.. _sphx_glr_api_gallery_electrical_engineering_transmission_lines:

Transmission lines
------------------

Distributed lines, reflections and the Smith chart.


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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="Kelvin&#x27;s cable theory ignored inductance. Oliver Heaviside, a self-taught former telegraph operator, kept all four line constants: series resistance R and inductance L, shunt conductance G and capacitance C per metre. In 1876 he wrote the telegrapher&#x27;s equations, whose sinusoidal waves decay and travel according to \gamma = \sqrt{(R + j\omega L)(G + j\omega C)} (~engineeringkit.electrical_engineering.propagation_constant). In 1887 he found that if R/L = G/C (~engineeringkit.electrical_engineering.distortionless_condition), every frequency is attenuated equally and travels at the same speed, so a signal arrives weaker but undistorted. Real cables have far too little inductance; Pupin&#x27;s and Campbell&#x27;s loading coils (1899-1900) added it and made long-distance telephony possible. This example compares a cable with and without enough inductance.">

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  .. image:: /api/gallery/electrical_engineering/transmission_lines/images/thumb/sphx_glr_plot_01_heaviside_telegrapher_thumb.png
    :alt:

  :doc:`/api/gallery/electrical_engineering/transmission_lines/plot_01_heaviside_telegrapher`

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      <div class="sphx-glr-thumbnail-title">Heaviside's telegrapher's equations and the distortionless line (1876-1887)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Phillip Hagar Smith, an engineer at Bell Labs, tired of evaluating the transmission-line equations with a slide rule. His 1939 chart plots the reflection coefficient \Gamma = (Z_L - Z_0)/(Z_L + Z_0) (~engineeringkit.electrical_engineering.reflection_coefficient) in the unit disc, overlaid with circles of constant normalised resistance and arcs of constant reactance. Moving along a lossless line just rotates \Gamma around the centre, at constant standing-wave ratio (~engineeringkit.electrical_engineering.standing_wave_ratio), so the input impedance (~engineeringkit.electrical_engineering.input_impedance) can be read off the grid. This example uses the chart to design a single-stub match, drawn with plot_smith_chart.">

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  .. image:: /api/gallery/electrical_engineering/transmission_lines/images/thumb/sphx_glr_plot_02_smith_chart_thumb.png
    :alt:

  :doc:`/api/gallery/electrical_engineering/transmission_lines/plot_02_smith_chart`

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      <div class="sphx-glr-thumbnail-title">Smith's chart (1939)</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/electrical_engineering/transmission_lines/plot_01_heaviside_telegrapher
   /api/gallery/electrical_engineering/transmission_lines/plot_02_smith_chart