# rcssphere

Radar cross section of sphere

## Syntax

## Description

## Examples

### Radar Cross Section of Sphere

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 (dBsm)')

### Radar Cross Section of Sphere as Function of Elevation

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 azimuth 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 (dBsm)') title('Sphere RCS as Function of Elevation') grid on

### Radar Cross Section of Sphere as Function of Frequency

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 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,azpat,elpat] = rcssphere(rad,c,fc,az,el); disp([azpat,elpat])

5 20

plot(fc/1e6,pow2db(squeeze(rcspat))) xlabel('Frequency (MHz)') ylabel('RCS (dBsm)') title('Sphere RCS as Function of Frequency') grid on

## Input Arguments

`r`

— Radius of sphere

positive scalar

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

**Example: **`5.5`

**Data Types: **`double`

`c`

— Signal propagation speed

positive scalar

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`

`fc`

— Frequency for computing radar cross section

positive scalar | positive, real-valued, 1-by-*L* row vector

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`

`az`

— Azimuth angles

`-180:180`

(default) | 1-by-*M* real-valued row vector

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`

`el`

— Elevation angles

`-90:90`

(default) | 1-by-*N* real-valued row vector

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

`rcspat`

— Radar cross section pattern

real-valued *N*-by-*M*-by-*L*
array

`azout`

— Azimuth angles

real-valued 1-by-*M* row vector

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`

`elout`

— Elevation angles

real-valued 1-by-*N* row vector

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`

## More About

### 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.

## References

[1] Mahafza, Bassem. *Radar
Systems Analysis and Design Using MATLAB, 2nd Ed.* Boca Raton, FL: Chapman &
Hall/CRC, 2005.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

## Version History

**Introduced in R2021a**

## See Also

`rcscylinder`

| `rcsdisc`

| `rcstruncone`

| `phased.BackscatterRadarTarget`

| `phased.RadarTarget`

## Open Example

You have a modified version of this example. Do you want to open this example with your edits?

## MATLAB Command

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

# Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

## How to Get Best Site Performance

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.

### Americas

- América Latina (Español)
- Canada (English)
- United States (English)

### Europe

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)