spiralEquiangular

Create equiangular spiral antenna

Description

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:

$$r=r_0{e}^{a\varphi }$$

, where:

• r₀ is the starting radius

• a is the growth rate

• ϕ is the winding angle of the spiral

Creation

Syntax

se = spiralEquiangular

se = spiralEquiangular(Name,Value)

Description

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.

Properties

GrowthRate — Equiangular spiral growth rate

0.3500 (default) | scalar

Equiangular spiral growth rate, specified as a scalar.

Example: 'GrowthRate',1.2

Data Types: double

InnerRadius — Inner radius of spiral

0.0020 (default) | scalar

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

Example: 'InnerRadius',1e-3

Data Types: double

OuterRadius — Outer radius of spiral

0.0189 (default) | scalar

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

Example: 'OuterRadius',1e-3

Data Types: double

WindingDirection — Direction of spiral turns (windings)

'CW' | 'CCW'

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

Example: 'WindingDirection','CW'

Data Types: char

Load — Lumped elements

[1x1 lumpedElement] (default) | lumped element object handle

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 — Tilt angle of antenna

0 (default) | scalar | vector

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

TiltAxis — Tilt axis of antenna

[1 0 0] (default) | three-element vector of Cartesian coordinates | two three-element vectors of Cartesian coordinates | 'X' | 'Y' | 'Z'

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

show	Display antenna or array structure; Display shape as filled patch
info	Display information about antenna or array
axialRatio	Axial ratio of antenna
beamwidth	Beamwidth of antenna
charge	Charge distribution on metal or dielectric antenna or array surface
current	Current distribution on metal or dielectric antenna or array surface
design	Design prototype antenna or arrays for resonance at specified frequency
EHfields	Electric and magnetic fields of antennas; Embedded electric and magnetic fields of antenna element in arrays
impedance	Input impedance of antenna; scan impedance of array
mesh	Mesh properties of metal or dielectric antenna or array structure
meshconfig	Change mesh mode of antenna structure
pattern	Radiation pattern and phase of antenna or array; Embedded pattern of antenna element in array
patternAzimuth	Azimuth pattern of antenna or array
patternElevation	Elevation pattern of antenna or array
returnLoss	Return loss of antenna; scan return loss of array
sparameters	S-parameter object
vswr	Voltage standing wave ratio of antenna

Examples

Create and View Equiangular Spiral Antenna

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,    ...
                          'OuterRadius',40e-3);
show(se)

Radiation Pattern of Equiangular Spiral Antenna

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

se = spiralEquiangular('GrowthRate',0.35, 'InnerRadius',0.65e-3, ...
                          'OuterRadius',40e-3);
pattern(se,4e9);

References

[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.