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 \(2 \pi N\), then these waves add up in phase; here \(N\) is the interference order.

Notation:

1. \(c\) (c) is speed_of_light.

frequency

temporal_frequency of the ring resonator.

Symbol:

f

Latex:

\(f\)

Dimension:

frequency

length

length of the circumference of the ring resonator.

Symbol:

l

Latex:

\(l\)

Dimension:

length

interference_order

Interference order, see positive_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

relative_permittivity

Effective relative_permittivity of the resonator.

Symbol:

epsilon_r

Latex:

\(\varepsilon_\text{r}\)

Dimension:

dimensionless

law

f = N * c / (l * sqrt(epsilon_r))

Latex:

\[f = \frac{N c}{l \sqrt{\varepsilon_\text{r}}}\]