# rcsdisc

Radar cross section of flat circular plate

## Description

example

rcspat = rcsdisc(r,c,fc) returns the radar cross section pattern of a flat circular plate of radius r. The radar cross section is a function of signal frequency, fc, and signal propagation speed, c. The plate is assumed to lie on the xy-plane. The center of the plate is located at the origin of the local coordinate system.

example

rcspat = rcsdisc(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] = rcsdisc(___) 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 circular plate as a function of azimuth and elevation. The plate radius is 22.5 cm. The operating frequency is 4.5 GHz.

Specify the plate geometry and signal parameters.

c = physconst('Lightspeed');
fc = 4.5e9;

Compute the RCS for all directions using the default direction values.

imagesc(azresp,elresp,pow2db(rcspat))
colorbar
xlabel('Azimuth Angle (deg)')
ylabel('Elevation Angle (deg)')
title('Circular Plate RCS (dBsm)')

Plot the radar cross section (RCS) pattern of a circular plate as a function of elevation angle for a fixed azimuth angle of 5${}^{\circ }$. The plate radius is 22.5 cm. The operating frequency is 4.5 GHz.

Define the plate radius and signal parameters.

c = physconst('Lightspeed');
fc = 4.5e9;

Compute the RCS as a function of elevation.

az = 5;
el = -90:90;
plot(elresp,pow2db(rcspat))
xlabel('Elevation Angle (deg)')
ylabel('RCS (dBsm)')
title('Circular Plate RCS as Function of Elevation')
grid on

Plot the radar cross section (RCS) pattern of a circular plate as a function of frequency for a single azimuth and elevation. The plate radius 22.5 cm.

Define the plate radius and signal parameters.

c = physconst('Lightspeed');

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

az = 5.0;
el = 20.0;
fc = (100:10:4000)*1e6;
disp([azpat,elpat])
5    20
plot(fc/1e6,pow2db(squeeze(rcspat)))
xlabel('Frequency (MHz)')
ylabel('RCS (dBsm)')
title('Circular Plate RCS as Function of Frequency')
grid on

## Input Arguments

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Radius of circular plate, 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.

## References

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