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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 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 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,    ...

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

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


[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