.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/noise/plot_01_johnson_nyquist_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_01_johnson_nyquist_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_01_johnson_nyquist_noise.py:


Johnson-Nyquist thermal noise
=============================

In 1926-1928 John B. Johnson at Bell Labs measured a random voltage across
every resistor, proportional to its resistance and absolute temperature and
independent of its material. Harry Nyquist explained it from
thermodynamics: the available noise power in a bandwidth :math:`B` is
:math:`kTB` (:func:`~engineeringkit.communications.thermal_noise_power`),
-174 dBm/Hz at 290 K. This example synthesises white Gaussian noise with that
power, measures it after band-limiting, and recovers the open-circuit
voltage :math:`\sqrt{4kTRB}`.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import BOLTZMANN, dbm, thermal_noise_power








.. GENERATED FROM PYTHON SOURCE LINES 22-24

-174 dBm per hertz
------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-28

.. code-block:: Python


    print(f"kT at 290 K: {float(dbm(thermal_noise_power(1.0))):.2f} dBm/Hz")
    print(f"noise in a 6 MHz TV channel: {float(dbm(thermal_noise_power(6e6))):.1f} dBm")





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

 .. code-block:: none

    kT at 290 K: -173.98 dBm/Hz
    noise in a 6 MHz TV channel: -106.2 dBm




.. GENERATED FROM PYTHON SOURCE LINES 29-35

Simulated resistor noise
------------------------

A 50 ohm resistor at 300 K sampled at 1 GHz: the open-circuit RMS voltage
in the full 500 MHz Nyquist band is :math:`\sqrt{4kTRB}`, and the power
delivered to a matched load is :math:`kTB`.

.. GENERATED FROM PYTHON SOURCE LINES 35-57

.. code-block:: Python


    rng = np.random.default_rng(1928)
    R, T, fs = 50.0, 300.0, 1e9
    B = fs / 2
    v_rms = np.sqrt(4 * BOLTZMANN * T * R * B)
    v = rng.normal(0, v_rms, 2**18)
    matched_power = np.mean((v / 2) ** 2) / R
    print(f"v_rms = {v_rms * 1e6:.2f} uV; matched-load power {matched_power:.3e} W vs kTB {float(thermal_noise_power(B, T)):.3e} W")
    assert np.isclose(matched_power, thermal_noise_power(B, T), rtol=0.02)

    spectrum = np.abs(np.fft.rfft(v)) ** 2 / (fs * v.size) * 2
    freq = np.fft.rfftfreq(v.size, 1 / fs)
    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    axes[0].plot(np.arange(400) / fs * 1e9, v[:400] * 1e6, lw=0.7)
    axes[0].set(xlabel="time [ns]", ylabel="voltage [uV]", title="Johnson noise, 50 ohm at 300 K")
    axes[1].semilogy(freq[1::64] / 1e6, spectrum[1::64], ".", ms=2)
    axes[1].axhline(4 * BOLTZMANN * T * R, color="C3", label="4kTR (flat)")
    axes[1].set(xlabel="frequency [MHz]", ylabel="voltage PSD [V²/Hz]")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/noise/images/sphx_glr_plot_01_johnson_nyquist_noise_001.png
   :alt: Johnson noise, 50 ohm at 300 K
   :srcset: /api/gallery/communications/noise/images/sphx_glr_plot_01_johnson_nyquist_noise_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    v_rms = 20.35 uV; matched-load power 2.069e-12 W vs kTB 2.071e-12 W





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

   **Total running time of the script:** (0 minutes 0.308 seconds)


.. _sphx_glr_download_api_gallery_communications_noise_plot_01_johnson_nyquist_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_01_johnson_nyquist_noise.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_johnson_nyquist_noise.ipynb <plot_01_johnson_nyquist_noise.ipynb>`

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

      :download:`Download Python source code: plot_01_johnson_nyquist_noise.py <plot_01_johnson_nyquist_noise.py>`

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

      :download:`Download zipped: plot_01_johnson_nyquist_noise.zip <plot_01_johnson_nyquist_noise.zip>`


.. only:: html

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

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