Transmission matrix equation
============================

The transmission matrix equation relates the input voltage and input current to the
output voltage and output current.

**Notes:**

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

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Two-port_network#ABCD-parameters>`__.

..
    TODO: rename file

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

.. py:data:: input_voltage

    Input :attr:`~symplyphysics.symbols.electrodynamics.voltage`.

Symbol:
    :code:`V_i`

Latex:
    :math:`V_\text{i}`

Dimension:
    :code:`voltage`


.. py:data:: output_voltage

    Output :attr:`~symplyphysics.symbols.electrodynamics.voltage`.

Symbol:
    :code:`V_o`

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

Dimension:
    :code:`voltage`


.. py:data:: input_current

    Input :attr:`~symplyphysics.symbols.electrodynamics.current`.

Symbol:
    :code:`I_i`

Latex:
    :math:`I_\text{i}`

Dimension:
    :code:`current`


.. py:data:: output_current

    Output :attr:`~symplyphysics.symbols.electrodynamics.current`.

Symbol:
    :code:`I_o`

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

Dimension:
    :code:`current`


.. 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:: law

    :code:`[V_i, I_i] = [[A, B], [C, D]]*[V_o, I_o]`


    Latex:
        .. math::
            \begin{pmatrix} V_\text{i} \\ I_\text{i} \end{pmatrix} = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} V_\text{o} \\ I_\text{o} \end{pmatrix}