.. include:: /project-links.txt
.. include:: /abbreviation.txt



.. getthecode:: thévenin-norton-theorem.py
    :language: python3
    :hidden:
    :notebook:

============================
 Thévenin and Norton Theorem
============================
The Thévenin's theorem holds that:

 * Any linear electrical network with voltage and current sources and only resistances can be
   replaced at terminals A-B by an equivalent voltage source Vth in series connection with an
   equivalent resistance Rth.

 * This equivalent voltage Vth is the voltage obtained at terminals A-B of the network with
   terminals A-B open circuited.

 * This equivalent resistance Rth is the resistance obtained at terminals A-B of the network
   with all its independent current sources open circuited and all its independent voltage
   sources short circuited.

The Norton's theorem holds that:

 * Any linear electrical network with voltage and current sources and only resistances can be
   replaced at terminals A-B by an equivalent current source INO in parallel connection with an
   equivalent resistance Rno.

 * This equivalent current Ino is the current obtained at terminals A-B of the network with
   terminals A-B short circuited.

 * This equivalent resistance Rno is the resistance obtained at terminals A-B of the network
   with all its voltage sources short circuited and all its current sources open circuited.

The Norton's theorem is the dual of the Thévenin's therorem and both are related by
these equations:

 .. math::

      \begin{align}
        R_{no} & = R_{th} \\
        I_{no} & = V_{th} / R_{th} \\
        V_{th} & = I_{No} R_{no}
      \end{align}

.. image:: thévenin-norton-theorem.png
    :align: center

In circuit theory terms, these theorems allows any one-port network to be reduced to a single
voltage or current source and a single impedance.

For AC circuits these theorems can be applied to reactive impedances as well as resistances.

.. code-block:: py3

    
    
    import PySpice.Logging.Logging as Logging
    logger = Logging.setup_logging()
    
    
    from PySpice.Spice.Netlist import Circuit
    from PySpice.Unit import *
    
    
    thevenin_circuit = Circuit('Thévenin Representation')
    
    thevenin_circuit.V('input', 1, thevenin_circuit.gnd, 10@u_V)
    thevenin_circuit.R('generator', 1, 'load', 10@u_Ω)
    thevenin_circuit.R('load', 'load', thevenin_circuit.gnd, 1@u_kΩ)
    
    simulator = thevenin_circuit.simulator(temperature=25, nominal_temperature=25)
    analysis = simulator.operating_point()
    
    load_node = analysis.load
    print('Node {}: {:5.2f} V'.format(str(load_node), float(load_node)))


.. code-block:: none

    Node load:  9.90 V
    


.. code-block:: py3

    
    norton_circuit = Circuit('Norton Representation')
    
    norton_circuit.I('input', norton_circuit.gnd, 'load',
                     thevenin_circuit.Vinput.dc_value/thevenin_circuit.Rgenerator.resistance)
    norton_circuit.R('generator', 'load', norton_circuit.gnd, thevenin_circuit.Rgenerator.resistance)
    norton_circuit.R('load', 'load', norton_circuit.gnd, thevenin_circuit.Rload.resistance)
    
    simulator = norton_circuit.simulator(temperature=25, nominal_temperature=25)
    analysis = simulator.operating_point()
    
    load_node = analysis.load
    print('Node {}: {:5.2f} V'.format(str(load_node), float(load_node)))


.. code-block:: none

    Node load:  9.90 V