Input impedance of lossy transmission line
==========================================

Knowing the length of the transmission line, the loss factor of the transmission line
and its surge impedance, as well as the propagation constant and load resistance, 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_lossy_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:: propagation_constant

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

Symbol:
    :code:`gamma`

Latex:
    :math:`\gamma`

Dimension:
    :code:`1/length`


.. py:data:: law

    :code:`Z_in = (cosh(gamma * l) * Z_L + Z_S * sinh(gamma * l)) / (Z_L * sinh(gamma * l) / Z_S + cosh(gamma * l))`


    Latex:
        .. math::
            Z_\text{in} = \frac{\cosh{\left(\gamma l \right)} Z_\text{L} + Z_\text{S} \sinh{\left(\gamma l \right)}}{\frac{Z_\text{L} \sinh{\left(\gamma l \right)}}{Z_\text{S}} + \cosh{\left(\gamma l \right)}}