Input impedance from transmission matrix
========================================

Knowing the transmission matrix of the device, it is possible to determine the input
impedance of this device.

**Notes:**

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

**Links:**

#. `Cadence System Analysis, derivable from here <https://resources.system-analysis.cadence.com/blog/msa2021-abcd-parameters-of-transmission-lines>`__.

..
    TODO: fix file name

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

.. 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:: voltage_voltage_parameter

    Ratio of input voltage to output voltage at idle at the output.

Symbol:
    :code:`A`

Latex:
    :math:`A`

Dimension:
    :code:`dimensionless`


.. py:data:: voltage_current_parameter

    Ratio of input voltage to output 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 current to output voltage at idle at the output.

Symbol:
    :code:`C`

Latex:
    :math:`C`

Dimension:
    :code:`conductance`


.. py:data:: current_current_parameter

    Ratio of input current to output current in case of a short circuit at the output.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`Z_in = (A * Z_L + B) / (C * Z_L + D)`


    Latex:
        .. math::
            Z_\text{in} = \frac{A Z_\text{L} + B}{C Z_\text{L} + D}