Useful Formulae

Tuned Circuits


1. The basic parallel resonant tuned circuit on the right includes a resistor representing the circuit losses. In practice the losses in the capacitor are significantly less than the inductor and can usually be ignored. In all cases C is in Farads, L is in Henries, frequency is in Hz and pi = 3.142


a) Resonant frequency:  f = 1 / (2 * pi * sqrt(L * C))


b) Quality factor:  Q = (2 * pi * f * L) / R  and may also be expressed as

Q = Fc / (Fh - Fl)  or  (Centre frequency) / (-3dB bandwidth). Q has no units.


c) Dynamic resistance at resonance = L / (C * R) ohms.


d) If you wish to move the resonant frequency of a tuned circuit from f1 to f2 using the same value of inductance then the new value of capacitance required can be calculated from the formula:  C2 / C1 = (f1 / f2)2 and this can be re-arranged as:

C2 = (f1 / f2)2 * C1


Where f1 is the resonant frequency for L and C1 and f2 is the resonant frequency for L and C2 i.e. L is the same value for both frequencies.


2. The basic series tuned circuit on the right also includes a resistor to represent the circuit losses, primarily in the inductor.


a) Impedance at resonance = R ohms.



This section is currently under construction