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Create equiangular spiral antenna


The spiralEquiangular object is a planar equiangular spiral antenna on the xy- plane. The equiangular spiral is always center fed and has two arms. The field characteristics of the antenna are frequency independent. A realizable spiral has finite limits on the feeding region and the outermost point of any arm of the spiral. This antenna exhibits a broadband behavior. The outer radius imposes the low frequency limit and the inner radius imposes the high frequency limit. The arm radius grows linearly as a function of the winding angle. As a result, outer arms of the spiral are shaped to minimize reflections.

The equation of the equiangular spiral is:


, where:

  • r0 is the starting radius

  • a is the growth rate

  • ϕ is the winding angle of the spiral



se = spiralEquiangular creates a planar equiangular spiral in the xy- plane. By default, the antenna operates over a broadband frequency 4–10 GHz.


se = spiralEquiangular(Name,Value) creates an equiangular spiral antenna, with additional properties specified by one, or more name-value pair arguments. Name is the property name and Value is the corresponding value. You can specify several name-value pair arguments in any order as Name1, Value1, ..., NameN, ValueN. Properties not specified retain their default values.


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Equiangular spiral growth rate, specified as a scalar.

Example: 'GrowthRate',1.2

Data Types: double

Inner radius of spiral, specified as a scalar in meters.

Example: 'InnerRadius',1e-3

Data Types: double

Outer radius of spiral, specified as a scalar in meters.

Example: 'OuterRadius',1e-3

Data Types: double

Direction of spiral turns (windings), specified as 'CW' or 'CCW'.

Example: 'WindingDirection','CW'

Data Types: char

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. For more information, see lumpedElement.

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

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

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

Example: Tilt=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.


The wireStack antenna object only accepts the dot method to change its properties.

Data Types: double

Tilt axis of the antenna, specified as:

  • 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, each specified as three-element vectors of Cartesian coordinates. In this case, the antenna rotates around the line joining the two points in space.

  • A string input describing simple rotations around one of the principal axes, 'X', 'Y', or 'Z'.

For more information, see Rotate Antennas and Arrays.

Example: TiltAxis=[0 1 0]

Example: TiltAxis=[0 0 0;0 1 0]

Example: TiltAxis = 'Z'

Data Types: double

Object Functions

showDisplay antenna, array structures or shapes
infoDisplay information about antenna or array
axialRatioAxial ratio 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
efficiencyRadiation efficiency of antenna
EHfieldsElectric and magnetic fields of antennas; Embedded electric and magnetic fields of antenna element in arrays
impedanceInput impedance of antenna; scan impedance of array
meshMesh properties of metal, dielectric antenna, or array structure
meshconfigChange mesh mode of antenna structure
optimizeOptimize antenna or array using SADEA optimizer
patternRadiation pattern and phase of antenna or array; Embedded pattern of antenna element in array
patternAzimuthAzimuth pattern of antenna or array
patternElevationElevation pattern of antenna or array
rcsCalculate and plot radar cross section (RCS) of platform, antenna, or array
returnLossReturn loss of antenna; scan return loss of array
sparametersCalculate S-parameter for antenna and antenna array objects
vswrVoltage standing wave ratio of antenna


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Create and view an equiangular spiral antenna with 0.35 growth rate, 0.65 mm inner radius and 40 mm outer radius.

se = spiralEquiangular('GrowthRate',0.35, 'InnerRadius',0.65e-3,    ...

Figure contains an axes object. The axes object with title spiralEquiangular antenna element, xlabel x (mm), ylabel y (mm) contains 3 objects of type patch, surface. These objects represent PEC, feed.

Plot the radiation pattern of equiangular spiral at a frequency of 4 GHz.

se = spiralEquiangular('GrowthRate',0.35, 'InnerRadius',0.65e-3, ...

Figure contains an axes object and other objects of type uicontrol. The axes object contains 3 objects of type patch, surface.


[1] Dyson, J. The equiangular spiral antenna.” IRE Transactions on Antennas and Propagation. Vol.7, Number 2, pp. 181, 187, April 1959.

[2] Nakano, H., K.Kikkawa, N.Kondo, Y.Iitsuka, J.Yamauchi. “Low-Profile Equiangular Spiral Antenna Backed by an EBG Reflector.” IRE Transactions on Antennas and Propagation. Vol. 57, No. 25, May 2009, pp. 1309–1318.

[3] McFadden, M., and Scott, W.R. “Analysis of the Equiangular Spiral Antenna on a Dielectric Substrate.” IEEE Transactions on Antennas and Propagation. Vol. 55, No. 11, Nov. 2007, pp. 3163–3171.

[4] Violakis, John Antenna Engineering Handbook, 4th Ed., McGraw-Hill.

Version History

Introduced in R2015a