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Create Sierpinski's Gasket fractal antenna on xy- plane


The fractalGasket object creates an equilateral triangle-shaped Sierpinski's Gasket fractal antenna. These fractals are used in building communications systems, wireless networks, universal tactic communications systems, mobile devices, telematics, and radio frequency identification (RFID) antennas.

A fractal antenna uses a self-similar design to maximize the length or increase the perimeter of a material that transmits or receives electromagnetic radiation within a given volume or area. The main advantage of fractal antennas is that they are compact, which is important requirement for small and complex circuits. Fractal antennas also have more input impedance or resistance due to increased length or perimeter.

All fractal antennas are printed structures that are etched on a dielectric substrate.



ant = fractalGasket creates an equilateral triangle-shaped Sierpinski’s gasket fractal antenna. The default planar fractal antenna is in the shape of a bowtie which is center-fed. The antenna resonates at a frequency of 1.3 GHz.


ant = fractalGasket(Name,Value) sets properties using one or more name-value pairs. For example, ant = fractalGasket('NumIterations',4) creates a Sierpinski's Gasket with four iterations.


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Number of iterations of the fractal antenna, specified as a scalar integer.

Example: 'NumIterations',2

Example: ant.NumIterations = 2

Data Types: double

Lengths for three sides of the triangle, specified as a scalar in meters or a two- or three-element vector in meters.

  • Scalar – The triangle is equilateral.

  • Two-element vector – The first value specifies the base of the triangle along the x-axis. The second value specifies the other two sides of the triangle. The triangle is isosceles.

  • Three-element vector – The first value specifies the base of the triangle along the x-axis. The remaining two values specify the other two sides of the triangle. The triangle is scalene.

Example: 'Side',[0.5000,1.000]

Example: ant.Side = [0.5000,1.000]

Data Types: double

Width at the neck of the fractal antenna where the feed is located, specified as a positive scalar integer in meters.

Example: 'NeckWidth',0.0050

Example: ant.NeckWidth = 0.0050

Data Types: double

Type of the metal used as a conductor, specified as a metal material object. You can choose any metal from the MetalCatalog or specify a metal of your choice. For more information, see metal. For more information on metal conductor meshing, see Meshing.

Example: m = metal('Copper'); 'Conductor',m

Example: m = metal('Copper'); ant.Conductor = m

Lumped elements added to the antenna feed, specified as a lumped element object. You can add a load anywhere on the surface of the antenna. By default, the load is at the origin. For more information, see lumpedElement.

Example: 'Load',lumpedelement. lumpedelement is the object for the load created using lumpedElement.

Example: ant.Load = lumpedElement('Impedance',75)

Tilt angle of the antenna in degrees, specified as a scalar or vector. For more information, see Rotate Antennas and Arrays.

Example: 90

Example: Tilt=[90 90],TiltAxis=[0 1 0;0 1 1] tilts the antenna at 90 degrees about the two axes defined by the vectors.

Data Types: double

Tilt axis of the antenna, specified as one of these values:

  • Three-element vector of Cartesian coordinates in meters. In this case, each coordinate in the vector starts at the origin and lies along the specified points on the x-, y-, and z-axes.

  • Two points in space, specified as a 2-by-3 matrix corresponding to two three-element vectors of Cartesian coordinates. In this case, the antenna rotates around the line joining the two points.

  • "x", "y", or "z" to describe a rotation about the x-, y-, or z-axis, respectively.

For more information, see Rotate Antennas and Arrays.

Example: [0 1 0]

Example: [0 0 0;0 1 0]

Example: "Z"

Data Types: double | string

Object Functions

axialRatioCalculate and/or plot axial ratio of antenna or array
bandwidthCalculate and/or plot absolute bandwidth of antenna
beamwidthBeamwidth of antenna
chargeCharge distribution on antenna or array surface
currentCurrent distribution on antenna or array surface
designDesign prototype antenna or arrays for resonance around specified frequency or create AI-based antenna from antenna catalog objects
efficiencyRadiation efficiency of antenna
EHfieldsElectric and magnetic fields of antennas or embedded electric and magnetic fields of antenna element in arrays
impedanceInput impedance of antenna or scan impedance of array
infoDisplay information about antenna, array, or platform
memoryEstimateEstimate memory required to solve antenna or array mesh
meshMesh properties of metal, dielectric antenna, or array structure
meshconfigChange meshing mode of antenna, array, custom antenna, custom array, or custom geometry
optimizeOptimize antenna or array using SADEA optimizer
patternPlot radiation pattern and phase of antenna or array or embedded pattern of antenna element in array
patternAzimuthAzimuth plane radiation pattern of antenna or array
patternElevationElevation plane radiation pattern of antenna or array
rcsCalculate and plot monostatic and bistatic radar cross section (RCS) of platform, antenna, or array
resonantFrequencyCalculate and/or plot resonant frequency of antenna
returnLossReturn loss of antenna or scan return loss of array
showDisplay antenna, array structures, shapes, or platform
sparametersCalculate S-parameters for antennas and antenna arrays
vswrVoltage standing wave ratio (VSWR) of antenna or array element


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Create and view a default fractal Sierpinski's Gasket.

ant = fractalGasket
ant = 
  fractalGasket with properties:

    NumIterations: 2
             Side: 0.2000
        NeckWidth: 0.0020
        Conductor: [1x1 metal]
             Tilt: 0
         TiltAxis: [1 0 0]
             Load: [1x1 lumpedElement]


Version History

Introduced in R2018b