.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/antennas/plot_01_friis_effective_aperture.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_01_friis_effective_aperture.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_01_friis_effective_aperture.py:


Friis's effective aperture: gain and area (1946)
================================================

Friis first wrote his transmission formula not with gains but with the
antennas' *effective areas*: :math:`P_r/P_t = A_t A_r/(d\lambda)^2`. A
receiving antenna collects the power falling on its effective area
:math:`A_e`, and reciprocity ties that area to its gain,
:math:`A_e = G\lambda^2/4\pi` (:func:`~engineeringkit.communications.effective_aperture`).
For a dish of physical area :math:`A` and aperture efficiency
:math:`\eta_a`, :math:`G = 4\pi\eta_a A/\lambda^2`
(:func:`~engineeringkit.communications.aperture_gain`). A dish of fixed size
gains 6 dB at every doubling of frequency, while an antenna of fixed gain
collects less and less power.

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import aperture_gain, db, effective_aperture, friis_received_power, wavelength








.. GENERATED FROM PYTHON SOURCE LINES 24-26

The area form and the gain form agree
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-36

.. code-block:: Python


    f, d = 12e9, 36_000e3  # Ku-band, geostationary distance
    dish_t, dish_r = np.pi * 1.2**2, np.pi * 0.3**2  # 2.4 m uplink dish, 60 cm TV dish
    Gt, Gr = aperture_gain(dish_t, f, 0.65), aperture_gain(dish_r, f, 0.65)
    by_area = effective_aperture(Gt, f) * effective_aperture(Gr, f) / (d * wavelength(f)) ** 2
    by_gain = friis_received_power(1.0, Gt, Gr, d, f)
    print(f"dish gains {float(db(Gt)):.1f} and {float(db(Gr)):.1f} dBi; Pr/Pt = {float(db(by_gain)):.1f} dB")
    assert np.isclose(by_area, by_gain)
    assert np.isclose(effective_aperture(Gr, f), 0.65 * dish_r)





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

 .. code-block:: none

    dish gains 47.7 and 35.7 dBi; Pr/Pt = -121.8 dB




.. GENERATED FROM PYTHON SOURCE LINES 37-39

Fixed area versus fixed gain
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 39-55

.. code-block:: Python


    freqs = np.logspace(8, 11, 61)
    fig, axes = plt.subplots(1, 2, figsize=(11, 3.8))
    axes[0].semilogx(freqs, db(aperture_gain(np.pi * 0.5**2, freqs, 0.6)), label="1 m dish")
    axes[0].semilogx(freqs, db(aperture_gain(np.pi * 1.5**2, freqs, 0.6)), label="3 m dish")
    axes[0].set(xlabel="frequency [Hz]", ylabel="gain [dBi]", title="A fixed aperture gains 6 dB per octave")
    axes[0].legend()
    axes[1].loglog(freqs, effective_aperture(1.0, freqs), label="isotropic, G = 1")
    axes[1].loglog(freqs, effective_aperture(1.64, freqs), label="half-wave dipole, G = 1.64")
    axes[1].set(xlabel="frequency [Hz]", ylabel="effective area [m$^2$]", title=r"A fixed gain collects $\lambda^2 G/4\pi$")
    axes[1].legend()
    fig.tight_layout()
    ratio = aperture_gain(1.0, 2 * f) / aperture_gain(1.0, f)
    assert np.isclose(float(db(ratio)), 6.0206, atol=1e-4)

    plt.show()



.. image-sg:: /api/gallery/communications/antennas/images/sphx_glr_plot_01_friis_effective_aperture_001.png
   :alt: A fixed aperture gains 6 dB per octave, A fixed gain collects $\lambda^2 G/4\pi$
   :srcset: /api/gallery/communications/antennas/images/sphx_glr_plot_01_friis_effective_aperture_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.262 seconds)


.. _sphx_glr_download_api_gallery_communications_antennas_plot_01_friis_effective_aperture.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_01_friis_effective_aperture.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_friis_effective_aperture.ipynb <plot_01_friis_effective_aperture.ipynb>`

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

      :download:`Download Python source code: plot_01_friis_effective_aperture.py <plot_01_friis_effective_aperture.py>`

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

      :download:`Download zipped: plot_01_friis_effective_aperture.zip <plot_01_friis_effective_aperture.zip>`


.. only:: html

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

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