.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/ac_circuits/plot_03_lodge_resonance.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_ac_circuits_plot_03_lodge_resonance.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_ac_circuits_plot_03_lodge_resonance.py:


Lodge's syntonic tuning: series resonance (1897)
================================================

Early spark transmitters splattered energy over a wide band, so every
receiver heard every transmitter. Oliver Lodge's 1897 patent on "syntonic"
telegraphy put an inductance in series with the antenna's capacitance at
both ends, tuning transmitter and receiver to the same frequency
:math:`f_0 = 1/2\pi\sqrt{LC}`
(:func:`~engineeringkit.electrical_engineering.resonance_frequency`). At
resonance the inductive and capacitive reactances cancel and the current
is limited only by the resistance; the sharpness of the peak is the quality
factor :math:`Q = \sqrt{L/C}/R`, and the half-power bandwidth is
:math:`f_0/Q`. Marconi bought the patent in 1912. This example measures the
bandwidth of a tuned circuit
(:class:`~engineeringkit.electrical_engineering.SeriesRLC`) and shows how
much tuning rejects a neighbouring station.

.. GENERATED FROM PYTHON SOURCE LINES 21-26

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.electrical_engineering import SeriesRLC, resonance_frequency








.. GENERATED FROM PYTHON SOURCE LINES 27-29

A tuned receiver
----------------

.. GENERATED FROM PYTHON SOURCE LINES 29-45

.. code-block:: Python


    L, C = 250e-6, 1e-9
    f0 = resonance_frequency(L, C)
    print(f"f0 = {f0 / 1e3:.1f} kHz")
    f = np.linspace(0.7 * f0, 1.3 * f0, 200_001)
    fig, ax = plt.subplots()
    for R in (5.0, 20.0, 50.0):
        circuit = SeriesRLC(R, L, C)
        gain = np.abs(1 / circuit.impedance(2 * np.pi * f)) * R  # current relative to its peak
        band = f[gain >= 1 / np.sqrt(2)]
        width = band[-1] - band[0]
        Q = circuit.quality_factor
        print(f"R = {R:4.0f} ohm: Q = {Q:6.1f}, half-power bandwidth {width:7.0f} Hz, f0/Q = {f0 / Q:7.0f} Hz")
        assert np.isclose(width, f0 / Q, rtol=1e-3)
        ax.plot(f / 1e3, gain, label=f"Q = {Q:.0f}")




.. image-sg:: /api/gallery/electrical_engineering/ac_circuits/images/sphx_glr_plot_03_lodge_resonance_001.png
   :alt: plot 03 lodge resonance
   :srcset: /api/gallery/electrical_engineering/ac_circuits/images/sphx_glr_plot_03_lodge_resonance_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    f0 = 318.3 kHz
    R =    5 ohm: Q =  100.0, half-power bandwidth    3182 Hz, f0/Q =    3183 Hz
    R =   20 ohm: Q =   25.0, half-power bandwidth   12732 Hz, f0/Q =   12732 Hz
    R =   50 ohm: Q =   10.0, half-power bandwidth   31831 Hz, f0/Q =   31831 Hz




.. GENERATED FROM PYTHON SOURCE LINES 46-51

Rejecting a neighbour
---------------------

A second station 10% higher in frequency is attenuated by the
high-:math:`Q` circuit far more than by the low-:math:`Q` one.

.. GENERATED FROM PYTHON SOURCE LINES 51-63

.. code-block:: Python


    neighbour = 1.1 * f0
    rejection = [abs(SeriesRLC(R, L, C).impedance(2 * np.pi * neighbour)) / R for R in (5.0, 50.0)]
    print(f"neighbour 10% away is {rejection[0]:.1f}x weaker at Q=100, {rejection[1]:.2f}x at Q=10")
    detuning = neighbour / f0 - f0 / neighbour
    assert np.allclose(rejection, [np.sqrt(1 + (q * detuning) ** 2) for q in (100, 10)])

    ax.axvline(neighbour / 1e3, color="gray", ls=":", label="neighbouring station")
    ax.set(xlabel="frequency [kHz]", ylabel="relative current", title="Series resonance")
    ax.legend()

    plt.show()




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

 .. code-block:: none

    neighbour 10% away is 19.1x weaker at Q=100, 2.16x at Q=10





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

   **Total running time of the script:** (0 minutes 0.036 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_ac_circuits_plot_03_lodge_resonance.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/ac_circuits/plot_03_lodge_resonance.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_lodge_resonance.ipynb <plot_03_lodge_resonance.ipynb>`

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

      :download:`Download Python source code: plot_03_lodge_resonance.py <plot_03_lodge_resonance.py>`

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

      :download:`Download zipped: plot_03_lodge_resonance.zip <plot_03_lodge_resonance.zip>`


.. only:: html

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

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