# pattern

Radiation pattern and phase of antenna or array; Embedded pattern of antenna element in array

## Syntax

``pattern(object,frequency)``
``pattern(object,frequency,azimuth,elevation)``
``pattern(___,Name,Value)``
``````[pat,azimuth,elevation] = pattern(object,frequency,azimuth,elevation)``````
``````[pat,azimuth,elevation] = pattern(___,Name,Value)``````

## Description

example

````pattern(object,frequency)` plots the 3-D radiation pattern of the antenna or array object over a specified frequency. By default, in Antenna Toolbox™, the far-field radius is set to `100λ`.```
````pattern(object,frequency,azimuth,elevation)` plots the radiation pattern of the antenna or array object using the specified `azimuth` and `elevation` angles.```
````pattern(___,Name,Value)` uses additional options specified by one or more Name, Value pair arguments. You can use any of the input arguments from previous syntaxes.Use the `'ElementNumber'` and `'Termination'` property to calculate the embedded pattern of the antenna element in an array connected to a voltage source. The voltage source model consists of an ideal voltage source of 1 volt in series with a source impedance. The embedded pattern includes the effect of mutual coupling due to the other antenna elements in the array.```
``````[pat,azimuth,elevation] = pattern(object,frequency,azimuth,elevation)``` returns the pattern value, `pat`, value of an antenna or array object at specified frequency. `azimuth` and `elevation` are the angles at which the pattern function calculates the directivity.```
``````[pat,azimuth,elevation] = pattern(___,Name,Value)``` uses additional options specified by one or more `Name,Value` pair arguments.```

## Examples

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Calculate radiation pattern of default linear array for a frequency of 70 MHZ.

```l = linearArray; pattern(l,70e6)```

Plot the radiation pattern of a helix antenna in xz-plane.

```h = helix; pattern (h, 2e9, 0, 1:1:360);```

`[pat,azimuth,elevation] = pattern (h, 2e9, 0, 1:1:360);`

Compute the maximum and the minimum value of the radiation pattern and the elevation angle.

`pattern_max = max(max(pat))`
```pattern_max = 8.6852 ```
`pattern_min = min(min(pat))`
```pattern_min = -11.3782 ```
`elevation_max = max(elevation) `
```elevation_max = 360 ```
`elevation_min = min(elevation) `
```elevation_min = 1 ```

Calculate the embedded element pattern of a linear array. Excite the first antenna element in the array. Terminate all the other antenna elements using a 50-ohm resistance.

```l = linearArray; pattern(l, 70e6,'ElementNumber', 1,'Termination', 50);```

Calculate the directivity of a helix antenna.

```h = helix; D = pattern(h, 2e9, 0, 1:1:360);```

Showing the first five directivity values.

`Dnew = D(1:5)`
```Dnew = 5×1 -6.2750 -6.0599 -5.8322 -5.5935 -5.3455 ```

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; pattern(ant,2e9,'patternOptions',p)```

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

This option overlays the helix antenna on the radiation pattern.

Plot radiation pattern of dipole antenna in rectangular cartesian co-ordinate system.

`pattern(dipole, 70e6:10e6:100e6, 0, 90, 'CoordinateSystem', 'rectangular')`

Directivity values of dipole antenna

`D = pattern(dipole, 70e6:10e6:100e6, 0, 90, 'CoordinateSystem', 'rectangular')`
```D = 4×1 -49.6264 -50.3098 -49.1815 -47.0042 ```

## Input Arguments

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Antenna or array element, specified as an object.

Frequency to calculate or plot the antenna or array radiation pattern, specified as a scalar or a vector with each element in Hz. The vector frequencies support rectangular coordinate system.

Example: 70e6

Data Types: `double`

Azimuth angles and spacing between the angles to visualize the radiation pattern, specified as a vector in degrees. If the coordinate system is set to uv, then the U values are specified in this parameter. The values of U are between `-1` to `1`.

Example: 90

Data Types: `double`

Elevation angles and spacing between the angles to visualize the radiation pattern, specified as a vector in degrees. If the coordinate system is set to uv, then the V values are specified in this parameter. The values of V are between `-1` to `1`.

Example: 0:1:360

Data Types: `double`

### Name-Value Pair Arguments

Example: `'CoordinateSystem'`, `'uv'`

Specify optional comma-separated pairs of `Name,Value` pair arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`''`). You can specify several name and value pair arguments in any order as ```Name1, Value1, ..., NameN, ValueN```.

Coordinate system to visualize the radiation pattern, specified as the comma-separated pair consisting of `'CoordinateSystem'` and one of these values: `'polar'`, `'rectangular'`, `'uv'`.

Example: `'CoordinateSystem'`, `'polar'`

Data Types: `char`

Quantity to plot, specified as a comma-separated pair consisting of `'Type'` and one of these values:

• `directivity` – Directivity in dBi (lossless antenna or array)

• `gain` – Gain in dBi (lossy antenna or array)

• `efield` – Electric field in volt/meter

• `power` – Power in watts

• `powerdb` – Power in dB

• `phase` – Phase in degrees.

Note

`Type` can only be set to `phase` when `Polarization` is provided.

The default value is `'directivity'` for a lossless antenna and `'gain'` for a lossy antenna. You cannot plot the `'directivity'` of a lossy antenna.

Example: `'Type'`, `'efield'`

Data Types: `char`

Normalize field pattern, specified as the comma-separated pair consisting of `'Normalize'` and either `true` or `false`.

Example: `'Normalize'`, `false`

Data Types: `logical`

2-D pattern display style when frequency is a vector, specified as the comma-separated pair consisting of `'PlotStyle'` and one of these values:

• `'overlay'` – Overlay frequency data in a 2-D line plot

• `'waterfall'` – Plot frequency data in a waterfall plot

You can use this property when using `pattern` function with no output arguments.

Example: `'PlotStyle'`, `'waterfall'`

Data Types: `char`

Field polarization, specified as the comma-separated pair consisting of `'Polarization'` and one of these values:

• `'H'` – Horizontal polarization

• `'V'` – Vertical polarization

• `'RHCP'` – Right-hand circular polarization

• `'LHCP'` – Left-hand circular polarization

By default, you can visualize a combined polarization.

Example: `'Polarization'`, `'RHCP'`

Data Types: `char`

Antenna element in array, specified as the comma-separated pair consisting of `'ElementNumber'` and scalar. This antenna element is connected to the voltage source.

Note

Use this property to calculate the embedded pattern of an array.

Example: `'ElementNumber'`,1

Data Types: `double`

Impedance value for array element termination, specified as the comma-separated pair consisting of `'Termination'` and scalar. The impedance value terminates other antenna elements of an array while calculating the embedded pattern of the antenna connected to the voltage source.

Note

Use this property to calculate the embedded pattern of an array.

Example: `'Termination'`,40

Data Types: `double`

Parameter to change pattern plot properties, specified as the comma-separated pair consisting of `'patternOptions'` and a `PatternPlotOptions` output. The properties that you can vary are:

• `Transparency`

• `SizeRatio`

• `AntennaOffset`

• `AntennaVisibility`

• `MagnitudeScale`

Example: `p = PatternPlotOptions('Transparency',0.1);` Create a pattern plot option with a transparency of 0.1. ```ant = helix;````pattern(ant,2e9,'patternOptions',p)`; Use this pattern plot option to visualize the pattern of a helix antenna.

Data Types: `double`

## Output Arguments

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Radiation pattern of antenna or array or embedded pattern of array, returned as a matrix of number f elevation values by number of azimuth values. The pattern is one of the following:

• `directivity` – Directivity in dBi (lossless antenna or array)

• `gain` – Gain in dBi (lossy antenna or array)

• `efield` – Electric field in volt/meter

• `power` – Power in watts

• `powerdb` – Power in dB

Matrix size is number of elevation values multiplied by number of azimuth values.

Azimuth angles to calculate the radiation pattern, returned as a vector in degrees.

Elevation angles to calculate the radiation pattern, returned as a vector in degrees.

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### Directivity

Directivity is the ability of an antenna to radiate power in a particular direction. It can be defined as ratio of maximum radiation intensity in the desired direction to the average radiation intensity in all other directions. The equation for directivity is:

`$D=\frac{4\pi U\left(\theta ,\varphi \right)}{{P}_{rad}}$`

where:

• D is the directivity of the antenna

• U is the radiation intensity of the antenna

• Prad is the average radiated power of antenna in all other directions

Antenna directivity is dimensionless and is calculated in decibels compared to the isotropic radiator (dBi).

### Gain

The gain of an antenna depends on the directivity and efficiency of the antenna. It can be defined as the ratio of maximum radiation intensity in the desired direction to the total power input of the antenna. The equation for gain of an antenna is:

`$G=\frac{4\pi U\left(\theta ,\varphi \right)}{{P}_{in}}$`

where:

• G is the gain of the antenna

• U is the radiation intensity of the antenna

• Pin is the total power input to the antenna

If the efficiency of the antenna in the desired direction is `100%`, then the total power input to the antenna is equal to the total power radiated by the antenna, that is, ${P}_{in}={P}_{rad}$. In this case, the antenna directivity is equal to the antenna gain.

### Array Factor and Pattern Multiplication

The basis of the array theory is the pattern multiplication theorem. This theorem states that the combined pattern of N identical array elements is expressed as the element pattern times the array factor.

The array factor is calculated using the formula:

`$AF=\sum _{i=0}^{N}V\left(i\right)·{e}^{j\left(k\mathrm{sin}\theta \mathrm{cos}\phi ·x\left(i\right)+k\mathrm{sin}\theta \mathrm{sin}\phi ·y\left(i\right)+k\mathrm{cos}\theta ·z\left(i\right)\right)}$`

where:

• N is the number of elements in the array.

• V is the applied voltage (amplitude and phase) at each element in the array.

• k is the wave number.

• theta and phi are the elevation and azimuth angles.

• x, y, and z are the Cartesian coordinates of the feed locations for every antenna element of the array.

Once the array factor is calculated using the above equation, you can calculate the beam pattern of the array as the product of the array factor and the beam pattern of the individual antenna element of the array.

Array pattern = AF* individual antenna element pattern

## References

[1] Makarov, Sergey N. Antenna and Em Modeling in MATLAB. Chapter3, Sec 3.4 3.8. Wiley Inter-Science.

[2] Balanis, C.A. Antenna Theory, Analysis and Design, Chapter 2, sec 2.3-2.6, Wiley.