Generating and using a model
----------------------------

The general idea of ImpedanceFitter
is to generate equivalent-circuit models
from the basic elements.
However, there are some more complex circuits and models
that are pre-implemented.
One example is the `Randles circuit <https://en.wikipedia.org/wiki/Randles_circuit>`_.

The Randles circuit
can be formulated in ImpedanceFitter as:

.. code-block:: python

       model = 'R_s + parallel(R_ct + W, C)'
 
The model consists of the basic elements
`R`, `W`, and `C` with respective suffix.

It can be drawn by 

.. code-block:: python

      impedancefitter.draw_scheme(model)

Note that the interface to draw the equivalent circuit is quite simplistic
and might not be correct for very complicated circuits!

For this circuit it yields

.. image:: scheme.*
        :width: 600

The impedance for a list of frequencies can the be 
computed by calling

.. code-block:: python

        frequencies = numpy.logspace(0, 8)
        Rct = 100.
        Rs = 20.
        Aw = 300.
        C0 = 25e-6

         model = 'R_s + parallel(R_ct + W, C)'
        lmfit_model = impedancefitter.get_equivalent_circuit_model(model)
        Z = lmfit_model.eval(omega=2. * numpy.pi * frequencies,
                             ct_R=Rct, s_R=Rs,
                             C=C0, Aw=Aw)


The same circuit has been pre-implemented and
is available as

.. code-block:: python

       model = 'Randles'
       lmfit_model = impedancefitter.get_equivalent_circuit_model(model)
       Z = lmfit_model.eval(omega=2. * numpy.pi * frequencies,
                             Rct=Rct, Rs=Rs,
                             C0=C0, Aw=Aw)


.. note::

        LMFIT names parameters with a prefix. 
        When writing equivalent circuits, it is
        usual to use suffixes.
        Hence, the models here are formulated using suffixes
        but the parameters need to be named with prefixes.
        Then, if the model is `R_ct`, the respective parameter is
        `ct_R`. 

.. warning::

        Make sure to add suffixes to each element or circuit if 
        there any elements with the same name!
        LMFIT does not (yet) support models, where you
        have for example `ct_R` and `R`. As shown here
        you need `s_R` AND (!) `ct_R`.
        


The computed impedance can also be visualized 

.. code-block:: python

        impedancefitter.plot_impedance(2. * numpy.pi * frequencies, Z)

The real and imaginary part are shown together with the Nyquist plot

.. image:: randles_results_overview.*
        :width: 600


See Also
^^^^^^^^

:download:`examples/Randles/randles_model.py <../../examples/Randles/randles_model.py>`.