Excitation Sources

At the start of a simulation, electric or magnetic fields are introduced into the simulation box, applying an initial energy and signal input to the system. This is done by setting the numerical values of the field at specified Yee cells. Some excitations only last one timestep, while most excitations are gradually applied over many timesteps.

Usually, the excitation source is created indirectly using high-level Ports. However, sometimes a satisfactory port is unavailable for the simulated structure, making it necessary to create custom excitation sources using low-level functions. This allows one to introduce an excitation with a specific location, field type, distribution, and weighting function.

Custom excitation is also needed for calculating a structure’s Radar Cross Section (RCS), which requires simulating a free-space plane wave in a special mode called Total-Field Scattered-Field (TFSF).

Standard Excitation

A standard excitation source is created by assigning it to a box primitive, which defines it position and size. Both E-field and H-field excitations are supported.

The excitation can either be hard or soft. A hard excitation forces the field at the source points to exactly take the field values of the source, ignoring any other incoming wave e.g. from reflections. For soft sources, the field values at source points are the superposition of the defined source and other fields or traveling waves.

AddExcitation() function definition:

CSX = AddExcitation(CSX, name, type, excite, varargin)

  • CSX: CSX-struct created by InitCSX

  • name: Property name for the excitation.

  • type:

    • 0: E-field soft excitation.

    • 1: E-field hard excitation.

    • 2: H-field soft excitation.

    • 3: H-field hard excitation.

    • 10: Plane wave excitation.

  • excite: Excitation vector, e.g. [2 0 0] for excitation of 2 V/m in x direction.

  • varargin: Additional options:

  • Delay: Setup an excitation time delay in seconds.

  • PropDir: Direction of plane wave propagation (plane wave excitation only).

Example

Add a 400 MHz sinusoidal line excitation (short dipole):

csx = InitCSX();
fdtd = InitFDTD();

f0 = 400e6;
dipole_length = 10;

csx = AddExcitation(
    csx, ...
    'infDipole', ...
    1, ...            % E-field
    [1 0 0] ...       % excitation vector
);
start = [-dipole_length/2 0 0];
stop  = [+dipole_length/2 0 0];
csx = AddBox(csx, 'infDipole', 1, start, stop);

% Don't forget to assign a signal waveform to the simulation (not CSXCAD).
fdtd = SetSinusExcite(fdtd, f0)

Total Field / Scattered Field Excitation

To create a plane wave excitation in the sense of a Total Field / Scattered Field (TFSF) approach, the AddPlaneWaveExcite() function is used. This type of source becomes useful if the scattered field of an object is of interest, such as in Radar Cross Section (RCS) simulations.

The field from the excitation is confined to the box defined for the source, the scattered field will propagate beyond the box. A plane wave excitation must not intersect with any kind of material. This excitation type can only be applies in air/vacuum and completely surrounding a structure. The plane wave source has to be assigned to a box primitive which defines the position and extend of the field.

As an example, see the Metal Sphere Radar Cross Section example in the Tutorial section.

AddPlaneWaveExcite() function definition:

CSX = AddPlaneWaveExcite(CSX, name, k_dir, E_dir, <f0, varargin>)

  • CSX: CSX struct created by InitCSX.

  • name: Property name for the excitation.

  • k_dir: Unit vector of wave progation direction.

  • E_dir: Electric field polarization vector (must be orthogonal to k_dir).

  • f0: Frequency for numerical phase velocity compensation (optional).

Example

Add a Gaussian pulse as a TFSF source:

fdtd = SetGaussExcite(fdtd, 0.5 * (f_start + f_stop), 0.5 * (f_stop - f_start));
inc_angle = 0 / 180 * pi; %incident angle on the x-axis
k_dir = [cos(inc_angle) sin(inc_angle) 0]; % plane wave direction
E_dir = [0 0 1]; % plane wave polarization --> E_z
f0 = 500e6;      % frequency for numerical phase velocity compensation

csx = AddPlaneWaveExcite(csx, 'plane_wave', k_dir, E_dir, f0);

% source is in the box defined by start and stop
start = [-100 -100 -100];
stop = [100 100 100];
csx = AddBox(csx, 'plane_wave', 0, start, stop);

Weighting Function

An excitation can be a function of position (spatial coordinates) by modulating its numerical field value by a weighting function via SetExcitationWeight() (Octave) or SetWeightFunction() (Python).

This feature is needed for hollow waveguides, which must be excited appropriately to launch the desired propagation mode. Transmission lines such as coaxial cables also work best with a custom field pattern to minimize artifacts due an abrupt field input.

The electric and magnetic fields are vector fields. At each point in space, they contain three values, representing their polarization along three coordinate axes. Thus weighting functions are always passed as arrays with three elements. Unwanted polarization can be masked by a excitation function of '0'.

Note

  • Each weighting function is a string, which contains the expression parsed by the fparser library, so the string should be a legal fparser expression with proper syntax.

  • See Symbolic Expression Parser: fparser for weighting function syntax.

Example

  • Excite a coaxial transmission line excitation in Cylindrical coordinates (r, a, z).

    coax_inner_od = 3;
coax_outer_id = 5;

csx = AddExcitation( ...
    csx, ...
    'excite', ...
    0, ...         % E-Field
    [1 0 0] ...    % excitation vector
);
csx = SetExcitationWeight(csx, 'excite', ['1 / rho' '0' '0']);

% radial field
start = [coax_inner_od     0   0];
stop  = [coax_outer_id  2*pi   0];

% Create a 2D disc to excite the region between the inner
% and outer conductor.
%
% By default this region is a vacuum, you may want to fill
% this region with your own materials too.
csx = AddBox(csx, 'excite', 0, start, stop);

  • Excite a coaxial transmission line excitation in Cartesian coordinates (x, y, z), for a wave traveling along the z axis.

    coax_inner_od = 3;
coax_outer_id = 5;

% r_o, r_i are placeholders
func_x = 'x / (x * x + y * y) * (sqrt(x * x + y * y) < r_o) * (sqrt(x * x + y * y) > r_i)';
func_y = 'y / (x * x + y * y) * (sqrt(x * x + y * y) < r_o) * (sqrt(x * x + y * y) > r_i)';

% substitute variable names in weighting function strings
func_x = strrep(func_x, 'r_i', num2str(coax_inner_od));
func_y = strrep(func_y, 'r_o', num2str(coax_outer_id));

% Construct excitation vector [1 1 0] shown here for clarity,
% not necessary, [1 1 1] is also acceptable since the unused
% polarization is masked by the zero weighting function
% [func_x func_y '0'] anyway
csx = AddExcitation(csx, "excite", 0, [1 1 0]);
csx = SetExcitationWeight(csx, "excite", [func_x func_y '0']);

% Create a 2D disc to excite the region between the inner
% and outer conductor.
%
% By default this region is a vacuum, you may want to fill
% this region with your own materials too.
start = [0 0 0]
stop  = [0 0 0]
csx = AddCylindricalShell(
    csx, "excite", ...
    0, ...
    ex_start, ...
    ex_stop, ...
    (coax_inner_od + coax_outer_id) * 0.5, ...
    (coax_outer_id - coax_inner_od) ...
);

  • Excite a coaxial transmission line excitation in Cartesian coordinates (x, y, z), for a wave traveling along any axis.

    % x, y, r_o, r_i are placeholders
func_x = 'x / (x * x + y * y) * (sqrt(x * x + y * y) < r_o) * (sqrt(x * x + y * y) > r_i)';
func_y = 'y / (x * x + y * y) * (sqrt(x * x + y * y) < r_o) * (sqrt(x * x + y * y) > r_i)';

% In a coax, the electric field's polarization is zero along the
% axis of propagation, and only exists along two axes orthogonal
% to the propagation direction.
%
% Depending on the actual field, the weighting function can be
%
%   * (  0, f_y, f_z)
%   * (f_x,   0, f_y)
%   * (f_x, f_y,   0)
%
% So our first problem is to rewrite the "x", "y" in the strings
% to the actual two axes orthogonal to the propagation direction

% change dir to {0, 1, 2} for propagating along the {x, y, z} axis
dir = 0;

% determine two direction indexes orthogonal to propagation direction
dir_ortho1 = mod(dir + 1, 3)
dir_ortho2 = mod(dir + 2, 3)

% determine the variable names orthogonal to propagation direction
dir_names = {'x', 'y', 'z'};

% Matlab/Octave uses 1-based index
dir_str = dir_names{dir + 1};
dir_ortho1_str = dir_names{dir_ortho1 + 1};
dir_ortho2_str = dir_names{dir_ortho2 + 2};

% substitute variable names in weighting function strings
func_x = strrep(func_x, 'x', dir_ortho1_str)
func_x = strrep(func_x, 'y', dir_ortho1_str)
func_y = strrep(func_y, 'x', dir_ortho2_str)
func_y = strrep(func_y, 'y', dir_ortho2_str)

% construct weighting function arrays
func_E{dir + 1} = '0';
func_E{dir_ortho1 + 1} = func_x;
func_E{dir_ortho2 + 1} = func_y;

% construct excitation vector
%
% shown here for clarity, it's not necessary, the unused polarization
% is masked by the zero weighting function anyway
excv = [1 1 1]
excv{dir + 1} = 0

csx = AddExcitation(csx, "excite", 0, excv);
csx = SetExcitationWeight(csx, "excite", func_E);

% Create a 2D disc to excite the region between the inner
% and outer conductor.
%
% By default this region is a vacuum, you may want to fill
% this region with your own materials too.
start = [0 0 0]
stop  = [0 0 0]
csx = AddCylindricalShell(
    csx, "excite", ...
    0, ...
    ex_start, ...
    ex_stop, ...
    (coax_inner_od + coax_outer_id) * 0.5, ...
    (coax_outer_id - coax_inner_od) ...
);

    Tip

    This is why choosing the correct coordinate system is important in electromagnetic problems!