Fractal antennas and fractal resonators

• US 7,256,751 B2
• Filed: 09/13/2002
• Issued: 08/14/2007
• Est. Priority Date: 08/09/1995
• Status: Expired due to Fees

• Current Assignee: Fractal Antenna Systems Inc.
• Original Assignee: Nathan Cohen
• Inventors: Cohen, Nathan
• Primary Examiner(s): Wimer; Michael C.
• Application Number:
  US10/243,444
• Publication Number:
  US 20030160723A1
• Time in Patent Office: 1,796 Days
• Field of Search: 343/846, 343/741, 343/795, 343/792.5
• US Class Current: 343/792.5
• 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 50Ω termination impedance without requiring impedance matching.

Claims

1. An apparatus comprising:

an antenna undefined by an opening angle and having a first element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of said first element, wherein said deterministic 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, wherein said antenna has a perimeter compression (PC) parameter defined by;

$\mathrm{PC}=\frac{\mathrm{full}<br><br>\text{-}<br><br>\mathrm{sized}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}{\mathrm{fractal}<br><br>\text{-}<br><br>\mathrm{reduced}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}$

where;

PC=A log [N(D+C)]

wherein 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; and

wherein iteration N=2, PC is approximately 1.9, termination impedance is substantially 50Ω

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

3. The antenna of claim 1 or 2, 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=, (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.

4. The antenna of claim 1 or 2, wherein said first element is fabricated in a mariner 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.

5. The antenna of claim 1 or 2, 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.

2. An apparatus comprising:

an antenna undefined by an opening angle and having a first element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of said first element, wherein said deterministic 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, wherein said antenna has a perimeter compression (PC) parameter defined by;

$\mathrm{PC}=\frac{\mathrm{full}<br><br>\text{-}<br><br>\mathrm{sized}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}{\mathrm{fractal}<br><br>\text{-}<br><br>\mathrm{reduced}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}$

where;

PC=A log [N(D+C)]

wherein 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), wherein L and r are one-dimensional antenna element lengths before and after fractalization, respectively; and

wherein iteration N=3, PC is approximately 2.4, termination impedance is substantially 50Ω

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

6. 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, wherein said deterministic 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; and

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

7. An apparatus comprising:

an antenna undefined by an opening angle and having an element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of the element; and

wherein said antenna has a perimeter compression (PC) parameter defined by;

$\mathrm{PC}=\frac{\mathrm{full}<br><br>\text{-}<br><br>\mathrm{sized}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}{\mathrm{fractal}<br><br>\text{-}<br><br>\mathrm{reduced}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}$

where;

PC=A log [N(D+C)]

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

wherein iteration N=2, PC is approximately 1.9, termination impedance is substantially 50Ω

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

8. An apparatus comprising:

an antenna undefined by an opening angle and having an element whose physical shape is defined substantially as a deterministic fractal of iteration N≧

2 for at least a portion of the element; and

wherein said antenna has a perimeter compression (PC) parameter defined by;

$\mathrm{PC}=\frac{\mathrm{full}<br><br>\text{-}<br><br>\mathrm{sized}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}{\mathrm{fractal}<br><br>\text{-}<br><br>\mathrm{reduced}<br><br><br><br>\mathrm{antenna}<br><br><br><br>\mathrm{element}<br><br><br><br>\mathrm{length}}$

where;

PC=A log [N(D+C)]

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

wherein iteration N=3, PC is approximately 2.4, termination impedance is substantially 50Ω

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