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# azel2phithetapat

Convert radiation pattern from azimuth/elevation to phi/theta form

## Syntax

• pat_phitheta = azel2phithetapat(pat_azel,az,el)
example
• pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta)
example
• [pat_phitheta,phi,theta] = azel2phithetapat(___)
example

## Description

example

pat_phitheta = azel2phithetapat(pat_azel,az,el) expresses the antenna radiation pattern pat_azel in φ/θ angle coordinates instead of azimuth/elevation angle coordinates. pat_azel samples the pattern at azimuth angles in az and elevation angles in el. The pat_phitheta matrix covers φ values from 0 to 180 degrees and θ values from 0 to 360 degrees. pat_phitheta is uniformly sampled with a step size of 1 for φ and θ. The function interpolates to estimate the response of the antenna at a given direction.

example

pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta) uses vectors phi and theta to specify the grid at which to sample pat_phitheta. To avoid interpolation errors, phi should cover the range [0, 180], and theta should cover the range [0, 360].

example

[pat_phitheta,phi,theta] = azel2phithetapat(___) returns vectors containing the φ and θ angles at which pat_phitheta samples the pattern, using any of the input arguments in the previous syntaxes.

## Examples

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Convert a radiation pattern to φ/θ form, with the φ and θ angles spaced 1 degree apart.

Define the pattern in terms of azimuth and elevation.

az = -180:180; el = -90:90; pat_azel = mag2db(repmat(cosd(el)',1,numel(az))); 

Convert the pattern to φ/θ space.

pat_phitheta = azel2phithetapat(pat_azel,az,el); 

Plot the result of converting a radiation pattern to space with the and angles spaced 1 degree apart.

The radiation pattern is the cosine of the elevation.

az = -180:180; el = -90:90; pat_azel = repmat(cosd(el)',1,numel(az)); 

Convert the pattern to space. Use the returned and angles for plotting.

[pat_phitheta,phi,theta] = azel2phithetapat(pat_azel,az,el); 

Plot the result.

H = surf(phi,theta,mag2db(pat_phitheta)); H.LineStyle = 'none'; xlabel('phi (degrees)'); ylabel('theta (degrees)'); zlabel('Pattern'); 

Convert a radiation pattern to space with and angles spaced 5 degrees apart.

The radiation pattern is the cosine of the elevation.

az = -180:180; el = -90:90; pat_azel = repmat(cosd(el)',1,numel(az)); 

Define the set of and angles at which to sample the pattern. Then, convert the pattern.

phi = 0:5:360; theta = 0:5:180; pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta); 

Plot the result.

H = surf(phi,theta,mag2db(pat_phitheta)); H.LineStyle = 'none'; xlabel('phi (degrees)'); ylabel('theta (degrees)'); zlabel('Pattern'); 

## Input Arguments

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Antenna radiation pattern in azimuth/elevation form, specified as a Q-by-P matrix. pat_azel samples the 3-D magnitude pattern in decibels, in terms of azimuth and elevation angles. P is the length of the az vector, and Q is the length of the el vector.

Data Types: double

Azimuth angles at which pat_azel samples the pattern, specified as a vector of length P. Each azimuth angle is in degrees, between –180 and 180.

Data Types: double

Elevation angles at which pat_azel samples the pattern, specified as a vector of length Q. Each elevation angle is in degrees, between –90 and 90.

Data Types: double

Phi angles at which pat_phitheta samples the pattern, specified as a vector of length L. Each φ angle is in degrees, between 0 and 360.

Data Types: double

Theta angles at which pat_phitheta samples the pattern, specified as a vector of length M. Each θ angle is in degrees, between 0 and 180.

Data Types: double

## Output Arguments

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Antenna radiation pattern in phi/theta form, returned as an M-by-L matrix. pat_phitheta samples the 3-D magnitude pattern in decibels, in terms of φ and θ angles. L is the length of the phi vector, and M is the length of the theta vector.

Phi angles at which pat_phitheta samples the pattern, returned as a vector of length L. Angles are expressed in degrees.

Theta angles at which pat_phitheta samples the pattern, returned as a vector of length M. Angles are expressed in degrees.

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### Azimuth Angle, Elevation Angle

The azimuth angle is the angle from the positive x-axis toward the positive y-axis, to the vector's orthogonal projection onto the xy plane. The azimuth angle is between –180 and 180 degrees. The elevation angle is the angle from the vector's orthogonal projection onto the xy plane toward the positive z-axis, to the vector. The elevation angle is between –90 and 90 degrees. These definitions assume the boresight direction is the positive x-axis.

 Note:   The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.

### Phi Angle, Theta Angle

The φ angle is the angle from the positive y-axis toward the positive z-axis, to the vector's orthogonal projection onto the yz plane. The φ angle is between 0 and 360 degrees. The θ angle is the angle from the x-axis toward the yz plane, to the vector itself. The θ angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.

The coordinate transformations between φ/θ and az/el are described by the following equations

$\begin{array}{l}\mathrm{sin}\left(\text{el}\right)=\mathrm{sin}\varphi \mathrm{sin}\theta \hfill \\ \mathrm{tan}\left(\text{az}\right)=\mathrm{cos}\varphi \mathrm{tan}\theta \hfill \\ \hfill \\ \mathrm{cos}\theta =\mathrm{cos}\left(\text{el}\right)\mathrm{cos}\left(\text{az}\right)\hfill \\ \mathrm{tan}\varphi =\mathrm{tan}\left(\text{el}\right)/\mathrm{sin}\left(\text{az}\right)\hfill \end{array}$