.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/noise/plot_02_friis_cascaded_noise.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_noise_plot_02_friis_cascaded_noise.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_noise_plot_02_friis_cascaded_noise.py:


Friis's noise formula for cascaded amplifiers
=============================================

Harald Friis (1944) defined a receiver's *noise factor* :math:`F` as the
ratio of input to output signal-to-noise ratio and showed that in a chain of
stages :math:`F = F_1 + (F_2-1)/G_1 + (F_3-1)/(G_1G_2) + \cdots`
(:func:`~engineeringkit.communications.cascaded_noise_factor`). Later stages
are suppressed by the gain ahead of them, so a low-noise amplifier belongs
first. The example checks the formula against a sample-by-sample simulation
of noisy amplifiers and compares two orderings of the same parts.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import cascaded_noise_factor, from_db, noise_figure








.. GENERATED FROM PYTHON SOURCE LINES 21-26

Simulate the chain
------------------

Each stage adds input-referred noise of power :math:`(F-1)N_0`, then
multiplies by its gain.

.. GENERATED FROM PYTHON SOURCE LINES 26-40

.. code-block:: Python


    rng = np.random.default_rng(1944)
    stages = [("LNA", from_db(20), from_db(1.0)), ("mixer", from_db(-7), from_db(8.0)), ("IF amp", from_db(30), from_db(4.0))]
    gains = np.array([g for _, g, _ in stages])
    factors = np.array([f for _, _, f in stages])
    n0, n = 1.0, 400_000
    noise = rng.normal(0, np.sqrt(n0), n)
    for _, g, f in stages:
        noise = np.sqrt(g) * (noise + rng.normal(0, np.sqrt((f - 1) * n0), n))
    simulated = np.var(noise) / (n0 * np.prod(gains))
    formula = cascaded_noise_factor(gains, factors)
    print(f"simulated F = {simulated:.3f}, Friis F = {formula:.3f} ({float(noise_figure(formula)):.2f} dB)")
    assert np.isclose(simulated, formula, rtol=0.02)





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

 .. code-block:: none

    simulated F = 1.385, Friis F = 1.388 (1.42 dB)




.. GENERATED FROM PYTHON SOURCE LINES 41-43

Put the low-noise amplifier first
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 43-54

.. code-block:: Python


    orders = {"LNA, mixer, IF": [0, 1, 2], "mixer, LNA, IF": [1, 0, 2], "mixer, IF, LNA": [1, 2, 0]}
    figures = {name: float(noise_figure(cascaded_noise_factor(gains[i], factors[i]))) for name, i in orders.items()}
    for name, nf in figures.items():
        print(f"{name:16s}: NF = {nf:5.2f} dB")
    fig, ax = plt.subplots(figsize=(6, 3.5))
    ax.barh(list(figures), list(figures.values()))
    ax.set(xlabel="system noise figure [dB]", title="Same parts, different order")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/noise/images/sphx_glr_plot_02_friis_cascaded_noise_001.png
   :alt: Same parts, different order
   :srcset: /api/gallery/communications/noise/images/sphx_glr_plot_02_friis_cascaded_noise_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    LNA, mixer, IF  : NF =  1.42 dB
    mixer, LNA, IF  : NF =  8.86 dB
    mixer, IF, LNA  : NF = 11.43 dB





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

   **Total running time of the script:** (0 minutes 0.095 seconds)


.. _sphx_glr_download_api_gallery_communications_noise_plot_02_friis_cascaded_noise.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/noise/plot_02_friis_cascaded_noise.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_friis_cascaded_noise.ipynb <plot_02_friis_cascaded_noise.ipynb>`

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

      :download:`Download Python source code: plot_02_friis_cascaded_noise.py <plot_02_friis_cascaded_noise.py>`

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

      :download:`Download zipped: plot_02_friis_cascaded_noise.zip <plot_02_friis_cascaded_noise.zip>`


.. only:: html

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

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