Transmission matrix for serial load in line
===========================================

Knowing the impedance of the load connected in series to the transmission line, it is
possible to calculate the parameters :math:`A, B, C, D` of the transmission matrix of
the load.

**Notes:**

#. See :ref:`Transmission Matrix <transmission_matrix_def>`.

**Conditions:**

#. The load is connected to the transmission line *in series*.

..
    TODO: find link

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

.. py:data:: voltage_voltage_parameter

    Ratio of input :attr:`~symplyphysics.symbols.electrodynamics.voltage` to output :attr:`~symplyphysics.symbols.electrodynamics.voltage` at idle at the output.

Symbol:
    :code:`A`

Latex:
    :math:`A`

Dimension:
    :code:`dimensionless`


.. py:data:: voltage_current_parameter

    Ratio of input :attr:`~symplyphysics.symbols.electrodynamics.voltage` to output :attr:`~symplyphysics.symbols.electrodynamics.current` in case of a short
    circuit at the output.

Symbol:
    :code:`B`

Latex:
    :math:`B`

Dimension:
    :code:`impedance`


.. py:data:: current_voltage_parameter

    Ratio of input :attr:`~symplyphysics.symbols.electrodynamics.current` to output :attr:`~symplyphysics.symbols.electrodynamics.voltage` at idle at the output.

Symbol:
    :code:`C`

Latex:
    :math:`C`

Dimension:
    :code:`conductance`


.. py:data:: current_current_parameter

    Ratio of input :attr:`~symplyphysics.symbols.electrodynamics.current` to output :attr:`~symplyphysics.symbols.electrodynamics.current` in case of a short
    circuit at the output.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`dimensionless`


.. 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:: law

    :code:`[[A, B], [C, D]] = [[1, Z_L], [0, 1]]`


    Latex:
        .. math::
            \begin{pmatrix} A & B \\ C & D \end{pmatrix} = \begin{pmatrix} 1 & Z_\text{L} \\ 0 & 1 \end{pmatrix}