Fractal antennas and fractal resonators

• US 6,452,553 B1
• Filed: 08/09/1995
• Issued: 09/17/2002
• Est. Priority Date: 08/09/1995
• Status: Expired due to Term

• Current Assignee: Fractal Antenna Systems Inc.
• Original Assignee: Fractal Antenna Systems Inc.
• Inventors: Cohen, Nathan
• Primary Examiner(s): WIMER, MICHAEL C
• Application Number:
  US08/512,954
• Time in Patent Office: 2,596 Days
• Field of Search: 343/741, 343/742, 343/702, 343/803, 343/804, 343/806, 343/792.5
• US Class Current: 343/702
• 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 antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point;

and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, 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, and wherein each of said first and second motifs 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.

2. An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point;

and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and wherein said antenna has a perimeter compression parameter (PC) defined by;

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

where;

 

PC=A−

log {N(D+C)}

in which A and C are constant coefficients for said first 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 lengths of said first element before and after fractalization, respectively.

3. An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point;

and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and 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).

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

a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exits at least one non-straight line locus connecting each said point; and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif;

wherein said first 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.

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

a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and

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}}$$\mathrm{PC}=A·<br><br>\log <br><br>\text{\hspace{1em}<br><br>}<br><br>\left\{N<br><br>\left(D+C\right)\right\}$

in which A and C are constant coefficients for 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 lengths of said element before and after fractalization, respectively.

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

a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and

wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and

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

(3 cm), and wherein said antenna is disposed within a housing of said handheld telephone.