uv2phithetapat

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

Syntax

pat_phitheta = uv2phithetapat(pat_uv,u,v)

pat_phitheta = uv2phithetapat(pat_uv,u,v,phi,theta)

[pat_phitheta,phi_pat,theta_pat]
= uv2phithetapat(___)

Description

pat_phitheta = uv2phithetapat(pat_uv,u,v) expresses the antenna radiation pattern pat_phitheta in φ/θ angle coordinates instead of u/v space coordinates. pat_uv samples the pattern at u angles in u and v angles in v. The pat_phitheta matrix uses a default grid that covers φ values from 0 to 360 degrees and θ values from 0 to 90 degrees. In this grid, 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 = uv2phithetapat(pat_uv,u,v,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, 360], and theta should cover the range [0, 90].

example

[pat_phitheta,phi_pat,theta_pat] = uv2phithetapat(___) 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.

example

Examples

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Convert Radiation Pattern to φ-θ

Open Live Script

Convert a radiation pattern to φ-θ space with the angles spaced 1° apart.

Define the pattern in terms of u and v. Because u and v values outside the unit circle are not physical, set the pattern values in this region to zero.

u = -1:0.01:1;
v = -1:0.01:1;
[u_grid,v_grid] = meshgrid(u,v);
pat_uv = sqrt(1 - u_grid.^2 - v_grid.^2);
pat_uv(hypot(u_grid,v_grid) >= 1) = 0;

Convert the pattern to φ-θ space.

[pat_phitheta,phi,theta] = uv2phithetapat(pat_uv,u,v);

Plot Converted Radiation Pattern

Open Live Script

Convert a radiation pattern to $ϕ - θ$ space with the angles spaced one degree apart.

Define the pattern in terms of $u$ and $v$ . For values outside the unit circle, $u$ and $v$ are undefined, and the pattern value is 0.

u = -1:0.01:1;
v = -1:0.01:1;
[u_grid,v_grid] = meshgrid(u,v);
pat_uv = sqrt(1 - u_grid.^2 - v_grid.^2);
pat_uv(hypot(u_grid,v_grid) >= 1) = 0;

Convert the pattern to $ϕ - θ$ space. Store the $ϕ$ and $θ$ angles for use in plotting.

[pat_phitheta,phi,theta] = uv2phithetapat(pat_uv,u,v);

Plot the result.

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

Figure contains an axes object. The axes object with xlabel Phi (degrees), ylabel Theta (degrees) contains an object of type surface.

Convert Radiation Pattern Using Specific Phi/Theta Values

Open Live Script

Convert a radiation pattern to $ϕ - θ$ space with the angles spaced five degrees apart.

Define the pattern in terms of $u$ and $v$ . For values outside the unit circle, $u$ and $v$ are undefined, and the pattern value is 0.

u = -1:0.01:1;
v = -1:0.01:1;
[u_grid,v_grid] = meshgrid(u,v);
pat_uv = sqrt(1 - u_grid.^2 - v_grid.^2);
pat_uv(hypot(u_grid,v_grid) >= 1) = 0;

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

phi = 0:5:360;
theta = 0:5:90;
pat_phitheta = uv2phithetapat(pat_uv,u,v,phi,theta);

Plot the result.

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

Figure contains an axes object. The axes object with xlabel Phi (degrees), ylabel Theta (degrees) contains an object of type surface.

Input Arguments

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`pat_uv` — Antenna radiation pattern in u/v form
Q-by-P matrix

Antenna radiation pattern in u/v form, specified as a Q-by-P matrix. pat_uv samples the 3-D magnitude pattern in decibels, in terms of u and v coordinates. P is the length of the u vector, and Q is the length of the v vector.

Data Types: double

`u` — u coordinates
vector of length P

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

Data Types: double

`v` — v coordinates
vector of length Q

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

Data Types: double

`phi` — Phi angles
`[0:360]` (default) | vector of length L

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` — Theta angles
`[0:90]` (default) | vector of length M

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 90. Such θ angles are in the hemisphere for which u and v are defined.

Data Types: double

Output Arguments

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`pat_phitheta` — Antenna radiation pattern in phi-theta coordinates
real-valued M-by-L matrix

Antenna radiation pattern in phi-theta coordinates, returned as a real-valued M-by-L matrix. pat_phitheta represents the magnitude pattern. L is the length of the phi_pat vector, and M is the length of the theta_pat vector. Units are in dB.

`phi_pat` — Phi angles
real-valued length-L vector

Phi angles at which the pat_phitheta pattern is sampled, returned as a real-valued length L vector. Units are in degrees.

`theta_pat` — Theta angles
real-valued length-M vector

Theta angles at which the pat_phitheta pattern is sampled, returned as a real-valued length-M vector. Units are in degrees.

More About

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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:

$\begin{array}{l} u = \sin θ \cos ϕ \\ v = \sin θ \sin ϕ \end{array}$

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

To convert azimuth and elevation to u and v use the transformation

$\begin{array}{l} u = \cos e l \sin a z \\ v = \sin e l \end{array}$

which is valid only in the range abs(az)≤=90.

The values of u and v satisfy the inequalities

$\begin{array}{l} - 1 \leq u \leq 1 \\ - 1 \leq v \leq 1 \\ u^{2} + v^{2} \leq 1 \end{array}$

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

$\begin{array}{l} \tan ϕ = v / u \\ \sin θ = \sqrt{u^{2} + v^{2}} \end{array}$

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

$\begin{array}{l} \sin e l = v \\ \tan a z = \frac{u}{\sqrt{1 - u^{2} - v^{2}}} \end{array}$

Phi Angle, Theta Angle

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

The figure illustrates phi and theta for a vector that appears as a green solid line.

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

$\begin{array}{l} \sin e l = \sin ϕ \sin θ \\ \tan a z = \cos ϕ \tan θ \\ \cos θ = \cos e l \cos a z \\ \tan ϕ = \tan e l / \sin a z \end{array}$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

Version History

Introduced in R2012a

uv2phithetapat

Syntax

Description

Examples

Convert Radiation Pattern to φ-θ

Plot Converted Radiation Pattern

Convert Radiation Pattern Using Specific Phi/Theta Values

Input Arguments

`pat_uv` — Antenna radiation pattern in u/v form
Q-by-P matrix

`u` — u coordinates
vector of length P

`v` — v coordinates
vector of length Q

`phi` — Phi angles
`[0:360]` (default) | vector of length L

`theta` — Theta angles
`[0:90]` (default) | vector of length M

Output Arguments

`pat_phitheta` — Antenna radiation pattern in phi-theta coordinates
real-valued M-by-L matrix

`phi_pat` — Phi angles
real-valued length-L vector

`theta_pat` — Theta angles
real-valued length-M vector

More About

U/V Space

Phi Angle, Theta Angle

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

uv2phithetapat

Syntax

Description

Examples

Convert Radiation Pattern to φ-θ

Plot Converted Radiation Pattern

Convert Radiation Pattern Using Specific Phi/Theta Values

Input Arguments

pat_uv — Antenna radiation pattern in u/v form Q-by-P matrix

u — u coordinates vector of length P

v — v coordinates vector of length Q

phi — Phi angles [0:360] (default) | vector of length L

theta — Theta angles [0:90] (default) | vector of length M

Output Arguments

pat_phitheta — Antenna radiation pattern in phi-theta coordinates real-valued M-by-L matrix

phi_pat — Phi angles real-valued length-L vector

theta_pat — Theta angles real-valued length-M vector

More About

U/V Space

Phi Angle, Theta Angle

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

`pat_uv` — Antenna radiation pattern in u/v form
Q-by-P matrix

`u` — u coordinates
vector of length P

`v` — v coordinates
vector of length Q

`phi` — Phi angles
`[0:360]` (default) | vector of length L

`theta` — Theta angles
`[0:90]` (default) | vector of length M

`pat_phitheta` — Antenna radiation pattern in phi-theta coordinates
real-valued M-by-L matrix

`phi_pat` — Phi angles
real-valued length-L vector

`theta_pat` — Theta angles
real-valued length-M vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.