Impedance of Wilkinson microstrip divider
=========================================

The Wilkinson divider is a device designed to divide the power of a microwave signal
into two output ports. Different sections of the divider consist of a microstrip line of
different widths. There are four such sections in total and each has its own impedance.

.. image:: https://habrastorage.org/getpro/habr/upload_files/c24/031/52e/c2403152e2b320ab1c4c44f970dee1f2.gif
    :width: 400px
    :align: center

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.couplers.impedances_for_wilkinson_microstrip_divider

.. py:data:: first_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance` of the first section.

Symbol:
    :code:`Z_1`

Latex:
    :math:`Z_{1}`

Dimension:
    :code:`impedance`


.. py:data:: second_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance` of the second section.

Symbol:
    :code:`Z_2`

Latex:
    :math:`Z_{2}`

Dimension:
    :code:`impedance`


.. py:data:: third_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance` of the third section.

Symbol:
    :code:`Z_3`

Latex:
    :math:`Z_{3}`

Dimension:
    :code:`impedance`


.. py:data:: fourth_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance` of the fourth section.

Symbol:
    :code:`Z_4`

Latex:
    :math:`Z_{4}`

Dimension:
    :code:`impedance`


.. py:data:: transmission_line_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance` of the transmission line to which the divider is
    connected.

Symbol:
    :code:`Z_0`

Latex:
    :math:`Z_{0}`

Dimension:
    :code:`impedance`


.. py:data:: power_ratio

    Ratio of the :attr:`~symplyphysics.symbols.basic.power` at the outputs of the divider.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`[Z_1, Z_2, Z_3, Z_4] = [Z_0 * sqrt(k * (1 + k^2)), Z_0 * sqrt((1 + k^2) / k^3), Z_0 * sqrt(k), Z_0 / sqrt(k)]`


    Latex:
        .. math::
            \begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \\ Z_{4} \end{pmatrix} = \begin{pmatrix} Z_{0} \sqrt{k \left(1 + k^{2}\right)} \\ Z_{0} \sqrt{\frac{1 + k^{2}}{k^{3}}} \\ Z_{0} \sqrt{k} \\ \frac{Z_{0}}{\sqrt{k}} \end{pmatrix}