rcstruncone

Radar cross section of truncated cone

Since R2021a

Syntax

rcspat = rcstruncone(r1,r2,height,c,fc)

rcspat = rcstruncone(r1,r2,height,c,fc,az,el)

[rcspat,azout,elout] = rcstruncone(___)

Description

rcspat = rcstruncone(r1,r2,height,c,fc) returns the radar cross section pattern of a truncated cone. r1 is the radius of the small end of the cone, r2 is the radius of the large end, and height is the cone height. The radar cross section is a function of signal frequency, fc, and signal propagation speed, c. You can create a non-truncated cone by setting r1 to zero. The cone points downward towards the xy-plane. The origin is located at the apex of a the non-truncated cone constructed by extending the truncated cone to an apex.

rcspat = rcstruncone(r1,r2,height,c,fc,az,el) also specifies the azimuth angles, az, and elevation angles, el, at which to compute the radar cross section.

[rcspat,azout,elout] = rcstruncone(___) 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

Radar Cross Section of Truncated Cone

Display the radar cross section (RCS) pattern of a truncated cone as a function of azimuth angle and elevation. The truncated cone has a bottom radius of 9.0 cm and a top radius of 12.5 cm. The cone height is 1 m. The operating frequency is 4.5 GHz.

Define the truncated cone geometry and signal parameters.

c = physconst('Lightspeed');
fc = 4.5e9;
radbot = 0.090;
radtop = 0.125;
hgt = 1;

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

[rcspat,azresp,elresp] = rcstruncone(radbot,radtop,hgt,c,fc);
imagesc(azresp,elresp,pow2db(rcspat))
xlabel('Azimuth Angle (deg)')
ylabel('Elevation Angle (deg)')
title('Truncated Cone RCS (dBsm)')
colorbar

Radar Cross Section of Truncated Cone as Function of Elevation

Plot the radar cross section (RCS) pattern of a truncated cone as a function of elevation for a fixed azimuth angle of 5 degrees. The cone has a bottom radius of 9.0 cm and a top radius of 12.5 cm. The truncated cone height is 1 m. The operating frequency is 4.5.

Define the truncated cone geometry and signal parameters.

c = physconst('Lightspeed');
fc = 4.5e9;
radbot = 0.090;
radtop = 0.125;
hgt = 1;

Compute the RCS at an azimuth angle of 5 degrees.

az = 5.0;
el = -90:90;
[rcspat,azresp,elresp] = rcstruncone(radbot,radtop,hgt,c,fc,az,el);
plot(elresp,pow2db(rcspat))
xlabel('Elevation Angle (deg)')
ylabel('RCS (dBsm)')
title('Truncated Cone RCS as Function of Elevation')
grid on

Radar Cross Section of Truncated Cone as Function of Frequency

Plot the radar cross section (RCS) pattern of a truncated cone as a function of frequency for a single direction. The cone has a bottom radius of 9.0 cm and a top radius of 12.5 cm. The truncated cone height is 1 m.

Specify the truncated cone geometry and signal parameters.

c = physconst('Lightspeed');
radbot = 0.090;
radtop = 0.125;
hgt = 1;

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

az = 5.0;
el = 20.0;
fc = (100:100:4000)*1e6;
[rcspat,azpat,elpat] = rcstruncone(radbot,radtop,hgt,c,fc,az,el);
disp([azpat,elpat])

     5    20

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

Radar Cross Section of Full Cone as Function of Elevation

Plot the radar cross section (RCS) pattern of a full cone as a function of elevation for a fixed azimuth angle. To define a full cone set the bottom radius to zero. Set the top radius to 20.0 cm and the cone height to 50 cm. Assume the operating frequency is 4.5 GHz and the azimuth angle is 5 degrees.

Define the cone geometry and signal parameters.

c = physconst('Lightspeed');
fc = 4.5e9;
radsmall = 0.0;
radlarge = 0.20;
hgt = 0.5;

Compute the RCS for a fixed azimuth angle of 5 degrees.

az = 5.0;
el = -89:0.1:89;
[rcspat,azresp,elresp] = rcstruncone(radsmall,radlarge,hgt,c,fc,az,el);
plot(elresp,pow2db(rcspat))
xlabel('Elevation Angle (deg)')
ylabel('RCS (dBsm)')
title('Full Cone RCS as Function of Elevation')
grid on

Input Arguments

r1 — Radius of small end of truncated cone

nonnegative scalar

Radius of small end of truncated cone, specified as a nonnegative scalar. Units are in meters.

Example: 5.5

Data Types: double

r2 — Radius of large end of truncated cone

positive scalar

Radius of large end of truncated cone, specified as a positive scalar. Units are in meters.

Example: 5.5

Data Types: double

height — Height of truncated cone

positive scalar

Height of truncated cone, specified as a positive scalar. Units are in meters.

Example: 3.0

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

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

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