Calculators to calculate the characteristics of a resonant series RLC circuit are presented.
Two calculators are included.
Calculator 1 may be used to calculate the resonanant, cutoff frequencies and the quality factor given the resistance \( R \), the capacitance \( C \) and the inductance \( L \) included in the series RLC circuit as shown above.
Calculator 2 may be used solve the inverse problem. The cutoff frequencies and the resistance are given and the capaciatance, inductance and the quality factor are calculated.
Several formula related to resonant series RLC circuit to be used in the calculators are reproduced here.
The resonant frequency \[ \omega_r = \dfrac{1}{\sqrt {L C}} \]
The cutoff frequencies
\[ \omega_{c1} = - \dfrac{R}{2 L} + \sqrt{ \left(\dfrac{R}{2 L}\right)^2 + \omega_r^2} \]
\[ \omega_{c2} = \dfrac{R}{2 L} + \sqrt{ \left(\dfrac{R}{2 L}\right)^2 + \omega_r^2} \]
Bandwidth
\[ \Delta \omega = \omega_{c2} - \omega_{c1} \]
The quality factor of the resonant circuit.
\( Q = \dfrac{\omega_r}{\Delta \omega} \)