Surge impedance of microstrip line when effective width is less than substrate thickness
========================================================================================

The microstrip line is a dielectric substrate on which a metal strip is applied. When a
wave propagates along a microstrip line, part of the field goes out, since the
microstrip line does not have metal borders on all sides, unlike, for example,
rectangular waveguides.

**Conditions:**

#. Effective width :math:`w_\text{eff}` of the microstrip line should be less than or
   equal to thickness :math:`h` of the substrate.

..
    TODO: find link

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

.. py:data:: surge_impedance

    :attr:`~symplyphysics.symbols.electrodynamics.surge_impedance` of the microstrip line.

Symbol:
    :code:`Z_S`

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

Dimension:
    :code:`impedance`


.. py:data:: effective_permittivity

    Effective :attr:`~symplyphysics.symbols.electrodynamics.relative_permittivity` of the microstrip line. See :ref:`Effective permittivity of microstrip line <effective_permittivity_microstrip_line_def>`.

Symbol:
    :code:`epsilon_eff`

Latex:
    :math:`\varepsilon_\text{eff}`

Dimension:
    :code:`dimensionless`


.. py:data:: substrate_thickness

    :attr:`~symplyphysics.symbols.classical_mechanics.thickness` of the substrate.

Symbol:
    :code:`h`

Latex:
    :math:`h`

Dimension:
    :code:`length`


.. py:data:: effective_width

    Effective width (see :attr:`~symplyphysics.symbols.classical_mechanics.length`) of the microstrip line. See :ref:`Effective width of microstrip line <effective_width_microstrip_line_def>`.

Symbol:
    :code:`w_eff`

Latex:
    :math:`w_\text{eff}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`Z_S = Z_0 / sqrt(epsilon_eff) * log(8 * h / w_eff + w_eff / (4 * h))`


    Latex:
        .. math::
            Z_\text{S} = \frac{Z_0}{\sqrt{\varepsilon_\text{eff}}} \log \left( \frac{8 h}{w_\text{eff}} + \frac{w_\text{eff}}{4 h} \right)