.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/propagation/plot_02_friis_transmission.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_propagation_plot_02_friis_transmission.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_propagation_plot_02_friis_transmission.py:


The Friis transmission formula
==============================

Harald Friis (1946) wrote the received power between two antennas in free
space as :math:`P_r = P_t G_t G_r (\lambda/4\pi d)^2`
(:func:`~engineeringkit.communications.friis_received_power`). The
:math:`1/d^2` factor is pure geometry: power spreads over a sphere of area
:math:`4\pi d^2`. The :math:`\lambda^2` factor comes from an antenna's
effective aperture, :math:`A_e = G\lambda^2/4\pi`. This example checks both
interpretations and the 6 dB-per-doubling slope of
:func:`~engineeringkit.communications.free_space_path_loss_db`.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import free_space_path_loss_db, friis_received_power, wavelength








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Spherical spreading times effective aperture
--------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-35

.. code-block:: Python


    Pt, Gt, Gr, f = 10.0, 30.0, 20.0, 5.8e9
    d = np.logspace(2, 5, 100)
    flux = Pt * Gt / (4 * np.pi * d**2)
    aperture = Gr * float(wavelength(f)) ** 2 / (4 * np.pi)
    assert np.allclose(friis_received_power(Pt, Gt, Gr, d, f), flux * aperture)

    slope = np.polyfit(np.log2(d), free_space_path_loss_db(d, f), 1)[0]
    print(f"path loss grows by {slope:.2f} dB per doubling of distance")
    print(f"received power at 10 km: {float(friis_received_power(Pt, Gt, Gr, 1e4, f)) * 1e9:.2f} nW")





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

 .. code-block:: none

    path loss grows by 6.02 dB per doubling of distance
    received power at 10 km: 1.02 nW




.. GENERATED FROM PYTHON SOURCE LINES 36-38

Higher frequency, same antennas: more loss
------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-49

.. code-block:: Python


    fig, axes = plt.subplots(1, 2, figsize=(9, 3.6))
    axes[0].loglog(d / 1e3, friis_received_power(Pt, Gt, Gr, d, f))
    axes[0].set(xlabel="distance [km]", ylabel="received power [W]", title="Inverse-square spreading")
    for freq in [900e6, 2.4e9, 28e9]:
        axes[1].semilogx(d / 1e3, free_space_path_loss_db(d, freq), label=f"{freq / 1e9:g} GHz")
    axes[1].set(xlabel="distance [km]", ylabel="free-space path loss [dB]")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/propagation/images/sphx_glr_plot_02_friis_transmission_001.png
   :alt: Inverse-square spreading
   :srcset: /api/gallery/communications/propagation/images/sphx_glr_plot_02_friis_transmission_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.448 seconds)


.. _sphx_glr_download_api_gallery_communications_propagation_plot_02_friis_transmission.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/propagation/plot_02_friis_transmission.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_friis_transmission.ipynb <plot_02_friis_transmission.ipynb>`

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

      :download:`Download Python source code: plot_02_friis_transmission.py <plot_02_friis_transmission.py>`

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

      :download:`Download zipped: plot_02_friis_transmission.zip <plot_02_friis_transmission.zip>`


.. only:: html

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

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