Quality factor of loaded resonator from circuit parameters¶

If the resonator is an oscillatory circuit to which an external circuit is connected, then the loaded Q-factor of the resonator depends on the resistances of the resonator and the external circuit, as well as on the inductance of the resonator and the angular oscillation frequency.

loaded_quality_factor¶: quality_factor of the loaded resonator.

Symbol:: Q_1
Latex:: \(Q_{1}\)
Dimension:: dimensionless

resistance¶: electrical_resistance of the oscillating circuit.

Symbol:: R_0
Latex:: \(R_{0}\)
Dimension:: impedance

inductance¶: inductance of the oscillating circuit.

Symbol:: L
Latex:: \(L\)
Dimension:: inductance

angular_frequency¶: angular_frequency of the current.

Symbol:: w
Latex:: \(\omega\)
Dimension:: angle/time

load_resistance¶: electrical_resistance of the load.

Symbol:: R_L
Latex:: \(R_\text{L}\)
Dimension:: impedance

law¶

Q_1 = R_L * R_0 / (w * L * (R_L + R_0))

Latex:: \[Q_{1} = \frac{R_\text{L} R_{0}}{\omega L \left(R_\text{L} + R_{0}\right)}\]