.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/antennas/plot_02_carter_half_wave_dipole.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_communications_antennas_plot_02_carter_half_wave_dipole.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_communications_antennas_plot_02_carter_half_wave_dipole.py:


Carter's half-wave dipole (1932)
================================

The half-wave dipole is the reference antenna of radio engineering. With
the sinusoidal current a thin wire carries, its far field varies as
:math:`\cos(\tfrac\pi2\cos\theta)/\sin\theta`
(:func:`~engineeringkit.communications.half_wave_dipole_pattern`), a little
narrower than the :math:`\sin\theta` of a short dipole. Integrating the
radiated power gives a directivity of 1.64, or 2.15 dBi
(:func:`~engineeringkit.communications.half_wave_dipole_directivity`), and a
radiation resistance of 73 ohms
(:func:`~engineeringkit.communications.half_wave_dipole_resistance`). Philip
Carter of RCA put such calculations in circuit form in 1932: his
induced-EMF method gave the self- and mutual impedances of dipoles, the
basis of every array design that followed.

.. GENERATED FROM PYTHON SOURCE LINES 20-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import integrate

    from engineeringkit.communications import (
        FREE_SPACE_IMPEDANCE,
        directivity,
        half_wave_dipole_directivity,
        half_wave_dipole_pattern,
        half_wave_dipole_resistance,
    )
    from engineeringkit.communications.visualizers import plot_antenna_pattern








.. GENERATED FROM PYTHON SOURCE LINES 34-36

Directivity and radiation resistance
------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-50

.. code-block:: Python


    theta = np.linspace(0, np.pi, 4001)
    half_wave = half_wave_dipole_pattern(theta) ** 2
    short = np.sin(theta) ** 2
    D_half, D_short = directivity(theta, half_wave), directivity(theta, short)
    print(f"directivity: short dipole {D_short:.4f}, half-wave {D_half:.4f} (closed form {half_wave_dipole_directivity():.4f})")
    assert np.isclose(D_short, 1.5, rtol=1e-5) and np.isclose(D_half, half_wave_dipole_directivity(), rtol=1e-5)

    # Radiated power with feed current I0: P = (eta I0^2 / 4 pi) * integral of F^2 sin(theta) d(theta).
    integral, _ = integrate.quad(lambda th: np.cos(np.pi / 2 * np.cos(th)) ** 2 / np.sin(th), 1e-9, np.pi - 1e-9)
    R = FREE_SPACE_IMPEDANCE / (2 * np.pi) * integral
    print(f"radiation resistance {R:.2f} ohm (closed form {half_wave_dipole_resistance():.2f} ohm)")
    assert np.isclose(R, half_wave_dipole_resistance(), rtol=1e-6)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    directivity: short dipole 1.5000, half-wave 1.6409 (closed form 1.6409)
    radiation resistance 73.08 ohm (closed form 73.08 ohm)




.. GENERATED FROM PYTHON SOURCE LINES 51-53

Beamwidth
---------

.. GENERATED FROM PYTHON SOURCE LINES 53-69

.. code-block:: Python


    half_power = theta[(half_wave >= 0.5) & (theta <= np.pi / 2)][0]
    beamwidth = np.degrees(np.pi - 2 * half_power)
    print(f"half-power beamwidth: half-wave {beamwidth:.1f} deg, short dipole 90 deg")
    assert abs(beamwidth - 78) < 0.5

    full = np.linspace(0, 2 * np.pi, 721)
    fig, axes = plt.subplots(1, 2, figsize=(10, 4.4), subplot_kw={"projection": "polar"})
    plot_antenna_pattern(full, half_wave_dipole_pattern(full) ** 2, ax=axes[0], label="half-wave")
    plot_antenna_pattern(full, np.sin(full) ** 2, ax=axes[0], label="short dipole")
    axes[0].set_title("Power patterns (axis vertical)")
    plot_antenna_pattern(full, half_wave_dipole_pattern(full) ** 2, ax=axes[1], db_range=30)
    axes[1].set_title("Half-wave dipole [dB]")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/antennas/images/sphx_glr_plot_02_carter_half_wave_dipole_001.png
   :alt: Power patterns (axis vertical), Half-wave dipole [dB]
   :srcset: /api/gallery/communications/antennas/images/sphx_glr_plot_02_carter_half_wave_dipole_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    half-power beamwidth: half-wave 78.0 deg, short dipole 90 deg





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.148 seconds)


.. _sphx_glr_download_api_gallery_communications_antennas_plot_02_carter_half_wave_dipole.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/communications/antennas/plot_02_carter_half_wave_dipole.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_carter_half_wave_dipole.ipynb <plot_02_carter_half_wave_dipole.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_carter_half_wave_dipole.py <plot_02_carter_half_wave_dipole.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_carter_half_wave_dipole.zip <plot_02_carter_half_wave_dipole.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_