.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/networks/plot_02_thevenin_equivalent.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_electrical_engineering_networks_plot_02_thevenin_equivalent.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_electrical_engineering_networks_plot_02_thevenin_equivalent.py:


Thévenin's equivalent circuit (1883)
====================================

Léon Charles Thévenin, an engineer of the French telegraph service, showed
in 1883 that any linear network seen from two terminals behaves like a
single EMF in series with a single resistance (Hermann von Helmholtz had
reached the same result in 1853). The EMF is the open-circuit voltage; the
resistance is that voltage divided by the short-circuit current, or the
resistance seen with every source zeroed. This example reduces a two-source
network with :func:`~engineeringkit.electrical_engineering.nodal_analysis`,
builds the equivalent with
:func:`~engineeringkit.electrical_engineering.thevenin_from_source`, and
checks that the two agree for every load.

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.electrical_engineering import nodal_analysis, thevenin_from_source








.. GENERATED FROM PYTHON SOURCE LINES 24-29

The network and its terminals
-----------------------------

A 10 V source and a 5 mA source feed a resistive network; the load is
connected between node 3 and ground.

.. GENERATED FROM PYTHON SOURCE LINES 29-46

.. code-block:: Python


    network = [(1, 2, 2e3), (2, 0, 3e3), (2, 3, 1e3)]
    vsrc, isrc = [(1, 0, 10.0)], [(0, 3, 5e-3)]


    def solve(load=None):
        resistors = network + ([] if load is None else [(3, 0, load)])
        return nodal_analysis(3, resistors, current_sources=isrc, voltage_sources=vsrc)


    v_open = solve().voltages[3]
    i_short = solve(1e-6).voltages[3] / 1e-6  # a 1 µohm load is a short
    vth, rth = thevenin_from_source(v_open, v_open / i_short)
    # The same resistance with both sources zeroed: 1 k + (2 k || 3 k).
    assert np.isclose(rth, 1e3 + 2e3 * 3e3 / 5e3, rtol=1e-6)
    print(f"V_th = {vth:.3f} V, R_th = {rth:.1f} ohm")





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

 .. code-block:: none

    V_th = 17.000 V, R_th = 2200.0 ohm




.. GENERATED FROM PYTHON SOURCE LINES 47-49

Any load sees the same thing
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 49-62

.. code-block:: Python


    loads = np.logspace(1, 5, 25)
    v_network = np.array([solve(r).voltages[3] for r in loads])
    v_thevenin = vth * loads / (rth + loads)
    assert np.allclose(v_network, v_thevenin, rtol=1e-6)

    fig, ax = plt.subplots()
    ax.semilogx(loads, v_network, "o", label="full network")
    ax.semilogx(loads, v_thevenin, label="Thévenin equivalent")
    ax.set(xlabel="load resistance [ohm]", ylabel="terminal voltage [V]", title="Thévenin's theorem")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/networks/images/sphx_glr_plot_02_thevenin_equivalent_001.png
   :alt: Thévenin's theorem
   :srcset: /api/gallery/electrical_engineering/networks/images/sphx_glr_plot_02_thevenin_equivalent_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.038 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_networks_plot_02_thevenin_equivalent.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/electrical_engineering/networks/plot_02_thevenin_equivalent.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_thevenin_equivalent.ipynb <plot_02_thevenin_equivalent.ipynb>`

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

      :download:`Download Python source code: plot_02_thevenin_equivalent.py <plot_02_thevenin_equivalent.py>`

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

      :download:`Download zipped: plot_02_thevenin_equivalent.zip <plot_02_thevenin_equivalent.zip>`


.. only:: html

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

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