Hybrid parameters matrix equation
=================================

The **hybrid parameters matrix** is one of the ways to describe a microwave device. The
:math:`H`-parameters of the device act as elements of this matrix. The matrix equation
relates the input voltage and output current to the input current and output voltage.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.transmission_lines.hybrid_parameters_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_parameter

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

Symbol:
    :code:`H_ii`

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

Dimension:
    :code:`impedance`


.. py:data:: input_output_parameter

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

Symbol:
    :code:`H_io`

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

Dimension:
    :code:`dimensionless`


.. py:data:: output_input_parameter

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

Symbol:
    :code:`H_oi`

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

Dimension:
    :code:`dimensionless`


.. py:data:: output_output_parameter

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

Symbol:
    :code:`H_oo`

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

Dimension:
    :code:`conductance`


.. py:data:: law

    :code:`[V_i, I_o] = [[H_ii, H_io], [H_oi, H_oo]]*[I_i, V_o]`


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