Admittance of rectangular loop coupler
======================================

The rectangular loop coupler consists of four sections. The admittance of each section
can be calculated by calculating the admittance of the transmission line to which the
coupler is connected and the power ratio at the outputs.

..
    TODO: find link
    TODO: rename file

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

.. py:data:: first_admittance

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

Symbol:
    :code:`Y_1`

Latex:
    :math:`Y_{1}`

Dimension:
    :code:`conductance`


.. py:data:: second_admittance

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

Symbol:
    :code:`Y_2`

Latex:
    :math:`Y_{2}`

Dimension:
    :code:`conductance`


.. py:data:: third_admittance

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

Symbol:
    :code:`Y_3`

Latex:
    :math:`Y_{3}`

Dimension:
    :code:`conductance`


.. py:data:: fourth_admittance

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

Symbol:
    :code:`Y_4`

Latex:
    :math:`Y_{4}`

Dimension:
    :code:`conductance`


.. py:data:: transmission_line_admittance

    :attr:`~symplyphysics.symbols.electrodynamics.admittance` of the transmission line.

Symbol:
    :code:`Y_0`

Latex:
    :math:`Y_{0}`

Dimension:
    :code:`conductance`


.. py:data:: power_ratio

    Ratio of the power at the outputs of the coupler.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`[Y_1, Y_2, Y_3, Y_4] = [Y_0 / sqrt(k), Y_0 * sqrt((k + 1) / k), Y_0 * sqrt((k + 1) / k), Y_0 / sqrt(k)]`


    Latex:
        .. math::
            \begin{pmatrix} Y_{1} \\ Y_{2} \\ Y_{3} \\ Y_{4} \end{pmatrix} = \begin{pmatrix} \frac{Y_{0}}{\sqrt{k}} \\ Y_{0} \sqrt{\frac{k + 1}{k}} \\ Y_{0} \sqrt{\frac{k + 1}{k}} \\ \frac{Y_{0}}{\sqrt{k}} \end{pmatrix}