.. _sphx_glr_api_gallery_communications_propagation:

Propagation
-----------

Wavelength, free-space path loss and link budgets.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Maxwell&#x27;s equations (1865) predicted electromagnetic waves travelling at the speed of light. Heinrich Hertz confirmed them in 1887-1888: a spark gap drove waves at a few hundred megahertz, a metal sheet reflected them into a standing wave, and the spacing of the nodes, half a wavelength, multiplied by the frequency gave the speed. wavelength computes \lambda = c/f; the example reconstructs Hertz&#x27;s standing-wave measurement and maps the radio spectrum.">

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  .. image:: /api/gallery/communications/propagation/images/thumb/sphx_glr_plot_01_hertz_wavelength_thumb.png
    :alt:

  :doc:`/api/gallery/communications/propagation/plot_01_hertz_wavelength`

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      <div class="sphx-glr-thumbnail-title">Hertz's electromagnetic waves and their wavelength</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Harald Friis (1946) wrote the received power between two antennas in free space as P_r = P_t G_t G_r (\lambda/4\pi d)^2 (~engineeringkit.communications.friis_received_power). The 1/d^2 factor is pure geometry: power spreads over a sphere of area 4\pi d^2. The \lambda^2 factor comes from an antenna&#x27;s effective aperture, A_e = G\lambda^2/4\pi. This example checks both interpretations and the 6 dB-per-doubling slope of free_space_path_loss_db.">

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  .. image:: /api/gallery/communications/propagation/images/thumb/sphx_glr_plot_02_friis_transmission_thumb.png
    :alt:

  :doc:`/api/gallery/communications/propagation/plot_02_friis_transmission`

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      <div class="sphx-glr-thumbnail-title">The Friis transmission formula</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Telstar 1 (1962) relayed the first live transatlantic television. Engineers planned such links with a link budget: transmitter power, antenna gains, path loss and miscellaneous losses added in decibels (~engineeringkit.communications.link_budget_db), then compared with the receiver noise floor. The figures below are representative of the 4 GHz Andover-Telstar downlink, not archival values.">

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  .. image:: /api/gallery/communications/propagation/images/thumb/sphx_glr_plot_03_telstar_link_budget_thumb.png
    :alt:

  :doc:`/api/gallery/communications/propagation/plot_03_telstar_link_budget`

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      <div class="sphx-glr-thumbnail-title">The Telstar satellite link budget</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/communications/propagation/plot_01_hertz_wavelength
   /api/gallery/communications/propagation/plot_02_friis_transmission
   /api/gallery/communications/propagation/plot_03_telstar_link_budget