Fractal antennas and fractal resonators

• US 20030160723A1
• Filed: 09/13/2002
• Published: 08/28/2003
• Est. Priority Date: 08/09/1995
• Status: Active Grant

• Current Assignee: Fractal Antenna Systems Inc.
• Original Assignee: Nathan Cohen
• Inventors: Cohen, Nathan
• Granted Patent: US 7,256,751 B2
• Time in Patent Office: Days
• US Class Current: 343/700MS
• CPC Class Codes: H01Q 1/246 specially adapted for base stations
• CPC Class Codes: H01Q 1/36 Structural form of radiating elements, e.g. cone, spiral, umbrella; Particular materials used therewithH01Q1/08, H01Q1/14 take precedence
• CPC Class Codes: H01Q 1/38 formed by a conductive layer on an insulating support patch antennas H01Q9/0407; microstrip dipole antennas H01Q9/065; microstrip slot antennas H01Q13/106; transmission line microstrip antennas H01Q13/206; manufacturing reflecting surfaces using insulating material for supporting the reflecting surface H01Q15/142
• CPC Class Codes: H01Q 21/205 providing an omnidirectional coverage turnstile aerials H01Q21/26
• CPC Class Codes: H01Q 21/28 Combinations of substantially independent non-interacting antenna units or systems multiple beam H01Q25/00

Abstract

An antenna includes at least one element whose physical shape is at least partially defined as a second or higher iteration deterministic fractal. The resultant fractal antenna does not rely upon an opening angle for performance, and may be fabricated as a dipole, a vertical, or a quad, among other configurations. The number of resonant frequencies for the fractal antenna increases with iteration number N and more such frequencies are present than in a prior art Euclidean antenna. Further, the resonant frequencies can include non-harmonically related frequencies. At the high frequencies associated with wireless and cellular telephone communications, a second or third iteration, preferably Minkowski fractal antenna is implemented on a printed circuit board that is small enough to fit within the telephone housing. A fractal antenna according to the present invention is substantially smaller than its Euclidean counterpart, yet exhibits at least similar gain, efficiency, SWR, and provides a 50 Ω termination impedance without requiring impedance matching.

Claims

1. An antenna undefined by an opening angle and having at least one element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of said element.

2. The antenna of claim 1, further including a second element whose physical shape is defined substantially as a fractal of iteration N′

≧

2, where (N−

N′

)>

≧

0.

3. The antenna of claim 1, wherein said fractal is defined as a superposition over at least N=2 iterations of a fractal generator motif, an iteration being placement of said fractal generator motif upon a base figure through at least one positioning selected from the group consisting of (i) rotation, (ii) stretching, and (iii) translation.

4. The antenna of claim 1, wherein said fractal generator motif has x-axis, y-axis coordinates for a next iteration N+1 defined by x_N+1=f(x_N, y_N) and y_N+1=g(x_N, y_N), where x_N, y_N are coordinates for iteration N, and where f(x,y) and g(x,y) are functions defining said fractal generator motif and behavior.

5. The antenna of claim 3, wherein said fractal generator motif is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey'"'"'s swing, (viii) Sierpinski gasket, and (ix) Julia.

6. The antenna of claim 1, wherein said antenna has a perimeter compression parameter (PC) defined by:

7. The antenna of claim 1, in which said element is fabricated in a manner selected from the group consisting of (i) shaping conductive wire into said fractal, (ii) forming upon an insulator substrate a conductive layer defining traces shaped to form said fractal, (iii) forming upon a flexible insulator substrate conductive traces shaped to form said fractal;

and (iv) forming upon a semiconductor substrate a layer of conductive material shaped to form said fractal.

8. The antenna of claim 6, wherein iteration N=2, PC is approximately 1.9, termination impedance is substantially 50 Ω

, and gain is substantially at least within 1 dB of unity.

9. The antenna of claim 6, wherein iteration N=3, PC is approximately 2.4, termination impedance is substantially 50 Ω

, and gain is substantially at least within 1 dB of unity.

10. The antenna of claim 1, wherein said antenna is selected from the group consisting of (i) a fractal quad, (ii) an at least third iteration fractal quad, (iii) a Minkowski fractal quad, (iv) a dipole, and (vi) a vertical.

11. The antenna of claim 1, wherein said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz, and having a side length KS approximately 1.2″

(3 cm).

12. A fractal antenna coupleable to a transceiver unit, the antenna comprising:

at least one element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of said element, said antenna being undefined by an opening angle.

13. The antenna of claim 12, wherein said fractal is defined as a superposition over at least N=2 iterations of a fractal generator motif, an iteration being placement of said fractal generator motif upon a base figure through at least one positioning selected from the group consisting of (i) rotation, (ii) stretching, and (iii) translation.

14. The antenna of claim 12, wherein said fractal generator motif has x-axis, y-axis coordinates for a next iteration N+1 defined by x_N+1=f(x_N, y_N) and y_N+1=g(x_N, y_N), where x_N, y_N are coordinates for iteration N, and where f(x,y) and g(x,y) are functions defining said fractal generator motif and behavior.

15. The antenna of claim 13, wherein said fractal generator motif is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey'"'"'s swing, (viii) Sierpinski gasket, and (ix) Julia.

16. The antenna of claim 12, wherein said antenna has a perimeter compression parameter (PC) defined by:

where;

$\mathrm{PC}=\frac{\mathrm{full}<br><br>\text{-}<br><br>\mathrm{sized}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{antenna}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{element}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{length}}{\mathrm{fractal}<br><br>\text{-}<br><br>\mathrm{reduced}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{antenna}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{element}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{length}}$PC=A·

log[N(D+C)]

in which A and C are constant coefficients for a given said fractal generator motif, N is an iteration number, and D is a fractal dimension given by log(L)/log(r), where L and r are one-dimensional antenna element lengths before and after fractalization, respectively.

17. The antenna of claim 12, in which said transceiver unit is hand holdable in size, and wherein said antenna is mounted within a housing of said transceiver unit, and said antenna is fabricated in a manner selected from the group consisting of (i) shaping conductive wire into said fractal, (ii) forming upon an insulator substrate a conductive layer defining traces shaped to form said fractal, (iii) forming upon a flexible insulator substrate conductive traces shaped to form said fractal;

and (iv) forming upon a semiconductor substrate a layer of conductive material shaped to form said fractal.

18. The antenna of claim 12, wherein said transceiver includes a plurality of said antennas in at least one configuration selected from the group consisting of (i) an array of substantially identical said antennas coupled to an electronic circuit that dynamically selects a chosen one of said antennas to be coupled to said transceiver unit, (ii) an array of substantially identical said antennas coupled to an electronic circuit that dynamically selects a chosen one of said antennas to be coupled to said transceiver unit, at least two antennas in said array having orientation differing from other antennas in said plurality, (iii) a plurality of antennas in which at least two antennas have elements differing from elements in other of said antennas.

19. The antenna of claim 12, wherein said transceiver unit is a self-contained handheld telephone operating in a frequency range of about 850 MHz to 900 MHz, and wherein said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz, having a side length KS approximately 1.2″

(3 cm), and being disposed within a housing of said handheld telephone.

20. A fractal resonating system, comprising:

an inductor including an element portion whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of said element; and

capacitance coupled with said inductor to define at least one resonant frequency for said system, including frequencies non-harmonically related to each other.