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.

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