Input impedance of lossless transmission line
=============================================

Knowing the length of the transmission line and its surge impedance, as well as the
propagation constant and load impedance, it is possible to determine the input impedance
of the transmission line.

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.transmission_lines.input_impedance_lossless_transmission_line

.. py:data:: input_impedance

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

Symbol:
    :code:`Z_in`

Latex:
    :math:`Z_\text{in}`

Dimension:
    :code:`impedance`


.. py:data:: load_impedance

    Load :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance`.

Symbol:
    :code:`Z_L`

Latex:
    :math:`Z_\text{L}`

Dimension:
    :code:`impedance`


.. py:data:: surge_impedance

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

Symbol:
    :code:`Z_S`

Latex:
    :math:`Z_\text{S}`

Dimension:
    :code:`impedance`


.. py:data:: length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the transmission line.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: phase_constant

    :attr:`~symplyphysics.symbols.electrodynamics.phase_constant`.

Symbol:
    :code:`beta`

Latex:
    :math:`\beta`

Dimension:
    :code:`1/length`


.. py:data:: law

    :code:`Z_in = Z_S * (Z_L + I * Z_S * tan(beta * l)) / (Z_S + I * Z_L * tan(beta * l))`


    Latex:
        .. math::
            Z_\text{in} = \frac{Z_\text{S} \left(Z_\text{L} + i Z_\text{S} \tan{\left(\beta l \right)}\right)}{Z_\text{S} + i Z_\text{L} \tan{\left(\beta l \right)}}