ParabolicDish Class Reference

Models a parabolic reflector dish with a circular rim. More...

Inheritance diagram for ParabolicDish:

Public Member Functions
function	ParabolicDish (in f, in d, in R, in alpha, in rho_res, in phi_res, in t_res)
	Constructor for ParabolicDish.
function	E_calc (in obj, in r, in theta, in phi, in usegreen)
	Computes the far-field E-theta and E-phi components.
function	J_calc (in obj, in feed_fields_fun, in freq)
	Computes surface current vectors from a given field function.
function	plot (in obj, in feed_typ_size)
	Plots the surface current magnitude and feed location.
function get	z0 (in obj)
	Getter for z0, the vertex height from the paraboloid.
function get	theta0 (in obj)
	Getter for theta0, the edge angle of the dish [rad].

Public Attributes
Property	f
	Focal length of the dish [m].
Property	d
	Diameter of the dish [m].
Property	R
	Radius of the rim [m].
Property	alpha
	Angle that the rim extends from the end of the dish [rad].
Property	omega
	Angular frequency of excitation [rad/s].
Property	rho_res
	Resolution of sampling along rho axis (dish)
Property	phi_res
	Resolution of sampling along phi axis (dish & rim)
Property	t_res
	Resolution of sampling along t axis (rim)
Property	rho_range
	Discrete rho sampling points (1D array)
Property	phi_range
	Discrete phi sampling points (1D array)
Property	t_range
	Discrete t sampling points (1D array)
Property	Jx
	X component of surface current in Cartesian coordinates.
Property	Jy
	Y component of surface current in Cartesian coordinates.
Property	Jz
	Z component of surface current in Cartesian coordinates.
Property	Jtheta
	Theta component of surface current in spherical coordinates.
Property	Jphi
	Phi component of surface current in spherical coordinates.
Property	X
	X coordinates of surface (cell array: 1=dish, 2=rim)
Property	Y
	Y coordinates of surface (cell array: 1=dish, 2=rim)
Property	Z
	Z coordinates of surface (cell array: 1=dish, 2=rim)
Property	nx
	X component of surface normals (cell array: 1=dish, 2=rim)
Property	ny
	Y component of surface normals (cell array: 1=dish, 2=rim)
Property	nz
	Z component of surface normals (cell array: 1=dish, 2=rim)
Property	z0
	z-coordinate of the dish vertex relative to the paraboloid
Property	theta0
	Angle between the dish edge and the focal axis [rad].

Private Member Functions
function	surface_dish (in obj)
	Generates the parametric surface of the parabolic dish reflector.
function	surface_rim (in obj)
	Generates the parametric surface of the dish rim (roll-off region).

Private Attributes
Property	k
	Wavenumber [rad/m].
Property	jacobian
	Surface Jacobians for integration (cell array: 1=dish, 2=rim)
Constant Property	ep0 = 8.85418782e
	Vacuum permittivity [F/m].
Constant Property	mu0 = 1.25663706e
	Vacuum permeability [H/m].
Constant Property	DISH = 1
	Index for dish surface.
Constant Property	RIM = 2
	Index for rim surface.
Constant Property	EXCLUDE_RIM = 0
	Flag to ignore rim in field calculations.

Detailed Description

Models a parabolic reflector dish with a circular rim.

This class defines the geometry, surface currents, and far-field radiation calculation for a parabolic dish antenna with an optional rim. It includes methods for surface mesh generation, current calculation, far-field integration, and visualization.

Constructor & Destructor Documentation

ParabolicDish()

function ParabolicDish	(	in	f,
		in	d,
		in	R,
		in	alpha,
		in	rho_res,
		in	phi_res,
		in	t_res )

Constructor for ParabolicDish.

Parameters

f	Focal length [m]
d	Diameter [m]
R	Rim radius [m]
alpha	Rim span angle [rad]
rho_res	Rho resolution
phi_res	Phi resolution
t_res	T resolution

Member Function Documentation

E_calc()

function E_calc	(	in	obj,
		in	r,
		in	theta,
		in	phi,
		in	usegreen )

Computes the far-field E-theta and E-phi components.

Parameters

r	Radial observation distance(s)
theta	Elevation angle(s) [rad]
phi	Azimuth angle(s) [rad]
usegreen	Flag to apply Green's function (default = 1)

Return values

Etheta	Theta-polarized electric field
Ephi	Phi-polarized electric field

J_calc()

function J_calc	(	in	obj,
		in	feed_fields_fun,
		in	freq )

Computes surface current vectors from a given field function.

Parameters

feed_fields_fun	Function handle to compute feed fields
freq	Operating frequency [Hz]

plot()

function plot	(	in	obj,
		in	feed_typ_size )

Plots the surface current magnitude and feed location.

Parameters

feed_typ_size

Approximate radius of the feed for visualization

surface_dish()

function surface_dish ( in obj )

private

Generates the parametric surface of the parabolic dish reflector.

This method computes the 3D Cartesian coordinates (X, Y, Z) of the reflective parabolic surface based on the paraboloid equation z = f - rho^2 / (4f), where f is the focal length. It also calculates surface normals (nx, ny, nz) and the surface Jacobian for integration.

• The surface is discretized using rho_res and phi_res.
• Normals are derived from the gradient of the paraboloid.
• The Jacobian is computed as RHO * sqrt(1 + (RHO/(2f))^2) for accurate surface integration.

Note

This function populates X{1}, Y{1}, Z{1}, nx{1}, ny{1}, nz{1}, and jacobian{1}.

surface_rim()

function surface_rim ( in obj )

private

Generates the parametric surface of the dish rim (roll-off region).

This method computes the coordinates, surface normals, and Jacobian for the rim region at the edge of the parabolic reflector. The rim is modeled as a circular arc orthogonal to the paraboloid.

• The rim is defined using polar arc equations r(t) and z(t) derived from the parabola edge.
• The arc is defined with radius R and offset based on geometric constraints to ensure smooth junction.
• Normals and Jacobians are calculated for proper field and current integration.

Note

This function populates X{2}, Y{2}, Z{2}, nx{2}, ny{2}, nz{2}, and jacobian{2}.

theta0()

function get theta0

(

in

obj

)

Getter for theta0, the edge angle of the dish [rad].

z0()

function get z0

(

in

obj

)

Getter for z0, the vertex height from the paraboloid.

Member Data Documentation

alpha

Property alpha

Angle that the rim extends from the end of the dish [rad].

d

Property d

Diameter of the dish [m].

DISH

Constant Property DISH = 1

private

Index for dish surface.

ep0

Constant Property ep0 = 8.85418782e

private

Vacuum permittivity [F/m].

EXCLUDE_RIM

Constant Property EXCLUDE_RIM = 0

private

Flag to ignore rim in field calculations.

f

Property f

Focal length of the dish [m].

jacobian

Property jacobian

private

Surface Jacobians for integration (cell array: 1=dish, 2=rim)

Jphi

Property Jphi

Phi component of surface current in spherical coordinates.

Jtheta

Property Jtheta

Theta component of surface current in spherical coordinates.

Jx

Property Jx

X component of surface current in Cartesian coordinates.

Jy

Property Jy

Y component of surface current in Cartesian coordinates.

Jz

Property Jz

Z component of surface current in Cartesian coordinates.

k

Property k

private

Wavenumber [rad/m].

mu0

Constant Property mu0 = 1.25663706e

private

Vacuum permeability [H/m].

nx

Property nx

X component of surface normals (cell array: 1=dish, 2=rim)

ny

Property ny

Y component of surface normals (cell array: 1=dish, 2=rim)

nz

Property nz

Z component of surface normals (cell array: 1=dish, 2=rim)

omega

Property omega

Angular frequency of excitation [rad/s].

phi_range

Property phi_range

Discrete phi sampling points (1D array)

phi_res

Property phi_res

Resolution of sampling along phi axis (dish & rim)

R

Property R

Radius of the rim [m].

rho_range

Property rho_range

Discrete rho sampling points (1D array)

rho_res

Property rho_res

Resolution of sampling along rho axis (dish)

RIM

Constant Property RIM = 2

private

Index for rim surface.

t_range

Property t_range

Discrete t sampling points (1D array)

t_res

Property t_res

Resolution of sampling along t axis (rim)

theta0

Property theta0

Angle between the dish edge and the focal axis [rad].

X

Property X

X coordinates of surface (cell array: 1=dish, 2=rim)

Y

Property Y

Y coordinates of surface (cell array: 1=dish, 2=rim)

Z

Property Z

Z coordinates of surface (cell array: 1=dish, 2=rim)

z0

Property z0

z-coordinate of the dish vertex relative to the paraboloid

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The documentation for this class was generated from the following file:

• ParabolicDish.m