Resonant frequency of ring resonator
====================================

The ring resonator is a microstrip line in the shape of a circle. 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. A wave
traveling through an ring resonator acquires a phase shift and interacts with a wave
incident on the resonator. If the phase shift is expressed as :math:`2 \pi N`, then
these waves add up in phase; here :math:`N` is the interference order.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`.

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.resonators.resonant_frequency_of_ring_resonator

.. py:data:: frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.temporal_frequency` of the ring resonator.

Symbol:
    :code:`f`

Latex:
    :math:`f`

Dimension:
    :code:`frequency`


.. py:data:: length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the circumference of the ring resonator.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: interference_order

    Interference order, see :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: relative_permittivity

    Effective :attr:`~symplyphysics.symbols.electrodynamics.relative_permittivity` of the resonator.

Symbol:
    :code:`epsilon_r`

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

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`f = N * c / (l * sqrt(epsilon_r))`


    Latex:
        .. math::
            f = \frac{N c}{l \sqrt{\varepsilon_\text{r}}}