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Are Prefractal Monopoles
Optimum Miniature Antennas?
J.M. González-Arbesú*, J. Romeu and J.M. Rius (UPC)
M. Fernández-Pantoja, A. Rubio-Bretones and R. Gómez-Martín (UG)Columbus, Ohio (USA)
June 21-28, 2003
2003 IEEE AP-S/URSI
2003 IEEE AP-S/URSI 2/21
Introduction: Small Antennas (i)
Maximum dimension less than the radianlegth (Wheeler): ka <1
Radiation pattern: doughnut-like.
Directive gain: 1.5
Radiation resistance:
Limitation in bandwidth.
a
( )2 80 kaR dipolesmallrad =
( )42 20 kaR loopsmallrad π=
Image from:http://www.elliskaiser.com/doughnuts/tips.html
2003 IEEE AP-S/URSI 3/21
Introduction: Q (ii)
Modelling the antenna as a resonant circuit Q could be used as a figure of merit:
mer
e WWPWQ >= 2ω
emr
m WWPWQ >= 2ω
( )311kaka
Q +=
a: radius of the smallest sphere enclosing the antenna;k: wave number at the operating frequency.
Fundamental limitation for linearly polarized antennas (propagation of only TM01 or TE01 spherical modes):
0 .1 0.3 0 .5 0.7 0 .9 1.1 1 .3 1.510
0
101
102
103
ka
Qu
alit
y fa
ctor
, Q
2003 IEEE AP-S/URSI 4/21
Introduction: Q (iii)
Fractional bandwith measured from the normalized spread between the half-power frequencies:
Q < 2 : imprecise but useful (potentially broad band)Q >> 1 : good aprox. for Bandwidth-1
narrow bandwidthlarge frequency sensitivityhigh reactive energy stored in the near zone of the antennalarge currentshigh ohmic losses
lowerupper
center
fff
BandwidthQ
−==
1
2003 IEEE AP-S/URSI 5/21
Introduction: Objective (iv)
Challenge: efficient radiation on large bandwidths with small antennas.Effective radiation associated with a proper use (TM01or TE01) of the volume that encloses the antenna and a dipole is one-dimensional.Some prefractals have the ability to fill the space thanks to their D > DT.
Space-filling prefractals seem interesting structures to build size-reduced or small antennas, but...
... are they effective enough?
2003 IEEE AP-S/URSI 6/21
Introduction: Objective (v)
Alternatives investigated:Prefractal curves as antennas: performances in terms of Qand η of several monopole configurations studied.
Planar prefractals3D prefractals
Prefractal curves as top-loading of antennas.GA design of fractals to achieve better performances.
Q and η computed using the RLC model of the antenna at resonance
+=
ωωω inin
r
XddX
RQ
2 Ω+=
RRR
r
rηXin
RΩ
Rr
2003 IEEE AP-S/URSI 7/21
Planar Prefractals (i)
Fractals are the attractors of infinite iterative algorithms: IFS (or NIFS).
We are limited to the use of prefractals.
[ ]1−= nn AWA[ ] [ ] [ ] [ ]AwAwAwAW N∪∪∪= ...21
[ ]:Awi affine transformation scale - rotation - translation
[ ] ∞− =∞→
=∞→
AAWn
An nn 1
limlim fractalIFS attractorindep. of A0
prefractal
2003 IEEE AP-S/URSI 8/21
Planar Prefractals (ii)
Several electrically small planar self-resonant wireprefractal monopoles simulated and measured:
1 < D ≤ 2Comparison of performance with some Euclidean monopoles.
K-1 K-4 SA-1 SA-5P-1 P-2
H-2 H-4
λ/4 MLM-1
MLM-4 MLM-8
2003 IEEE AP-S/URSI 9/21
Planar Prefractals (iii)
Though increasing complexity, quite similar behavior.
Far away from the fundamental limit.
Intuitively generated monopoles perform better.
measured results
2003 IEEE AP-S/URSI 10/21
Planar Prefractals (iv)
Increasing ohmic losses with intricacy and iteration.
Worst results than simulated due to the substrate.
measured results
2003 IEEE AP-S/URSI 11/21
3D Prefractals (i)
2D prefractals are far from the fundamental limit.2D antennas do not use effectively the space inside the randiansphere (k0a<1).Do 3D antennas perform better because of their greater use of space?
3D-Hilbert monopoles are a continuous mapping of a segment into a cube.A monopole based on a 3D-Hilbert curve was simulated.
2003 IEEE AP-S/URSI 12/21
3D Prefractals (ii)
In the first segments the current distribution tends to be more uniform.First segments do radiate and the rest act as a load.Non-radiating wire length with high currents: increase in ohmic losses.
2003 IEEE AP-S/URSI 13/21
3D Prefractals (iii)
High reductions in size but unpractical values of η and Q.
@ copper wire h=89.8 mm φ: 0.4 mm
1st iterationh=15 mms=27 mm
2nd iterationh=5 mms=17 mm
3rd iterationh=10 mms=23 mm
2003 IEEE AP-S/URSI 14/21
Prefractal Loading (i)
While characterizing prefractal monopoles, we observed
high Q values high stored energya strong dependence of η and Q with the length of the first segment of the prefractal
Analysis of prefractals (Hilbert) as top loads for shorting monopoles.Comparison with a banner monopole.Comparison with a conventional top loaded monopole (circular plate).
2003 IEEE AP-S/URSI 15/21
Prefractal Loading (ii)
Modelled antennas...Circular plate
Monopole
Ground Plane
Top Loaded Monopole
@ copper wire h=89.8 mm φ: 0.4 mm ∆/a>2.5 ∆/λ < 0.01
2003 IEEE AP-S/URSI 16/21
Prefractal Loading (iii)
High η and low Q when small loads used.Electrically smaller self-resonant monopoles when increasing the relative size of the prefractal.
0 .2 0.4 0 .6 0.8 1 1.2 1 .4 1.60
50
100
150
200
Elec tric al s iz e a t re s onance , k0a
Qu
alit
y fa
ctor
, Q
Hilbert-1Hilbert-2Hilbert-3TLMBanne rλ/4
0 .2 0.4 0 .6 0.8 1 1.2 1 .4 1.650
60
70
80
90
100
Ele c tric al s iz e a t re s onance , k0aR
adia
tion
effic
ienc
y, η
(%)
Hilbert-1Hilbert-2Hilbert-3TLMBanne rλ/4
0.6 0.8 1 1.2 1.496
98
100Increas ing Size of th
e Load
Increasing size of the Load
Q increases with the iteration of the prefractal for almost the same η, but the improvement is not significant.Pre-fractals admit greater size-reductions than conventional TLM, though unpractical Q and η.
2003 IEEE AP-S/URSI 17/21
GA Design (i)
GA multiobjective optimization: design of wire Koch-like antennas optimized in terms of Q, η and electrical size.
@ h=6.22 cm w=1.73 cm
Meander typeZigzag type Koch-like initiator
2003 IEEE AP-S/URSI 18/21
GA Design (ii)
Optimization on Q-η-ka: from the Pareto front 3 designs with the same wire length (L~10.22 cm) have been selected and analyzed.
Meander type
Zigzag typeKoch-like
Antenna Resonant
Frequency (MHz)
Quality Factor
Efficiency (%)
Koch 864.5 13.57 96.8 Meander 826.5 12.67 97.19 Zigzag 824 13.99 96.79
Antenna Resonant
Frequency (MHz)
Quality Factor
Efficiency (%)
Koch 905 12.67 87.64 Meander 850 12.60 88.78 Zigzag 870 13.89 87.34
measured
computed
2003 IEEE AP-S/URSI 19/21
GA Design (iii)
GA multiobjective optimization: design of Euclidean planar structures with better performances than prefractals for the same electrical size.
0.0622 m750883959405
757755080088838833959955949944050055
1-bit example individual
Coding of Search SpaceZigzag monopole
Meander monopole
2003 IEEE AP-S/URSI 20/21
GA Design (iv)
Optimization on Q-η-ka : 12-wires meander and zigzag antennas.
H-1
H-4
H-4
H-1
Pareto fronts
2003 IEEE AP-S/URSI 21/21
Conclusion (i)
Small planar prefractal monopoles do not perform better than conventional Euclidean structures.Better η and Q factors when the (Hilbert) prefractal is used as a top-load than as an antenna but higher ka ratios.3D prefractal designs use more space but are unpractical designs as radiating elements.Even in the case of GA optimized prefractals Euclidean antennas achieve better performance than prefractals with less geometrical complexity.