Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

phitheta2uvpat

Convert radiation pattern from phi/theta form to u/v form

Syntax

pat_uv = phitheta2uvpat(pat_phitheta,phi,theta)
pat_uv = phitheta2uvpat(pat_phitheta,phi,theta,u,v)
[pat_uv,u_pat,v_pat] = phitheta2uvpat(___)

Description

example

pat_uv = phitheta2uvpat(pat_phitheta,phi,theta) expresses the antenna radiation pattern pat_phitheta in u/v space coordinates instead of φ/θ angle coordinates. pat_phitheta samples the pattern at φ angles in phi and θ angles in theta. The pat_uv matrix uses a default grid that covers u values from –1 to 1 and v values from –1 to 1. In this grid, pat_uv is uniformly sampled with a step size of 0.01 for u and v. The function interpolates to estimate the response of the antenna at a given direction. Values in pat_uv are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.

example

pat_uv = phitheta2uvpat(pat_phitheta,phi,theta,u,v) uses vectors u and v to specify the grid at which to sample pat_uv. To avoid interpolation errors, u should cover the range [–1, 1] and v should cover the range [–1, 1].

example

[pat_uv,u_pat,v_pat] = phitheta2uvpat(___) returns vectors containing the u and v coordinates at which pat_uv samples the pattern, using any of the input arguments in the previous syntaxes.

Examples

collapse all

Convert a radiation pattern to u-v form, with the u and v coordinates spaced by 0.01.

Define the pattern in terms of φ and θ.

phi = 0:360;
theta = 0:90;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

Convert the pattern to u-v form.

pat_uv = phitheta2uvpat(pat_phitheta,phi,theta);

Convert a radiation pattern to coordinates, with the and coordinates spaced by 0.01.

Define the pattern in terms of and .

phi = 0:360;
theta = 0:90;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

Convert the pattern to coordinates. Store the and coordinates for use in plotting.

[pat_uv,u,v] = phitheta2uvpat(pat_phitheta,phi,theta);

Plot the result.

H = surf(u,v,pat_uv);
H.LineStyle = 'none';
xlabel('u');
ylabel('v');
zlabel('Pattern');

Convert a radiation pattern to coordinates, with the and coordinates spaced by 0.05.

Define the pattern in terms of and .

phi = 0:360;
theta = 0:90;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

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

u = -1:0.05:1;
v = -1:0.05:1;
pat_uv = phitheta2uvpat(pat_phitheta,phi,theta,u,v);

Plot the result.

H = surf(u,v,pat_uv);
H.LineStyle = 'none';
xlabel('u');
ylabel('v');
zlabel('Pattern');

Input Arguments

collapse all

Antenna radiation pattern in phi/theta form, specified as a Q-by-P matrix. pat_phitheta samples the 3-D magnitude pattern in decibels, in terms of φ and θ angles. P is the length of the phi vector, and Q is the length of the theta vector.

Data Types: double

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

Data Types: double

Theta angles at which pat_phitheta samples the pattern, specified as a vector of length Q. Each θ angle is in degrees, between 0 and 90. Such angles are in the hemisphere for which u and v are defined.

Data Types: double

u coordinates at which pat_uv samples the pattern, specified as a vector of length L. Each u coordinate is between –1 and 1.

Data Types: double

v coordinates at which pat_uv samples the pattern, specified as a vector of length M. Each v coordinate is between –1 and 1.

Data Types: double

Output Arguments

collapse all

Antenna radiation pattern in u/v form, returned as an M-by-L matrix. pat_uv samples the 3-D magnitude pattern in decibels, in terms of u and v coordinates. L is the length of the u vector, and M is the length of the v vector. Values in pat_uv are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.

u coordinates at which pat_uv samples the pattern, returned as a vector of length L.

v coordinates at which pat_uv samples the pattern, returned as a vector of length M.

More About

collapse all

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

sin(el)=sinϕsinθtan(az)=cosϕtanθcosθ=cos(el)cos(az)tanϕ=tan(el)/sin(az)

U/V Space

The u and v coordinates are the direction cosines of a vector with respect to the y-axis and z-axis, respectively.

The u/v coordinates for the hemisphere x ≥ 0 are derived from the phi and theta angles, as follows:

u=sinθcosϕv=sinθsinϕ

In these expressions, φ and θ are the phi and theta angles, respectively.

In terms of azimuth and elevation, the u and v coordinates are

u=coselsinazv=sinel

The values of u and v satisfy the inequalities

1u11v1u2+v21

Conversely, the phi and theta angles can be written in terms of u and v using

tanϕ=u/vsinθ=u2+v2

The azimuth and elevation angles can also be written in terms of u and v

sinel=vtanaz=u1u2v2

Extended Capabilities

Introduced in R2012a

Was this topic helpful?