Impedance matrix equation
=========================

The impedance matrix is one of the ways to describe a microwave device. The
:math:`Z`-parameters of the device act as elements of this matrix. The matrix equation
relates the input and output voltages to the input and output currents.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Two-port_network#Impedance_parameters_(z-parameters)>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.transmission_lines.total_resistance_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:: input_input_impedance

    Ratio of :attr:`~input_voltage` to :attr:`~input_current` at idle at the output. See
    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance`.

Symbol:
    :code:`Z_ii`

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

Dimension:
    :code:`impedance`


.. py:data:: input_output_impedance

    Ratio of :attr:`~input_voltage` to :attr:`~output_current` at idle at the output. See
    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance`.

Symbol:
    :code:`Z_io`

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

Dimension:
    :code:`impedance`


.. py:data:: output_input_impedance

    Ratio of :attr:`~output_voltage` to :attr:`~input_current` at idle at the output. See
    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance`.

Symbol:
    :code:`Z_oi`

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

Dimension:
    :code:`impedance`


.. py:data:: output_output_impedance

    Ratio of :attr:`~output_voltage` to :attr:`~output_current` at idle at the output. See
    :attr:`~symplyphysics.symbols.electrodynamics.electrical_impedance`.

Symbol:
    :code:`Z_oo`

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

Dimension:
    :code:`impedance`


.. py:data:: law

    :code:`[V_i, V_o] = [[Z_ii, Z_io], [Z_oi, Z_oo]]*[I_i, I_o]`


    Latex:
        .. math::
            \begin{pmatrix} V_\text{i} \\ V_\text{o} \end{pmatrix} = \begin{pmatrix} Z_\text{ii} & Z_\text{io} \\ Z_\text{oi} & Z_\text{oo} \end{pmatrix} \begin{pmatrix} I_\text{i} \\ I_\text{o} \end{pmatrix}