Create helix or conical helix antenna on ground plane


Use the helix object to create a helix or conical helix antenna on a circular ground plane. The helix antenna is a common choice in satellite communication.

The width of the strip is related to the diameter of an equivalent cylinder by the equation



  • w is the width of the strip.

  • d is the diameter of an equivalent cylinder.

  • r is the radius of an equivalent cylinder.

For a given cylinder radius, use the cylinder2strip utility function to calculate the equivalent width. The default helix antenna is end-fed. The circular ground plane is on the X-Y plane. Commonly, helix antennas are used in axial mode. In this mode, the helix circumference is comparable to the operating wavelength and the helix has maximum directivity along its axis. In normal mode, the helix radius is small compared to the operating wavelength. In this mode, the helix radiates broadside, that is, in the plane perpendicular to its axis. The basic equation for the helix is



  • r is the radius of the helix.

  • θ is the winding angle.

  • S is the spacing between turns.

For a given pitch angle in degrees, use the helixpitch2spacing utility function to calculate the spacing between the turns in meters.


In an array of helix antennas, the circular ground plane of the helix is converted to rectangular ground plane.



ant = helix creates a helix antenna operating in axial mode. The default antenna operates around 2 GHz.


ant = helix(Name,Value) sets properties using one or more name-value pairs. For example, ant = helix('Radius',28e-03) creates a helix with turns of radius 28e-03 m.

Output Arguments

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Helix antenna, returned as a helix object.


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Radius of the turns, specified as a positive scalar integer in meters or a two element vector with each element unit in meters. In the two-element vector, the first element specifies the bottom radius and the second element specifies the top radius of the conical helix antenna.

Example: 'Radius',[28e-03 30e-03]

Example: ant.Radius = [28e-03 30e-03]

Data Types: double

Strip width, specified as a scalar in meters.


Strip width should be less than 'Radius'/5 and greater than 'Radius'/250. [4]

Example: 'Width',5

Example: ant.Width = 5

Data Types: double

Number of turns of the helix, specified as a scalar.

Example: 'Turns',2

Example: ant.Turns = 2

Data Types: double

Spacing between turns, specified as a scalar in meters.

Example: 'Spacing',1.5

Example: ant.Spacing = 1.5

Data Types: double

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

Example: 'WindingDirection',CW

Example: ant.WindingDirection = CW

Data Types: char | string

Ground plane radius, specified as a scalar in meters. By default, the ground plane is on the X-Y plane and is symmetrical about the origin.

Example: 'GroundPlaneRadius',2.05

Example: ant.GroundPlaneRadius = 2.05

Data Types: double

Feeding stub height from ground, specified as a scalar in meters. B

Example: 'FeedStubHeight',2.000e-03

Example: ant.FeedStubHeight = 2.000e-03


The default value is chosen to allow backward compatibility.

Data Types: double

Lumped elements added to the antenna feed, specified as a lumped element object handle. 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 handle for the load created using lumpedElement.

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

Data Types: double

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 a helix antenna that has a 28 mm turn radius, 1.2 mm strip width, and 4 turns.

hx = helix('Radius',28e-3,'Width',1.2e-3,'Turns',4)
hx = 
  helix with properties:

               Radius: 0.0280
                Width: 0.0012
                Turns: 4
              Spacing: 0.0350
     WindingDirection: 'CCW'
       FeedStubHeight: 1.0000e-03
    GroundPlaneRadius: 0.0750
                 Tilt: 0
             TiltAxis: [1 0 0]
                 Load: [1x1 lumpedElement]


Plot the radiation pattern of a helix antenna.

hx = helix('Radius',28e-3,'Width',1.2e-3,'Turns',4);

Calculate the spacing of a helix that has a pitch of 12 degrees and a radius that varies from 20 mm to 22 mm in steps of 0.5 mm.

s = helixpitch2spacing(12,20e-3:0.5e-3:22e-3)
s = 1×5

    0.0267    0.0274    0.0280    0.0287    0.0294

Plot the radiation pattern of a helix antenna with transparency specified as 0.5.

p = PatternPlotOptions
p = 
  PatternPlotOptions with properties:

      Transparency: 1
         SizeRatio: 0.9000
    MagnitudeScale: []
     AntennaOffset: [0 0 0]

p.Transparency = 0.5;
ant = helix;

To understand the effect of Transparency, chose Overlay Antenna in the radiation pattern plot.

This option overlays the helix antenna on the radiation pattern.


[1] Balanis, C.A. Antenna Theory. Analysis and Design, 3rd Ed. New York: Wiley, 2005.

[2] Volakis, John. Antenna Engineering Handbook, 4th Ed. New York: Mcgraw-Hill, 2007.

[3] Zhang, Yan, Q. Ding, J. Chen, S. Lu, Z. Zhu and L. L. Cheng. “A Parametric Study of Helix Antenna for S-Band Satellite Communications.” 9th International Symposium on Antenna Propagation and EM Theory (ISAPE). 2010, pp. 193–196.

[4] Djordjevic, A.R., Zajic, A.G., Ilic, M. M., Stuber, G.L. “Optimization of Helical antennas (Antenna Designer's Notebook)” IEEE Antennas and Propagation Magazine. December, 2006, pp. 107, pp.115.

Introduced in R2015a