Admittance matrix equation
==========================

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

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.transmission_lines.total_conductivities_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_admittance

    Ratio of :attr:`~input_current` to :attr:`~input_voltage` in case of a short circuit at
    the output. See :attr:`~symplyphysics.symbols.electrodynamics.admittance`.

Symbol:
    :code:`Y_ii`

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

Dimension:
    :code:`conductance`


.. py:data:: input_output_admittance

    Ratio of :attr:`~input_current` to :attr:`~output_voltage` in case of a short circuit at
    the output. See :attr:`~symplyphysics.symbols.electrodynamics.admittance`.

Symbol:
    :code:`Y_io`

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

Dimension:
    :code:`conductance`


.. py:data:: output_input_admittance

    Ratio of :attr:`~output_current` to :attr:`~input_voltage` in case of a short circuit at
    the output. See :attr:`~symplyphysics.symbols.electrodynamics.admittance`.

Symbol:
    :code:`Y_oi`

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

Dimension:
    :code:`conductance`


.. py:data:: output_output_admittance

    Ratio of :attr:`~output_current` to :attr:`~output_voltage` in case of a short circuit
    at the output. See :attr:`~symplyphysics.symbols.electrodynamics.admittance`.

Symbol:
    :code:`Y_oo`

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

Dimension:
    :code:`conductance`


.. py:data:: law

    :code:`[I_i, I_o] = [[Y_ii, Y_io], [Y_oi, Y_oo]]*[V_i, V_o]`


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