phased.SincAntennaElement

Sinc antenna element

Since R2021b

Description

The SincAntennaElement System object™ models an antenna with a Sinc Response. A sinc antenna is representative of a uniformly illuminated rectangular antenna. Sinc antenna patterns are often used as an approximation for sector or array antennas. The sidelobes are –13.6 dB relative to the main beam gain. The 0° azimuth and 0° elevation is considered to be the main response axis of the antenna. When placed in a linear or a rectangular array, the main response axis is aligned with the array normal.

To compute the response of the antenna element for specified directions:

Create the phased.SincAntennaElement object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

antenna = phased.SincAntennaElement

antenna = phased.SincAntennaElement(Name=Value)

Description

antenna = phased.SincAntennaElement creates a sinc antenna System object, antenna. This object models an antenna element whose response is a sinc antenna, which is representative of a uniformly illuminated rectangular antenna. The sidelobes are –13.6 dB relative to the main beam gain.

antenna = phased.SincAntennaElement(Name=Value) creates a sinc antenna object, antenna, with each specified property set to the specified value. You can specify multiple name-value arguments in any order. For example, FrequencyRange=[1e6 1e9] specifies that the antenna operates in a frequency range from 1 MHz to 1 GHz.

example

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`FrequencyRange` — Operating frequency range
`[0 1e20]` (default) | nonnegative, real-valued 1-by-2 row vector

Operating frequency range of the antenna, specified as a nonnegative, real-valued, 1-by-2 row vector in the form [LowerBound HigherBound]. The antenna element has no response outside the specified frequency range. Units are in Hz.

Data Types: double

`Beamwidth` — Beamwidth of antenna pattern
`[10 10]` (default) | scalar | 1-by-2 real-valued vector

Beamwidth of the antenna pattern, specified as either a scalar or a 1-by-2 real-valued vector. When the specified value is a 1-by-2 vector, it has the form of [AzimuthBeamwidth ElevationBeamwidth]. If the specified value is a scalar, the azimuth and elevation beamwidths are equal. Units are in degrees.

Example: 15

Data Types: double

Usage

Syntax

RESP = antenna(FREQ,ANG)

Description

RESP = antenna(FREQ,ANG) returns the antenna voltage response RESP at operating frequencies specified in FREQ and directions specified in ANG.

example

Input Arguments

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`FREQ` — Operating frequency of antenna element
nonnegative scalar | nonnegative, real-valued 1-by-L row vector

Operating frequency of the antenna element, specified as a nonnegative scalar or nonnegative, real-valued 1-by-L row vector. Frequency units are in Hz.

FREQ must lie within the range of values specified by the FrequencyRange or the FrequencyVector property of the element. Otherwise, the element produces no response and the response is returned as –Inf. Element objects use the FrequencyRange property, except for phased.CustomAntennaElement, which uses the FrequencyVector property.

Example: [1e8 2e6]

Data Types: double

`ANG` — Azimuth and elevation angles of response directions
real-valued 1-by-M row vector | real-valued 2-by-M matrix

Azimuth and elevation angles of the response directions, specified as a real-valued 1-by-M row vector or a real-valued 2-by-M matrix, where M is the number of angular directions. Angle units are in degrees. The azimuth angle must lie in the range –180° to 180°, inclusive. The elevation angle must lie in the range –90° to 90°, inclusive.

If ANG is a 1-by-M vector, each element specifies the azimuth angle of the direction. In this case, the corresponding elevation angle is assumed to be zero.
If ANG is a 2-by-M matrix, each column of the matrix specifies the direction in the form [azimuth;elevation].

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy-plane. This angle is positive when measured from the x-axis toward the y-axis. The elevation angle is the angle between the direction vector and xy-plane. This angle is positive when measured toward the z-axis. See the definition of Azimuth and Elevation Angles.

Example: [110 125; 15 10]

Data Types: double

Output Arguments

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`RESP` — Voltage response of antenna
M-by-L matrix

Voltage response of the antenna element, returned as a matrix of size M-by-L. In this matrix, M represents the number of angles specified in ANG and L represents the number of frequencies specified in FREQ.

Data Types: double

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Specific to Antenna and Transducer Element System Objects

`directivity`	Directivity of antenna or transducer element
`beamwidth`	Compute and display beamwidth of sensor element pattern
`pattern`	Plot antenna or transducer element directivity and patterns
`patternAzimuth`	Plot antenna or transducer element directivity and pattern versus azimuth
`patternElevation`	Plot antenna or transducer element directivity and pattern versus elevation
`isPolarizationCapable`	Antenna element polarization capability

Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Sinc Antenna Response

Open Live Script

Create a sinc antenna and plot its azimuth response. The antenna can work between 800 MHz and 1.2 GHz and has an operating frequency of 1 GHz.

element = phased.SincAntennaElement( ...
    FrequencyRange=[800e6 1.2e9]);
fc = 1e9;

pattern(element,fc,-180:180,0,CoordinateSystem="polar")

Figure contains an axes object. The hidden axes object contains 3 objects of type line, text. This object represents 1 GHz .

Find the response of the antenna at the boresight.

ang = [0 0]';
resp = element(fc,ang)

resp = 
1

More About

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Sinc Response

The phased.SincAntennaElement object returns the field response (also called field pattern) of the sinc antenna element.

If az is the azimuth angle in degrees and el is the elevation angle in degrees, the field response is

$f (a z, e l) = \frac{\sin (u_{a z})}{u_{a z}} \frac{\sin (u_{e l})}{u_{e l}},$

where:

The azimuth factor u_az depends on az and the azimuth half-power beamwidth HPBW_az:

$u_{a z} = \frac{x_{0} \sin (a z)}{\sin (\frac{1}{2} \times {HPBW}_{a z})} .$
Specify HPBW_az as the first element of Beamwidth.
The elevation factor u_el depends on el and the elevation half-power beamwidth HPBW_el:

$u_{e l} = \frac{x_{0} \sin (e l)}{\sin (\frac{1}{2} \times {HPBW}_{e l})} .$
Specify HPBW_el as the second element of Beamwidth.
The normalization factor x₀ ensures the power is ½ at the half-power beamwidth angle. The factor is a solution of

$\sin x = \frac{x}{\sqrt{2}} .$

References

[1] Blake, Lamont V. Machine Plotting of Radar Vertical-Plane Coverage Diagrams. Naval Research Laboratory Report 7098, 1970.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The pattern, patternAzimuth, and patternElevation object functions are not supported.
See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2021b

phased.SincAntennaElement

Description

Creation

Syntax

Description

Properties

`FrequencyRange` — Operating frequency range
`[0 1e20]` (default) | nonnegative, real-valued 1-by-2 row vector

`Beamwidth` — Beamwidth of antenna pattern
`[10 10]` (default) | scalar | 1-by-2 real-valued vector

Usage

Syntax

Description

Input Arguments

`FREQ` — Operating frequency of antenna element
nonnegative scalar | nonnegative, real-valued 1-by-L row vector

`ANG` — Azimuth and elevation angles of response directions
real-valued 1-by-M row vector | real-valued 2-by-M matrix

Output Arguments

`RESP` — Voltage response of antenna
M-by-L matrix

Object Functions

Specific to Antenna and Transducer Element System Objects

Common to All System Objects

Examples

Sinc Antenna Response

More About

Sinc Response

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

phased.SincAntennaElement

Description

Creation

Syntax

Description

Properties

FrequencyRange — Operating frequency range [0 1e20] (default) | nonnegative, real-valued 1-by-2 row vector

Beamwidth — Beamwidth of antenna pattern [10 10] (default) | scalar | 1-by-2 real-valued vector

Usage

Syntax

Description

Input Arguments

FREQ — Operating frequency of antenna element nonnegative scalar | nonnegative, real-valued 1-by-L row vector

ANG — Azimuth and elevation angles of response directions real-valued 1-by-M row vector | real-valued 2-by-M matrix

Output Arguments

RESP — Voltage response of antenna M-by-L matrix

Object Functions

Specific to Antenna and Transducer Element System Objects

Common to All System Objects

Examples

Sinc Antenna Response

More About

Sinc Response

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

`FrequencyRange` — Operating frequency range
`[0 1e20]` (default) | nonnegative, real-valued 1-by-2 row vector

`Beamwidth` — Beamwidth of antenna pattern
`[10 10]` (default) | scalar | 1-by-2 real-valued vector

`FREQ` — Operating frequency of antenna element
nonnegative scalar | nonnegative, real-valued 1-by-L row vector

`ANG` — Azimuth and elevation angles of response directions
real-valued 1-by-M row vector | real-valued 2-by-M matrix

`RESP` — Voltage response of antenna
M-by-L matrix

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.