.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/decibels/plot_01_bell_decibel.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_communications_decibels_plot_01_bell_decibel.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_communications_decibels_plot_01_bell_decibel.py:


The decibel: the Bell System's transmission unit
================================================

Early telephone engineers measured loss in "miles of standard cable", a unit
that depended on frequency. In 1924 the Bell System replaced it with the
*transmission unit*, ten times the base-ten logarithm of a power ratio, and in
1929 W. H. Martin named it the decibel. Logarithms turn the products of gains
and losses along a line into sums, so a long chain of amplifiers and cables
can be budgeted by addition. :func:`~engineeringkit.communications.db`,
:func:`~engineeringkit.communications.dbm` and their inverses convert both ways.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import db, dbm, from_db, from_dbm








.. GENERATED FROM PYTHON SOURCE LINES 21-25

Products become sums
--------------------

A 1 mW source feeds a chain of cable sections (loss) and repeaters (gain).

.. GENERATED FROM PYTHON SOURCE LINES 25-32

.. code-block:: Python


    stages = [("cable", 0.05), ("repeater", 40.0), ("cable", 0.02), ("repeater", 25.0), ("cable", 0.1)]
    linear = 1e-3 * np.prod([g for _, g in stages])
    in_db = float(dbm(1e-3)) + sum(float(db(g)) for _, g in stages)
    print(f"linear product: {linear:.4e} W, decibel sum: {in_db:.2f} dBm -> {float(from_dbm(in_db)):.4e} W")
    assert np.isclose(from_dbm(in_db), linear)





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

 .. code-block:: none

    linear product: 1.0000e-04 W, decibel sum: -10.00 dBm -> 1.0000e-04 W




.. GENERATED FROM PYTHON SOURCE LINES 33-35

Reference points worth memorising
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 35-50

.. code-block:: Python


    for ratio in [2, 10, 100, 0.5]:
        print(f"x{ratio:<5} = {float(db(ratio)):+6.2f} dB")
    assert np.isclose(from_db(3.0103), 2, rtol=1e-4)

    level = [float(dbm(1e-3))]
    for _, g in stages:
        level.append(level[-1] + float(db(g)))
    fig, ax = plt.subplots(figsize=(6.5, 3.5))
    ax.step(range(len(level)), level, where="post")
    ax.set_xticks(range(len(level)), ["source"] + [name for name, _ in stages], rotation=30)
    ax.set(ylabel="signal level [dBm]", title="A decibel level diagram")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/decibels/images/sphx_glr_plot_01_bell_decibel_001.png
   :alt: A decibel level diagram
   :srcset: /api/gallery/communications/decibels/images/sphx_glr_plot_01_bell_decibel_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    x2     =  +3.01 dB
    x10    = +10.00 dB
    x100   = +20.00 dB
    x0.5   =  -3.01 dB





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

   **Total running time of the script:** (0 minutes 0.092 seconds)


.. _sphx_glr_download_api_gallery_communications_decibels_plot_01_bell_decibel.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/communications/decibels/plot_01_bell_decibel.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_bell_decibel.ipynb <plot_01_bell_decibel.ipynb>`

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

      :download:`Download Python source code: plot_01_bell_decibel.py <plot_01_bell_decibel.py>`

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

      :download:`Download zipped: plot_01_bell_decibel.zip <plot_01_bell_decibel.zip>`


.. only:: html

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

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