.. 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_03_norton_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_03_norton_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_03_norton_equivalent.py:


Norton's equivalent circuit (1926)
==================================

In 1926 Edward Lawry Norton at Bell Labs, and independently Hans Ferdinand
Mayer at Siemens, gave the dual of Thévenin's theorem: a linear two-terminal
network also behaves like a current source :math:`I_N = V_{th}/R_{th}` in
parallel with the same resistance
(:func:`~engineeringkit.electrical_engineering.norton_from_thevenin`).
Norton wrote it in an internal memorandum on filter design; Mayer used it
to model the vacuum-tube amplifier, which acts more like a current source
than a voltage source. This example checks that the Thévenin and Norton
forms are indistinguishable at the terminals, and that converting sources
back and forth simplifies a ladder to a single source.

.. 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, norton_from_thevenin, parallel_resistance, thevenin_from_source








.. GENERATED FROM PYTHON SOURCE LINES 24-26

Same terminal behaviour
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-35

.. code-block:: Python


    vth, rth = thevenin_from_source(9.0, 300.0)
    i_n, r_n = norton_from_thevenin(vth, rth)
    print(f"Thévenin {vth:.1f} V + {rth:.0f} ohm  <->  Norton {i_n * 1e3:.1f} mA || {r_n:.0f} ohm")
    loads = np.logspace(0, 4, 30)
    v_thevenin = [nodal_analysis(2, [(1, 2, rth), (2, 0, r)], voltage_sources=[(1, 0, vth)]).voltages[2] for r in loads]
    v_norton = [nodal_analysis(1, [(1, 0, r_n), (1, 0, r)], current_sources=[(0, 1, i_n)]).voltages[1] for r in loads]
    assert np.allclose(v_thevenin, v_norton)





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

 .. code-block:: none

    Thévenin 9.0 V + 300 ohm  <->  Norton 30.0 mA || 300 ohm




.. GENERATED FROM PYTHON SOURCE LINES 36-41

Source transformations
----------------------

Two batteries with internal resistance in parallel: convert each to
Norton form, add the currents and the conductances, convert back.

.. GENERATED FROM PYTHON SOURCE LINES 41-58

.. code-block:: Python


    batteries = [(12.0, 0.5), (11.4, 0.3)]
    nortons = [norton_from_thevenin(v, r) for v, r in batteries]
    i_total = sum(i for i, _ in nortons)
    r_total = parallel_resistance(*(r for _, r in nortons))
    v_eq = i_total * r_total
    direct = nodal_analysis(3, [(1, 3, 0.5), (2, 3, 0.3)], voltage_sources=[(1, 0, 12.0), (2, 0, 11.4)]).voltages[3]
    print(f"open-circuit voltage of the pair: {v_eq:.4f} V (nodal analysis {direct:.4f} V), R = {r_total:.4f} ohm")
    assert np.isclose(v_eq, direct)

    fig, ax = plt.subplots()
    ax.semilogx(loads, v_thevenin, label="Thévenin form")
    ax.semilogx(loads, v_norton, "--", label="Norton form")
    ax.set(xlabel="load resistance [ohm]", ylabel="load voltage [V]", title="Norton's equivalent")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/networks/images/sphx_glr_plot_03_norton_equivalent_001.png
   :alt: Norton's equivalent
   :srcset: /api/gallery/electrical_engineering/networks/images/sphx_glr_plot_03_norton_equivalent_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    open-circuit voltage of the pair: 11.6250 V (nodal analysis 11.6250 V), R = 0.1875 ohm





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

   **Total running time of the script:** (0 minutes 0.037 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_networks_plot_03_norton_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_03_norton_equivalent.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_norton_equivalent.ipynb <plot_03_norton_equivalent.ipynb>`

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

      :download:`Download Python source code: plot_03_norton_equivalent.py <plot_03_norton_equivalent.py>`

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      :download:`Download zipped: plot_03_norton_equivalent.zip <plot_03_norton_equivalent.zip>`


.. only:: html

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

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