used herein, second order of iteration or N=2 means the fundamental motif has been replicated, after rotation, translation, scaling (or a combination of each) into the first order iteration pattern. A higher order, e.g., N=3, iteration means a third fractal pattern has been generated by including yet another rotation, translation, and/or scaling of the first order motif.
In
FIG. 1D
, a portion of
FIG. 1C
has been subjected to a further iteration (N=3) in which scaled-down versions
20
-
1
″ of the triangle motif
20
-
1
have been inserted into each segment of the left half of FIG.
1
C.
FIGS. 2A-2C
follow what has been described with respect to
FIGS. 1A-1C
, except that a rectangular motif
20
-
2
has been adopted, which motif is denoted
20
-
2
′ in
FIG. 2C
, and
20
-
2
″ in FIG.
2
D.
FIG. 2D
shows a pattern in which a portion of the left-hand side is an N=3 iteration of the
20
-
2
rectangle motif, and in which the center portion of the figure now includes another motif, here a
20
-
1
type triangle motif, and in which the right-hand side of the figure remains an N=2 iteration.
Traditionally, non-Euclidean designs including random fractals have been understood to exhibit antiresonance characteristics with mechanical vibrations. It is known in the art to attempt to use non-Euclidean random designs at lower frequency regimes to absorb, or at least not reflect sound due to the antiresonance characteristics. For example, M. Schroeder in
Fractals, Chaos, Power Laws
(1992), W. H. Freeman, New York discloses the use of presumably random or chaotic fractals in designing sound blocking diffusers for recording studios and auditoriums.
Experimentation with non-Euclidean structures has also been undertaken with respect to electromagnetic waves, including radio antennas. In one experiment, Y. Kim and D. Jaggard in
The Fractal Random Array,
Proc. IEEE 74, 1278-1280 (1986) spread-out antenna elements in a sparse microwave array, to minimize sidelobe energy without having to use an excessive number of elements. But Kim and Jaggard did not apply a fractal condition to the antenna elements, and test results were not necessarily better than any other techniques, including a totally random spreading of antenna elements. More significantly, the resultant array was not smaller than a conventional Euclidean design.
Prior art spiral antennas, cone antennas, and V-shaped antennas may be considered as a continuous, deterministic first order fractal, whose motif continuously expands as distance increases from a central point. A log-periodic antenna may be considered a type of continuous fractal in that it is fabricated from a radially expan

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