Wave impedance of Lange coupler
===============================

The Lange coupler is based on microstrip transmission lines. When this coupler is in
operation, both even and odd modes are distributed. Knowing the wave impedance for even
and odd modes, it is possible to calculate the equivalent wave impedance of the
coupler.

.. image:: https://habrastorage.org/r/w1560/getpro/habr/upload_files/054/d02/c8d/054d02c8d91c06425ae079d34b18ce15.jpeg
    :width: 400px
    :align: center

..
    TODO: find link
    TODO: rename file

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

.. py:data:: wave_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.wave_impedance` of the Lange coupler.

Symbol:
    :code:`eta`

Latex:
    :math:`\eta`

Dimension:
    :code:`impedance`


.. py:data:: odd_mode_wave_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.wave_impedance` of the odd mode.

Symbol:
    :code:`eta_o`

Latex:
    :math:`\eta_\text{o}`

Dimension:
    :code:`impedance`


.. py:data:: even_mode_wave_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.wave_impedance` of the even mode.

Symbol:
    :code:`eta_e`

Latex:
    :math:`\eta_\text{e}`

Dimension:
    :code:`impedance`


.. py:data:: segment_count

    Number of the segments of the Lange coupler. See :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`eta = sqrt(eta_o * eta_e * (eta_o + eta_e)^2 / ((eta_o + eta_e * (N - 1)) * (eta_e + eta_o * (N - 1))))`


    Latex:
        .. math::
            \eta = \sqrt{\frac{\eta_\text{o} \eta_\text{e} \left(\eta_\text{o} + \eta_\text{e}\right)^{2}}{\left(\eta_\text{o} + \eta_\text{e} \left(N - 1\right)\right) \left(\eta_\text{e} + \eta_\text{o} \left(N - 1\right)\right)}}