Quality factor of filled rectangular resonator

A rectangular resonator consists of metal walls and a material filling it. In the case when the resonator is empty, its quality factor depends only on the losses in the metal walls of the resonator. In the case of a filled resonator, the Q factor also depends on the losses in the dielectric.

filled_quality_factor

quality_factor of the filled resonator.

Symbol:

Q_1

Latex:

\(Q_{1}\)

Dimension:

dimensionless

empty_quality_factor

quality_factor of the empty resonator.

Symbol:

Q_0

Latex:

\(Q_{0}\)

Dimension:

dimensionless

loss_tangent

dielectric_loss_tangent.

Symbol:

tan(delta)

Latex:

\(\tan \delta\)

Dimension:

dimensionless

law

Q_1 = 1 / (1 / Q_0 + tan(delta))

Latex:

\[Q_{1} = \frac{1}{\frac{1}{Q_{0}} + \tan \delta}\]