Fractal Antennas - Pt 1

7/25/2019 Fractal Antennas - Pt 1

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N

B

FR CT L NTENN

P RT

Introduction and the ractal Quad


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of the antenna. a

tures. It has been

has dominated a

the electromagn

In 1985.Land

monogra*'h on a

point about Max

tioned the assum

and antenna reso

reversed the pro

give dipoles and

results look far f

domly bent wire

far better results

simple geometr

duce the best an

be, a defined ad

sic geometric de

antennas. This p

use a branch of

ly unexploited i


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segment seems simple enough; but after doing

this, we can continue with another iteration and

put a triangle on each one of those line seg-

ments. For the third iteration we put triangles

on top of each of those line segments, and so

on, ad infinitum. The result is a structure that

on every scale has triangles, and looks the same

at all magnifications.

One can construct a star-like structure by

attaching several iterated Koch fractal ends into

a closed unit, which for obvious reasons mathe-

maticians call "islands."

Figure

6 is a Koch

island star, the result of this amusing labor.

Now let's consider a strange trick of fractals.

Looking at the star reveals that the perimeter is

unrelated to the re of the island. In fact, as

the number of iterations becomes large, the

perimeter of the star has triangles on triangles

down to an infinitesimal scale, and the perime-

ter goes on to infinity Contrast this to a circle,

square, or other closed Euclidean shape: the

re andperimeter are intimately related, and

Figure

5

A von Koch fractal for iterat


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as a Euclidean

this simulation

product: a seri

recording stud

In the 1960s

clear use of sel

I've been unab

his work, but m

recalls a huge 2

of the spreader

supported anot

quad elements

motivation in c

another, simply

of distributing

Any way it's an

was fractally fi

D.L. Jaggard

apply the conc

objective, like

tioned above, w


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antennas use double ridges to decrease the

resonant fr eq ue n~ y. ~variety of shrunken

quads (the Maltese quad, for example), delta

loops, and other useful antennas all incorporate

some type of loading using rectangles, boxes,

and triangles to shorten the element dimen-

sions. Pfeiffer brought this to a logical limit

recently with a fan-shaped quad design of unre-

ported gain and

impedance.8 Yet all of these

designs use a fractal motif of thef irs t iteration;

they basically load Euclidean structures with

another Euclidean structure in a repetitive fash-

ion, using the same size in the repetition. They

do not exploit the multiple scale self-similarity

of real fractals. They could just be an exotic

loading scheme and, therefore, of no particular

importance when compared to other (lossy)

methods of shrinking antennas, such as loading

with

L

circuits, capacitive hats, dielectrics,

Table

1

Some resonant fr


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are better resonators than others through

Commandment 4:

Optimized fractal antennas approach their

asymptotic PCs in fewer iterations than nonop-

timized ones.

In other words, the best fractals for anten-

nas have large values of A and C. They shrink

the most and the fastest.

Finally, the odd property of non-small radia-

tion resistance invites yet another command-

ment, Commandment 5:

The radiation resistance of a fractal antenna

drops as some small power of the perimeter

compression, PC. A fractal island always has a

substantially higher radiation resistance than a

small Euclidean loop of equal size.


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Freq

42 3 HHz

J . .


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general corroborati

of the Minkowski f

before ELNEC mo

I ran ELNEC in

One source was att

was divided into at

pulse densities cou

ond iteration Mink

memory and softw

to keep the pulse d

various iterations.

Minkowski Island

ment, each segmen

cent of a waveleng

es was thus very hi

I show the antenna

derive the lowest r

terns, up to and inc

designs were const


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Table 4.2-meter antenna measurements.


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Table 5. MI2

MI3

efficiencies.

MI2

d B

QUAD

attenuation, wh

ance) for the re

at resonance for

attempt to meas

ticular antennas

of a noise bridg

With this pro

duced quite not

several dB diffe

ones. Removal

excess of a 20 d

this way, I was

tortions in my r

in a meaningful

For each ante

ward gain and o

made no attemp

nor to measure

demonstrate the

The results of th

rized in Table 4


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on a side will be discussed in Part 2.

At this point, it's important to know the effi-

ciencies of MI2 and MI3, because these com-

pact designs offer real advantages over a full-

sized quad element. As I stated, it wasn't possi-

ble to attempt this for the 2-meter versions, but

I built and tested 6-meter versions of MI2 and

MI3 (see Figure 13). I attached an RX-noise

bridge between these antennas and a JST 245

transceiver. By nulling the receiver at about 54

MHz, and calibrating the 50-ohm resistance

bridge with

5

and 10-ohm resistors, I obtained

the results of Table 5.

Efficiency was defined as:

where Z is the measured impedance. R was

obtained by subtracting the ohmic and reactive

3

PC

I

/


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15/16


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Part

2

will continue this intriguing saga of tiny,

multiband fractal antennas and arrays.

cknowledgments

Paradigm shifts12 are challenging and some-

times pleasurable. This one had its share of

both. My thinking and resolve were sharpened

by comments from individuals in many differ-

ent fields. I would like to thank them all, in a

random fractal order: Alexander Filippov,

Frank Drake, Benoit Mandlebrot, Bruce Tis,

Carl Helmers, Andrew Pfeiffer, Paul Pagel,

Paul Horowitz, Bernard Steinberg, Seth

Shostak, Darren Leigh, William Vetterling,

Maury Peiperl, Robert Hohlfeld, D.L. Jaggard,

Eugene Hastings, Enders Robinson. For obvi-

ous reasons, I acknowledge the management of

Charles River Park

commentary on frac

REFERENCES

1.

F.

Landstorfer and R. Sacher,

York, 1985.

2. N. Cohen,

G r u ~ i t y s L e n s ,

. W

3. B. Mandlebrot, Fractal Geom

1984.

4. M. Schroeder, F~ ac tnl s , hao

1992.

5. M. Berry, Diffractals, Journ

6. Y. Kim and D. Jaggard, The

IEEE,

74. 1278-1280, 1986.

7. J. Kraus, Antennas, McGraw-H

8. A. Pfeiffer,

The

Pfeiffer Qua

28-32.

9 . E. D a v ~ d ,

F

Anrenna Collec

10. J. Krau$,Antennas, 1st editio

11 H. Lauwener, Frar.talr, Prin

12. T. Kuhn, Str.uctur.e ofSc ienti

York, 1986.

Fractal Antennas - Pt 1

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