Documentation

# rcssphere

## Syntax

``rcspat = rcssphere(r,c,fc)``
``rcspat = rcssphere(r,c,fc,az,el)``
``[rcspat,azout,elout] = rcssphere(___)``

## Description

example

````rcspat = rcssphere(r,c,fc)` returns the radar cross section pattern of a sphere of radius `r` as a function of signal frequency, `fc`, and signal propagation speed, `c`. The center of the sphere is assumed to be located at the origin of the local coordinate system.```

example

````rcspat = rcssphere(r,c,fc,az,el)` also specifies the azimuth angles, `az`, and elevation angles, `el`, at which to compute the radar cross section.```

example

````[rcspat,azout,elout] = rcssphere(___)` also returns the azimuth angles, `azout`, and elevation angles, `elout`, at which the radar cross sections are computed. You can use these output arguments with any of the previous syntaxes.```

## Examples

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Display the radar cross section (RCS) pattern of a sphere as a function of azimuth and elevation. The sphere radius is 20.0 cm. The operating frequency is 4.5 GHz.

Define the sphere radius and signal parameters.

```c = physconst('Lightspeed'); fc = 4.5e9; rad = 0.20;```

Compute the RCS over all angles. The image shows that the RCS is constant over all directions.

```[rcspat,azresp,elresp] = rcssphere(rad,c,fc); image(azresp,elresp,pow2db(rcspat)) colorbar ylabel('Elevation angle (deg)') xlabel('Azimuth Angle (deg)') title('Sphere RCS (dB)')``` Plot the radar cross section (RCS) pattern of a sphere as a function of elevation angle for a fixed azimuth angle of 5 degrees. The sphere radius is 20.0 cm. The operating frequency is 4.5 GHz.

Specify the sphere radius and signal parameters.

```c = physconst('LightSpeed'); rad = 0.20; fc = 4.5e9;```

Compute the RCS over a constant azimith slice. The plot shows that the RCS is constant.

```az = 5.0; el = -90:90; [rcspat,azresp,elresp] = rcssphere(rad,c,fc,az,el); plot(elresp,pow2db(rcspat)) xlabel('Elevation Angle (deg)') ylabel('RCS (dB)') title('Sphere RCS as Function of Elevation') grid on``` Plot the radar cross section (RCS) pattern of a sphere as a function of frequency for a single azimuth and elevation. The radius of the sphere is 20.0 cm

Define the sphere radius and signal parameters.

```c = physconst('Lightspeed'); rad = 0.20;```

Compute the RCS over a range of frequencies for a single direction.

```az = 5.0; el = 20.0; fc = (100:10:4000)*1e6; rcspat = rcssphere(rad,c,fc,az,el); plot(fc/1e6,pow2db(squeeze(rcspat))) xlabel('Frequency (MHz)') ylabel('RCS (dB)') title('Sphere RCS as Function of Frequency') grid on``` ## Input Arguments

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Radius of sphere, specified as a positive scalar. Units are in meters.

Example: `5.5`

Data Types: `double`

Signal propagation speed, specified as a positive scalar. Units are in meters per second. For the SI value of the speed of light, use `physconst('LightSpeed')`.

Example: `3e8`

Data Types: `double`

Frequency for computing radar cross section, specified as a positive scalar or positive, real-valued, 1-by-L row vector. Frequency units are in Hz.

Example: `[100e6 200e6]`

Data Types: `double`

Azimuth angles for computing directivity and pattern, specified as a real-valued 1-by-M row vector where M is the number of azimuth angles. Angle units are in degrees. Azimuth angles must lie between –180° and 180°, inclusive.

The azimuth angle is the angle between the x-axis and the projection of a direction vector onto the xy-plane. The azimuth angle is positive when measured from the x-axis toward the y-axis.

Example: `-45:2:45`

Data Types: `double`

Elevation angles for computing directivity and pattern, specified as a real-valued, 1-by-N row vector where N is the number of desired elevation directions. Angle units are in degrees. Elevation angles must lie between –90° and 90°, inclusive.

The elevation angle is the angle between a direction vector and xy-plane. The elevation angle is positive when measured towards the z-axis.

Example: `-75:1:70`

Data Types: `double`

## Output Arguments

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Radar cross section pattern, returned as a real-valued N-by-M-by-L array. N is the length of the vector returned in the `elout` argument. M is the length of the vector returned in the `azout` argument. L is the length of the `fc` vector. Units are in meters-squared.

Data Types: `double`

Azimuth angles for computing directivity and pattern, returned as a real-valued 1-by-M row vector where M is the number of azimuth angles specified by the `az` input argument. Angle units are in degrees.

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy-plane. The azimuth angle is positive when measured from the x-axis toward the y-axis.

Data Types: `double`

Elevation angles for computing directivity and pattern, returned as a real-valued 1-by-N row vector where N is the number of elevation angles specified in `el` output argument. Angle units are in degrees.

The elevation angle is the angle between the direction vector and xy-plane. The elevation angle is positive when measured towards the z-axis.

Data Types: `double`

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### Azimuth and Elevation

This section describes the convention used to define azimuth and elevation angles.

The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy-plane. The angle is positive when going from the x-axis toward the y-axis. Azimuth angles lie between –180° and 180° degrees, inclusive. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy-plane. Elevation angles lie between –90° and 90° degrees, inclusive. Mahafza, Bassem. Radar Systems Analysis and Design Using MATLAB, 2nd Ed. Boca Raton, FL: Chapman & Hall/CRC, 2005.