# 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.```

example

``` `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

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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 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: `ant.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.

Note

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'.

Example: `'TiltAxis',[0 1 0]`

Example: `'TiltAxis',[0 0 0;0 1 0]`

Example: `ant.TiltAxis = 'Z'`

Note

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

Data Types: `double`

## 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 `efficiency` Radiation efficiency of antenna `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 `optimize` Optimize antenna or array using SADEA optimizer `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

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

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.