Create equiangular spiral antenna


The spiralEquiangular object is a planar equiangular spiral antenna on the X-Y 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 X-Y 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

Lumped elements added to the antenna feed, specified as a lumped element object handle. For more information, see lumpedElement.

Example: 'Load',lumpedelement. lumpedelement is the object handle 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 degree about two axes, defined by vectors.

Data Types: double

Tilt axis of the antenna, specified as:

  • Three-element vectors of Cartesian coordinates in meters. In this case, each 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: ant.TiltAxis = 'Z'

Object Functions

showDisplay antenna or array structure; Display shape as filled patch
infoDisplay information about antenna or array
axialRatioAxial ratio of antenna
beamwidthBeamwidth of antenna
chargeCharge distribution on metal or dielectric antenna or array surface
currentCurrent distribution on metal or dielectric antenna or array surface
designDesign prototype antenna or arrays for resonance at specified frequency
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 or dielectric antenna or array structure
meshconfigChange mesh mode of antenna structure
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
returnLossReturn loss of antenna; scan return loss of array
sparametersS-parameter object
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,    ...

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

Introduced in R2015a