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Analytical comparisons

This section presents comparisons between analytical solutions and modelled solutions using gprMax.

Hertzian dipole in free space

:download:`hertzian_dipole_fs.in <../../tests/models_basic/hertzian_dipole_fs/hertzian_dipole_fs.in>`

This example is of a Hertzian dipole, i.e. an additive source (electric current density), in free space.

.. literalinclude:: ../../tests/models_basic/hertzian_dipole_fs/hertzian_dipole_fs.in
    :language: none
    :linenos:

The function hertzian_dipole_fs, which can be found in the analytical_solutions module in the tests sub-package, computes the analytical solution.

Results

:numref:`hertzian_dipole_fs_results` shows the time history of the electric and magnetic field components of the modelled and analytical solutions. The responses completely overlap one another due to their similarity. Therefore, :numref:`hertzian_dipole_fs_results_diffs` shows the percentage differences between the modelled and analytical solutions.

../../tests/models_basic/hertzian_dipole_fs_analytical/hertzian_dipole_fs_analytical.png

Time history of the electric and magnetic field components of the modelled and analytical solutions ('Ref', in this case, indicates solution calculated from theory).

../../tests/models_basic/hertzian_dipole_fs_analytical/hertzian_dipole_fs_analytical_diffs.png

Percentage differences between the modelled and analytical solutions.

The match between the analytical and numerically modelled solutions is excellent. The maximum difference is approximately 1%, which is observed in the Ez field component (the same direction as the Hertzian dipole source). The other electric field components exhibit maximum differences of approximately 0.5%, and the magnetic field components 0.25%.

Half-wave dipole in free space

See the :ref:`section on antenna example models <example-wire-dipole>` for the simulated s11 parameter and input impedance of a half-wave dipole antenna in free space. The resonant frequency and input impedance from the model agree very well with the theoretical predictions for a half-wave dipole antenna.